Shogi and some variants now available in Ai Ai — play against AI or online!

UPDATE (12 April): Stephen has updated Ai Ai to fix a bug with Chu Shogi’s Lion, and we also added several new variants including Goro Goro Shogi, Goro Goro Plus and Wa Shogi!  Grab the updated version here.

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For the last few weeks, Stephen Tavener and I have been collaborating to bring Shogi and several of its variants to his amazing Ai Ai software, a general game-playing program that lets you play hundreds of abstract strategy games against strong AI, or against human opposition online.

Last year Stephen added a general Chess-playing engine to Ai Ai, and has been steadily adding lots of great Chess variants to it such as Capablanca Chess, Chess960 and Grand Chess.  I had been embarking on a project to playtest some of the more promising large Chess variants — on 10×8 boards and larger — and so Stephen added a huge array of new piece types into Ai Ai so that these variants could be added in (more on these games in a future post).  Then we got started on Shogi, which turned into quite a project — Stephen had to cope with some incredible coding challenges throughout, from implementing drops to Chu Shogi’s complex Lion-trading rules.  On top of that there was lots of design work to do, because we wanted to offer multiple piece graphic sets to help people who have trouble learning Japanese kanji characters.

In the end we went with three sets of pieces: traditional pieces using a single kanji character for each piece; mnemonic pieces that combine the kanji with mnemonic diagrams designed by HG Muller; and diagrammatic pieces, where each piece is a simple square shape with a diagram of the piece’s move on it.  With these three options in place, these games should be accessible to a larger audience.

Modern Shogi

First and foremost in Ai Ai’s new Shogi assortment we have modern Shogi, played on a 9×9 board with ten different types of pieces.  For those who aren’t familiar with Shogi, it has several major differences from Western Chess:

  1. Pieces that are captured are truly captured — they become the property of the capturing side, and are placed on the side of the board under their control.  At any time, a player may ‘drop’ a captured piece to any empty square on the board in lieu of a normal move (with some restrictions).  Drops make Shogi a very dynamic and aggressive game, and drastically change the feel in comparison to Chess.  Because pieces keep coming back to life, the board stays mostly full of pieces throughout the game; endgames are often an exciting race to checkmate as both sides’ defences break down and they start launching brutal attacks back and forth.
  2. Nearly all pieces can promote — unlike in Chess, where only Pawns may promote upon reaching the opponent’s back rank, in Shogi nearly all pieces can promote when they reach the opponent’s starting area.  Pieces promote by flipping over and revealing a new piece on the opposite side, which is more powerful than the original.  Promoted pieces are demoted again once captured, though.
  3. Shogi is a bigger game than Chess, taking place on a 9×9 board with 81 squares as opposed to Chess’ 8×8 board with 64 squares.  Shogi also has ten types of pieces, significantly more than the six types present in Chess.

There’s a lot more to it than that, of course, but these three changes alone make Shogi stand out among the modern variants of Chess played around the world.  It’s a vibrant and exciting game and well worth trying if you’ve ever enjoyed a game of Chess.

Shogi games tend to take a bit longer than Chess; a typical Chess game lasts about 80 moves in total, whereas a Shogi game generally lasts around 120 moves.  Some small variants of Shogi have been designed to generate some quick-playing games that still capture the feel of the full game, and that serve as useful introductions for new players or children.  In Ai Ai we’ve added a couple of these:

In Minishogi, Shogi gets shrunken down to a tiny 5×5 board with just six pieces per player.  Surprisingly the game is still remarkably deep at this size, thanks to the complexities of drops.  Judkins Shogi is similar, but uses a 6×6 board with seven pieces per player, adding the Knight back into the mix.

Sho Shogi, Chu Shogi and Dai Shogi

As readers of this blog will know, I have a certain fascination with the ancient variations of Shogi, particularly the ambitious and gigantic ones.  I’m delighted to say that Stephen has implemented some of these variants in Ai Ai as well!

Back in the early days of Shogi, from the 13th-16th centuries or so, the game came in three sizes —  Sho Shogi on a 9×9 board (Small Shogi, which became modern Shogi), Chu Shogi (Middle Shogi) on a 12×12 board, and Dai Shogi (Large Shogi) on a 15×15 board.   At this time drops were not in the game, so pieces that are captured are removed from the game permanently.  Sho Shogi was considered a quick game, often played with children, while Chu Shogi was the most popular form and the enormous Dai Shogi was for a time the most prestigious variation.

Eventually drops entered the game sometime in the late 16th century, and this innovation suddenly catapulted Sho Shogi to the forefront of the Shogi world.  Today Chu Shogi still survives, and is considered by some to be the best large Chess game ever invented, whereas Dai Shogi is still played as well but much less frequently than Chu.

All three of Shogi’s closest ancestors are now playable in Ai Ai:

The eagle-eyed among you will notice that Sho Shogi sports an additional piece sat in front of the King.  This is the Drunk Elephant, a powerful defender that promotes to a Crown Prince, which functions as a second King!  If you manage to make a Crown Prince, your opponent must capture both your Prince and your King to win the game.  Both Chu and Dai Shogi have Drunk Elephants as well, and numerous other new pieces; Chu Shogi has 28 piece types, and Dai Shogi has 36!  As you might expect, the larger games are challenging for the AI to play well, so be sure to set the AI’s thinking times quite high if you’d like a challenge.

I highly recommend trying these historical variants, particularly Chu Shogi and Dai Shogi, which I’ve written about extensively before.  Chu and Dai are wonderful games, richly strategic and packed full of variety, and I hope some of you out there may try your hand at them now that they’re available in Ai Ai.

Tori Shogi

For those who prefer quicker and tighter gameplay, we also added a more recent historical variant of Shogi — Tori Shogi, or Bird Shogi.  Tori Shogi gets its name from the fact that all the pieces have names related to birds — even the Pawns are changed to Swallows.  Tori Shogi was invented by Toyota Genryu in 1799, and has the unique distinction of being one of only two historical variants for which we have recorded games played by professional players (the other being Chu Shogi).  Tori Shogi has gained a certain amount of popularity in the West, and there’s even a fine English-language book available on the game for those who want to learn to play well.

Tori Shogi is played on a 7×7 board with eight different types of pieces, two of which only appear by promotion.  The small 49-square board starts packed with 16 pieces for each player, making the early game quite claustrophobic!  The game uses drops as in modern Shogi, but with one major difference: in modern Shogi, you may never drop a Pawn to a file that already contains one of your Pawns, but in Tori Shogi you may have two Pawns on the same file at a time.  This small change hugely alters the game’s tactics and gives it a very different feel from standard Shogi.

Below you can see the initial position of the game, and a sample game in animated GIF form.

Next Moves

We are forging ahead with some additional variants for the next release.  First up we have Goro Goro Shogi, a modern small variant developed in 2012 as a way to help young kids in Japan to learn modern Shogi.  This game is played on a 5×6 board with a limited selection of pieces, but unlike Minishogi and Judkins Shogi, there are three Pawns per side instead of just one.  In my opinion this makes Goro Goro a much better introduction to Shogi, as the use of Pawns is essential in the full game (much as in Chess).

We have also added Goro Goro Plus, a fantastic little variant that takes Goro Goro and gives each player a Lance and Knight in hand at the start of the game, available for drops.  This addition really spices up the game and makes Goro Goro more than just a Shogi learning tool, and turns it into an exciting game in its own right.

On the historical variants side of things, we have Wa Shogi, an 11×11 game that shares with Tori Shogi a certain flair for exotic, animal-based piece names.  Unusually for a Shogi variant, Wa is playable both with and without drops, and is a great game either way!  I slightly prefer playing with drops, which gives the game an exciting pace and added tactical sharpness.  Without drops Wa Shogi becomes a delicate strategic affair, where players often try to establish coordinated invading legions that can escort the weaker pieces to the promotion zone (the weakest pieces in Wa have strong promotions).  The two faces of Wa play really differently, so it’s like having two games in one.

I highly recommend Wa Shogi for fans of modern Shogi; particularly when played with drops, it feels like a clever expansion of Shogi with a distinct feel due to its asymmetric starting position and unusual pieces.  I firmly believe that if a concerned effort were made to promote this game it could achieve a decent level of popularity!

So that’s a quick roundup of all the Shogi goodness now available in Ai Ai, and a little preview of what’s to come — please go give the games a try, and of course give me a shout if any of you out there fancy a game!

Sometime down the line I’ll be back with another roundup, in which we’ll be taking a look at the large Chess variants available in Ai Ai as well.  I’m also nearly done with an in-depth analysis of a Chu Shogi game, and an introduction to Tenjiku Shogi, so look out for those posts coming soon (-ish).

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Permute: Move by Move

Some time ago I introduced you all to my game, Permute — an abstract strategy game inspired by the Rubik’s Cube.  Since then, the game was implemented on Christian Freeling’s MindSports — an essential site for any fan of the genre — and in Stephen Tavener’s wonderful Ai Ai software.  Hopefully some of you may have tried the game since then, and have discovered that the game has a unique feel in play and supports some unusual strategies and tactics.

Since developing the idea I’ve played a great deal of Permute, mostly against Ai Ai’s stiff opposition, but also some games against human opponents.   In this post I’ll walk you through a game I played against Simon R on MindSports, and explain some basic tactical and strategic considerations to keep in mind while playing Permute.  This sample game contains a few instructive moments that should be enlightening for any new player.

Here’s an animation of the full game, courtesy of Ai Ai:

permute12-game2-simonR-final

Full game — Simon was Orange, I was Yellow. Final score — Orange 16, Yellow 43.

The game is also viewable on MindSports, if you want to step through it move by move yourself.

Permute Move Notation

In order to record games of Permute and replicate them later, we need some form of notation to keep track of what moves have been played.  Ed van Zon of MindSports came up with a simple notation system that is very easy to learn:

Permute 12x12 -- notation sample-01

This small sample board illustrates how the notation works.  In this case, Yellow has made a move, rotating a 2×2 face clockwise.  We can translate this move into notation easily:

  1. We start by noting the direction of the twist, with a capital C for a clockwise twist, or A for anti-clockwise.
  2. Then we note the square on the board that is in the bottom-left corner of the 2×2 face we twisted, in this case d3 (indicated by the green square in the diagram).  So our move so far is Cd3
  3. Next we add in the square marking the top-right of the twisted face, in this case e4 (the red square in the diagram).  Our move is now Cd3e4
  4. Finally, we add a hyphen for readability, then add the square we chose to bandage, which is d4 in this case (the blue square in the diagram).  So our complete move can be written as Cd3e4-d4.

That’s it!  If we note down every move in this way, in proper sequence, we can easily reconstruct a game later for analysis.  In Ai Ai the notation works basically the same, except moves are written with the word Clockwise for clockwise twists and Widdershins for anti-clockwise twists.

Preliminaries

This post is very long, so I will not recap the rules here; if you are totally new to the game, please read my previous introductory post and follow-up about the Ai Ai implementation so that you can learn how the game plays, and get yourself set up to play it.

This particular game was played on a 12×12 board, which is the standard size available at MindSports.  A board that size contains 144 pieces, which seems like a large amount, but each move in Permute directly moves a set of four pieces and also locks down a portion of the board afterward, so games on 12×12 are surprisingly fast and brutal.  Typically a full game will last between 20-25 moves per player (note I’m counting a twist + bandage as a single ‘move’).

The board size has a strong impact on play in Permute, as it does in other territory games like Go.  Playing Permute on 12×12 is similar to playing Go on a 9×9 board — fighting starts immediately, and tactics are a major focus of the game.  Controlling the centre of the board early is very important, as this offers great opportunities both for expanding your own groups and blocking your opponent’s growth.

For a deeper, more strategic battle, I recommend playing on a 16×16 board.  At this size, games will last between 40-50 moves per player, about the same length as a typical game of Chess.  Opening play on this board size will tend to focus more around the corners and edges of the board, with the centre becoming more important once territories have been settled around the sides.  If you want the territorial aspect of the game to really dominate, then you can play on a 20×20 or even 24×24 board; on 24×24 a game will last about as long as a game of 19×19 Go (generally somewhat shorter).  Ai Ai supports Permute play on all these sizes.

The Ai Ai implementation also allows numerous variants of the game to be played.  The most notable of these is the option for a 1[1]2[2]* move protocol.  This means the first player on their first turn twists and bandages once, and from then on players alternate twisting two faces, then bandaging a stone of their colour in the second face they twisted.  I highly recommend trying this variant, which allows some very clever manoeuvring, and also lengthens the game on smaller boards.  For serious strategic play however I still advocate 16×16/20×20 single-twist rules as the best option; the two-twist variant makes useful tactics substantially harder to see, because two twists can cause so many changes to the board state in a single turn.

In any case, 12×12 with single twists is the ideal introduction to the game, and that will be our focus in this article.  In a future article, I will cover strategic tips and techniques for play on the larger boards, aimed at advanced players.

Permute 12×12 — Simon R vs Eric S

The opening begins!  Simon was playing Orange, meaning he gets to move first.  He strikes out for the centre immediately, which is a sensible play on the 12×12 board.  After just that single move, both of us now have two 3-groups each — each move in Permute substantially changes the local group composition, particularly in the early game, where few pieces have been bandaged.

I respond with an anti-clockwise twist at e4f5, aiming to contain any ideas of Orange extending to the western or southern edges.  In the process I connect my two 3-groups into a single 6-group.

Orange responds by growing their own 3-group by twisting f8g9.  Expansion is never a bad thing, but this move is a bit passive; the resulting group is still smaller than my largest, and this move does not really hamper my expansion.  In response, I twist h4i5, connecting two more pieces to the 6-group by rotating a piece into the connecting corner on h5.  From there, I can extend by adding to the piece attached to the north of h5 — I like to call these one-square extensions from bandaged friendly pieces anchors, as they are good bases for expansion — or I can connect two more pieces on the eastern edge of the group in two different ways, thanks to the 3-group covering i3-i4-j4.

Orange spots the threat of more pieces connecting to my group, so he instead connects his own pieces beneath and around my group by twisting h3i4.  This is a good move, in that it serves two purposes — it instantly gives him a nice-sized group, and it actively blocks my group from expanding to the south.  I was prepared for this, though, thanks to the anchor on h6, so I connect three more pieces with a twist at g7h8.  Note that my group is quite secure; each extension has bandaged pieces one space apart, which cannot be separated by any opposing twists.  When building your groups, one-space extensions are the safest way to connect new pieces.

We’re very early in the game, but the centre is already taking shape.  Here Orange decides to secure some more pieces for their southern group by twisting e3f4.  Again this move is a bit passive; Orange has the opportunity to sandwich my centre group between their upper and lower groups, and my hopes of extension rest on me being able to protect the corner of my group at e5, or the northern extension at g8-h8.  Better would have been Ae5d6-e5 — that would have severed my corner at e5, blocking expansion to the west, while further securing Orange’s biggest group.

Having been spared a squeeze on e5 from Orange, I twist c4d5 and bandage d5 to secure that vulnerable corner and gain space on the west side, with ambitions of connecting to the western edge and cutting off the bottom of the board, so that Orange cannot connect their upper and lower groups on that side.

Orange takes action to prevent my group heading west, but in actuality this move only delays me very briefly.  My group is also still expandable to the east and north, thanks to the anchors on h8 and i7.  This move does give Orange a large group in a commanding position over the southern reaches of the board, but at this stage of the game, exerting influence and securing areas for future growth is more important.  A nice move here would have been Cg8h9-h8, which would have blocked off any northern expansion for my group.

I respond by moving forward with my plan to connect to the western edge, which restricts Orange’s growth opportunities and gives me an anchor on b4.  At this point I also notice Orange’s vulnerable corner on i8, which is an important weakness now that Orange has invested several moves in growing this southern group.

We will take a close look at Orange’s next move, which is a crucial moment in the game.  Orange elected to twist i5j6, extending their group closer to the eastern edge while interfering with my group’s potential expansion on that side.  Unfortunately this move does not protect the vulnerable corner at i4, which gives me a huge attacking opportunity.

The middle diagram shows one potential alternative — securing the corner at i5 increases Orange’s hold on the bottom of the board, but it also further cramps their space for extension, confining their largest group mostly to the bottom.  A better alternative would have been the block at h8 I recommended previously — this move is still effective now, forcing a response from Yellow and adding some tactical complications.  However, at this point Ai Ai estimates Orange’s winning chances at just 36% even if they had chosen to block at h8.

Seeing that Orange has not protected the corner at i5, I launch my attack and twist out Orange’s piece on i5 (marked with an X in the diagram).  In one stroke this slices Orange’s largest group in half.  Bandaging at j5 ensures Orange cannot easily repair this damage, and claims further space toward the lower-right corner, making it very hard for Orange to even attempt to connect around this new blockage at i5.

At this point, Ai Ai estimates my winning chances at 88%.  Orange had invested a lot of moves in this group, and now the bottom portion has been entirely cut off from the section on the right, and is unlikely to form the basis of a winning group.  I have control over the centre and plenty of expansion options on the northern and eastern edges of my largest group.

Orange can see they are in trouble, so they respond with a twist at i8j9, in an attempt to constrict my expansion options to the north.  Orange now has to defend perfectly to have a hope of victory; when forced to play moves like this which do not extend one’s own groups, the opponent is often free to build up their advantage further.

This exchange gives us perhaps the most important message to take away from this game: protect your corners!  In Permute you will often need to bend your group around to connect pieces in various directions, and any corner piece in your group left unbandaged is a potential weakness.  One twist can potentially slice your group to ribbons and leave you struggling.

Now that Orange is on the defensive, I decide to aim for connection to the northern edge.  When ahead and in command of a large group, a useful strategic sub-goal is to try to split the board.  The group doing the splitting is then unassailable, assuming you have bandaged it well, and your opponent is heavily constricted in any attempts to connect large chunks of pieces.

Orange responds by constraining my group’s northern expansion, squeezing it from the west.  This does secure the northwestern section of the board for Orange, which could allow them to build a decent-sized group, and their current group stretching down to f6 is currently pretty secure.  However, this move still gives me the chance to connect to the north or east sides.  Ai Ai recommends moves that either disrupt the unbandaged, unsecured Yellow pieces at i6-i8, or blocking Yellow’s anchor at h10 and preventing the northern connection attempt.  In either case, though, Ai Ai pegs Orange’s winning chances now at only about 3.5%.

As it happens, I elected not to complete the northern connection, and instead disrupt Orange’s newest largest group.  My Yellow piece at f9 makes connection for Orange’s group quite awkward, so my hope is that further incursion into Orange’s northwestern territory will further decrease their chances to build a competitive group in that area.

Orange hits back by disrupting my 3-group around h11, ensuring that my bandaged piece at h9 remains isolated for the time being.  However, this leaves me with an opening to cut off three Orange pieces from potential connection via a later twist at f11g12.

At this point I can see that my central group is very strong, so I decide to continue my plan to disrupt Orange’s opportunities for expansion while securing my position.  By extending down from my anchor at b4, I further constrict Orange in the south, while adding a couple more pieces to my central group.

Orange elects to start enlarging their group in the northwest, establishing a bandaged piece at e7 that also prevents further extension of the Yellow group from e6.

I estimate at this stage that Orange’s northwestern group could not grow large enough to challenge my lead, but just in case I decide to extend my group and bandage at j8, in the process securing the vulnerable piece at i8.  Orange fights back by twisting my pieces at j9-j10 into the corner and firmly blocking them off from my group.  This also builds a nice group connecting through to the northwestern section, but those Orange pieces at f11-g11 remain vulnerable.

My first impulse here was to cut off Orange’s group on the top with Cf11g12-g12, but then I spot a move that looks bigger.  The clockwise twist at c2d3 grows my own largest group by three while simultaneously blocking out three Orange pieces permanently, which seems like a favourable exchange.

Orange responds sensibly, forgetting about the unfortunate southern group for now and further building on their central group.  Orange knows that at some point I will be forced to respond if I want to restrict Orange’s growth there.

Now that Orange’s southern group is well contained, I believe that their only chance to win is to connect their central and northern groups, then extend far down the eastern edge to pick up sufficient additional pieces.  I decide to try to connect to the east to completely cut off any ideas of expansion down that edge for Orange.

Orange sees an opportunity to place a secure bandaged corner at k7, extending their northern group a bit further.

Orange was able to extend that northern group a bit, but I could immediately follow up with Ck5l6-k6, completing my goal of connecting to the eastern edge.  Now Orange has no way to connect to the bottom groups, and the bottom groups themselves are cut off from each other thanks to the bandaged piece at j3.

Orange follows up with a prudent move, securing their vulnerable corner at i10 with a bandaged piece at j10.  Unfortunately, at this point the game is fully out of each; Ai Ai sees no future for Orange, giving them a winning percentage of a flat 0%.  There is no way for Orange to make a larger group at this stage.

My goal at this point is to firmly block off any remaining threats Orange has to increase their score substantially.  Having cut off the bottom with my last two moves, now I close the door along the top as well with Cf11g12-g11, splitting the top group and ensuring it cannot connect to Orange’s central group.

Orange has seen the writing on the wall by this time, but is valiantly fighting to the end.  He extends the southern group with two more pieces, and generates a possible threat of winding around the blockage at j3, though this would require several additional moves to achieve.

I can see that Orange may be hoping to connect around j3, so I close that door as well by placing another bandaged piece at k2.  Now there is no way through on the bottom.

Orange now pursues the last viable option for building a good-sized group, which is to extend their central group as much as possible.  I have almost no presence in the northwestern part of the board, so Orange has some chances to build up a score here potentially.

Finally I respond to the threats in the northwest, and place a bandaged piece at d11, which seems a suitably annoying placement.  The idea is to blockade the 4-group extending from f10 from the Orange pieces in the top-left corner, reducing Orange’s potential for growth.  Orange is still able to grow their central group by connecting two more pieces at b10, but those four pieces around f10 are now isolated.  At best Orange could attach the piece at d10, turning the 4-group into a 5-group, but there’s no way to connect those pieces to the larger group below.

Here I get greedy, and try to connect my central group across the 2nd row along the bottom.  The plan is to construct a pair of pieces that I can then bridge between the bandaged pieces at c2 and f2, but I actually made a mistake.  By choosing the twist at e2f3, I actually ensured that I would be unable to connect my newly-formed pair.

Orange makes precisely the right reply here, placing the Yellow pair where I want it, but unbandaged.  Now I have no chance to connect across the bottom, because in order to secure those pieces I would need to bandage one of them, which means a twist must be made.  But, given that the pair is already in the right position, any twist I make will only move them out of position!

This sort of problem comes up fairly often in Permute, and I was annoyed at myself for not seeing it.  When you have set up your pieces properly, you should have them placed so that they are ready to be twisted into place, but crucially, are not already in place and unbandaged.  That means you can make a move at that location, twist the pieces into place and secure a bandaged piece in the right spot.  If you try a setup for connecting a few pieces but misjudge your plan, as I did, then your pieces may be prematurely placed, and your opponent is then able to prevent your plan at any time by twisting your pieces out of position and locking them down with a bandage.

In truth, this move sequence was overly optimistic anyway; given the two-space gap between c2 and f2 and my lack of well-placed pieces nearby, the only way my attempt to connect would work is if my opponent chose to allow me to make that final twist of the free pair.  I had no way to force that connection in the first place, and Orange had no intention of allowing it, so effectively that was a wasted move.  In a tight endgame, throwing away a move like that could cost me the game!

I cannot secure the connected pair between c2 and f2, so instead I opt to insert another bandage at g2, trapping another Orange piece on the bottom edge at the same time.  Orange then extends that bottom edge group further, but this also connects my pieces to the bottom-right corner group.

I still cannot secure the extension in the south, so instead I opt to harass Orange’s central group some more by blocking two pieces in on the western edge.  This has no effect on the size of my Yellow group, so it is a safe move that still causes some trouble for my opponent.  Orange extends the bottom edge group once more, after which I lock out two more Orange pieces from their central group, and at this point Orange resigns.

If we remove the bandaged pieces we can get a clear picture of the final position:

Permute 12x12 -- move41 -- count-01

There we have it — a final score of Orange 16 to Yellow 43.  Had we played to the bitter end, my final score would have been significantly lower of course, as Orange could disrupt my connecting pair at d2-e2 at any time.  But even then the score would still be convincingly in Yellow’s favour.

Permutation Principles

As you can see, the 12×12 game is intense right from the start, and opening moves are very consequential.  AI testing shows though that between strong players, the outcome is usually decided about 60-70% through the game (during these tests I did not allow the AI to resign).  So, while the opening is very important, most games will be decided during the middlegame.  Our goal in the early stretches of a 12×12 game should be to come out of the opening with a stable central position, with some viable options for future extensions of our largest groups; during the middlegame we want to extend our groups effectively and safely, while denying opportunities for our opponent to attack our groups or build their own.

Of course, if we want to reach that point in our games, we need some guiding principles to help us along in our efforts to become stronger players.  Here I will outline some basic principles of Permute play that will help you play more effectively.

Make multipurpose moves

This general principle applies to many games, of course, but in Permute every move is inherently multifaceted and directly affects both players.  Every twist we make moves opposing pieces as well as ours, since faces consisting of only one colour cannot be twisted.  This means that every single move has the potential to grow or shrink our opponent’s groups as well as our own.

When I am choosing a move in Permute, I tend to evaluate it on a few dimensions to see how it measures up against other candidate moves, and I aim for the moves that can accomplish more than one of these general objectives at once:

  • How much does it add to my groups?  All else being equal, a move that grows my groups more is of course preferable to one that grows them less.
  • How much does it disrupt enemy groups?  If I have a choice of two moves, both of which grow my group by 3 pieces, but one shrinks an enemy group by two while the other doesn’t, then the first move is a better choice.
  • Does this move gain space?  Gaining useful space on the board and restricting the opponent’s growth options is really important, especially in the early game.  If a move grows my groups less than another move, but allows me to connect a group to an edge and block enemy expansion for the longer term, that move may well be the more sound strategic choice.
  • Does this move have follow-up options?  A useful beginner’s metric to judge this is whether a move leaves you anchors — single pieces extending from a bandaged piece that can serve as a launchpad for further expansion.  Again this is more of a strategic consideration; sometimes a move that adds fewer pieces can still be stronger, if it produces anchors that allow for a bigger extension later.  Anchors also create threats for your opponent, as they must keep an eye on those anchors and consider which may need to be blocked, which in turn may disrupt their own expansion plans.

Like any complex strategy game, all of these guidelines will have exceptions, and there are many other ways we might judge the effectiveness of a move as we get stronger.  However, I believe that keeping these principles in mind is very valuable as you are learning the game, because each of them focusses on the longer-term consequences of our moves.

In Permute we have to fight against the impulse to play reactively, and start twisting purely in response to local threats from your opponent; each move in Permute can be so destructive that we often will feel the need to react to every attack, leaving ourselves with no chances to attack in return or to build a coherent plan for expanding our groups.  If we instead train ourselves to evaluate each move in terms of its impact on both the groups local to that move and the wider strategic situation, by considering space gains and anchors, then we are more likely to choose moves that not only protect our groups in the short term but also create longer-term challenges for the opponent.

Protect Your Corners!

This is a straightforward tip, but definitely worth emphasising!  In this game we saw the consequences of leaving a vulnerable corner on your largest group — the opponent gets an opportunity to slice the group in two, and if the group is already contained and there is no alternate path to reconstruct the connection, then that one move is enough to ensure your group cannot be saved.  However, we may not want to develop a habit of taking time to protect every corner in every group; instead, we must judge when a group has enough prospects for future expansion that we need to secure its position.

Stronger players may experiment here and there with group sacrifices, where they lure the opponent to spend moves on disrupting a vulnerable corner when their actual growth ambitions lie elsewhere on the board.  However given the high price for getting this kind of sacrifice wrong, this is a tactic that should only be used very carefully!  Generally speaking, if you spot a weak corner in one of your important groups, you should act immediately to protect it.

Bandaging is just as important as twisting

Each move we make in Permute is, to some extent, irreversible.  In Chess, if we move a Knight to the wrong place, we can potentially reverse that move in the future to recover our position, but if we make a bad twist in Permute, the bandaging ensures that at least some of the damage is permanent.  Because of this, we need to be sure that when we bandage a piece as part of an effort to grow a group, we protect as many of our pieces as possible:

Permute 12x12 -- bandaging examples-01

Here we can see some basic examples of this principle.  In the leftmost diagram, Yellow has created a secure L-shaped group — the bandage on d4 protects the corner, and ensures the pieces on d2 and c4 are fully protected as well.  In the middle diagram, Yellow’s misplaced bandage on d5 has protected none of the pieces in the middle of this group!  On the right, this T-junction formation is also safe, giving Yellow three potential avenues of expansion with the bandages on b4, d3 and d5.  Our objective when setting up our groups should be to maximise our reach, while always being careful not to leave weak points that can be twisted out of position.  One-space extensions, T-junctions, and secure corners are important ingredients in any effort to build a large group.

Conversely, if we are attacking the opponent, we should place our bandages so as to create maximum disruption.  Let’s go back to that fateful 12th move in the game, where I was able to split Orange’s group via the vulnerable corner, and zoom in a bit:

Permute 12x12 -- attacking examples-01

On the left is the move I made.  When twisting at c2d3, I placed my bandage at d2, a diagonal step away from the diagonal corner I had just disrupted.  This ensures that not only is the vulnerable corner at c3 permanently cut, but also the Orange piece at d3 is blocked in, preventing Orange from twisting around the obstruction to continue building the group.  The Orange pair at c1-c2 is still twistable, but cannot get around the bandage at d2.

In the middle diagram, we see the position if I had bandaged at c3 instead — note that Orange now has two pairs at c1-c2 and d3-e3 that can potentially be brought to bear, expanding the group around my obstructing piece.  On the right we see a potential result of this mistake: Orange twists Ad2e3-d2, completely isolating my piece at c3 and building the group southwards with a secure connection.

The lesson here is to always observe the local patterns of bandaged pieces when attacking an enemy group, and think not just about the immediate damage you can do, but also whether you can potentially block off any more pieces by setting up your bandages differently.  Make sure your attack has as much lasting impact as possible, and then you can make advances elsewhere while your opponent scrambles to repair what damage they can!

Split the board when ahead

At several points in the game above, you saw me aim to split the board into sections by connecting my main group across the whole board.  When you have a decent-sized lead and the opportunity, connecting securely can be very beneficial; by cutting across the board, you prevent the opponent making board-spanning connections of their own, and restrict their options for catching up to your lead.

Let us go back to the game for a moment and look more closely at my middlegame connection to the eastern edge of the board:

On the left is the move I played in the game, which connected my largest group to the eastern edge.  Orange is now firmly cut off from connecting their upper group to the bottom half of the board, and their attempt to move south has been contained.

On the right, we see what could have happened if I had not attempted to reach the edge, but instead had played elsewhere (in this case, bolstering my group in the bottom-right with Ch2i3-h3).  Orange is then able to generate threats by connecting significantly more pieces down that right side.

In this particular position Orange cannot make massive gains this way; on the right we see that after a couple more moves, Yellow is able to contain the advance once again.  But Orange did manage to gain two more pieces even in this constrained position, and in a close game two pieces may make all the difference.

So, when the opportunity to cut off your opponent presents itself, taking advantage of that opportunity is often a good way to consolidate your advantage and deny your opponent chances to create more threats.

Twists are local, scores are global

Finally, an important reminder — Permute is a game full of complex tactics, but the ultimate goal of the game is inherently global in nature.  When fighting for your groups to stay live, never forget that all moves should be in service of the larger goal: building the biggest group of pieces on the board.  If you get deep into a tactical battle and realise you will not be able to make any more profitable exchanges, do not be afraid to abandon your group and seek a bigger move elsewhere!

Similarly, we can easily get tied down defending only our largest group, and forget that the group scores in Permute are cascading — this means that if the two players tie for the largest group, then we compare the second-largest, then the third-largest if those are tied, and so on.  So if a game is close, remember to nurture a secondary group in addition to your largest one.  Tight games between equally-skilled opponents will most certainly have games go to the second-largest group, and occasionally the third-largest (though this is rare).

Remember too that playing strategically and planning your group-building effectively will also help you tactically; the more secure your groups are, the better-placed you are to defend them, and the more you constrict your opponent’s growth options with well-planned extensions, the more vulnerable they are to attack.

Next moves

At this point, hopefully you have a clearer picture of how a game of Permute flows, and you have picked up some useful tools in your toolbox for your next twisty battle.  Permute feels quite odd at first if you are used to something like Go or Chess, given the fact that the board starts full and every move directly affects both players’ pieces.  But once we spend some time getting acquainted with the properties of the game, these unusual aspects will start to feel natural, and you can focus on increasing your playing strength.

From here, I recommend having a bunch of games on the 12×12 board, and focussing on developing plans for each of your groups as you play.  Always keep an eye on the score, and check that each move is advancing your own groups while hindering your opponent’s.  Once you become confident navigating the sharp openings of the 12×12 board, then you can try moving up to 16×16, where you have an even more dizzying array of opening options, and the game opens out to become even more strategically interesting.

I have a large backlog of posts to work on at the moment, but at some point down the line I will come back with some more Permute tips, shown off through a fully-analysed 16×16 game.  If any of you out there are interested in a game on the larger board, let me know in the comments; I am always happy to find new opponents!

Some of you may have noticed too that Ai Ai lets you play Permute with four colours, which makes the game feel even more like a twisty puzzle.  I am still in the process of getting acquainted with the nuances of the four-colour game — which works very well with the 1[1]2[2]* move protocol — but I will cover this at some point as well.

In the meantime, I hope you will give Permute a try — Permute is my game so I naturally will have some bias towards it, but at least I can say that after many, many games of Permute so far, I have yet to get bored with it.  I hope some of you out there will have as much fun with it as I have!

Until next time, here’s a little preview of what’s to come — a tense game of 16×16 Permute that came down to a single point:

permute16-5s-tight1

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A Beginner’s Guide to Hex, Part II: Sample Games

In Part I of our Beginner’s Guide to Hex, we covered some critical tactical and strategic concepts that will help you get a flying start in your journey to become a strong Hex player.  This time, we’ll look at a full game played on the 15×15 board between two strong players, so you can get a sense of how those principles manifest during actual play.  After that, we’ll take a look at another game, this time from the Game of Y, to see how Hex principles can apply in other connection games as well.

Commented Hex Game: LG #2195354, kspttw vs Arek Kulczycki

This game was played on a 15×15 board on LittleGolem.net, the most popular place to play Hex in correspondence style.   15×15 Hex is a relatively recent addition to Little Golem, but is already proving popular.  Other board sizes are also available on LG: 11×11 for quicker, more tactical games; 13×13, which is the most popular size (and is the focus of Matthew’s brilliant Hex strategy guide); and 19×19 for deeply strategic contests.

If you’d like to follow along with the game and investigate the variations Matthew recommends, you can do so via the online Hex board on MinorTriad; this site allow you to go through the game step-by-step and experiment with different moves at any point.  

diagram1_5-01

Move 1: Black opens at c2. This is a popular opening on the 13×13 board, but here I would classify it as being likely on the losing side.  All Hex openings are either winning or losing, there are no neutral ones; the best openings are right on the border between clearly winning and clearly losing openings, in that they may give some advantage but likely won’t immediately provoke a swap. On 15×15 c2 is probably weaker than on 13×13, since on larger boards we expect that winning openings will be a bit more centralised than on smaller boards. As a consequence, White elects to not swap sides.

Move 2: The 5-4 point (five rows from your own edge, four rows from your opponent’s edge) is by far the most popular acute corner opening. This move is connected by Template A-5, and it escapes second- and third-row ladders.

Move 3-4: This is a common joseki. Black’s (3) is connected by Template A-4, and escapes second-row ladders while threatening White (2). White’s response connects back to the edge with Template A-4, while restoring their ladder escapes.

Move 5: The 5-5 point is a popular opening in the obtuse corner. Lately, 4-4 has become more popular on the 13×13 board, a development spurred by the play of very strong AlphaGo-style bots. On the larger 15×15 board, it’s an open question whether 4-4 or 5-5 is stronger.

Whether on the 4th or 5th row, having a stone in your obtuse corner is always a plus. These corners are almost always taken early in the game.

diagram6-01

Move 6: White needs something on his southwest edge. You may be wondering why this of all spots was chosen. One principle is that you want stones that are “attacking,” in the sense that they can reach the edge through bridge moves to the side (see the dots in the diagram). Stones like this are harder to block. This is the closest a stone on the sixth row can get to the acute corner and still be attacking. If not for the black stone on c2, White would likely have played this move at f5. You want your stone as close to the corner as possible because it does more to disrupt your opponent.

Note also that (2) was “attacking” in this sense in the east corner. This is part of why the 5-4 point is so popular.

diagram7_9-01

Move 7: This is a popular combination with c2. Together, these stones form Template I-5, and they can escape just about any ladder from the second to sixth row along this edge. This Template is rather difficult to attack. Note also that this move invades the “attacking zone” of White’s f7 stone. 

Move 8: White plays here at the center of the board. This move is somewhat of a distant response to (7). With (7) invading the attacking zone of the f7 stone, Black could potentially block that stone now. But White doesn’t want to overcommit to this area — it’s important to spread influence around the board, especially early in the game when the potential lines of play are so fluid. This stone can support the f7 stone while also increasing White’s influence over the centre of the board and towards the northeast edge.

Move 9: Counterintuitively, in Hex it’s often stronger to play on your opponent’s edge than on your own. Having stones separated by two empty hexes on the opponent’s second row can be quite strong. Notice how White is unable to fit Template A-3 in between (7) and (9) (nor in between (7) and c2). This stone (9) is basically connected to Black’s northwest edge now, because White’s only reasonable blocks (such as at b6 or b7) allow Black to go around to the north (at c6 or c7, respectively). Ultimately, White will need to connect to the southwest edge in the area between (9) and the obtuse corner.

diagram10_19-01

Moves 10-19: White can’t break the connection of b8 to the northwest edge. Instead, White allows Black to connect. But how does this help White? This is an attack I call “undermining.” Note first that the 10-12 group is connected to White’s edge (White can connect at either A or B; Black cannot block both). Because of this, the points D and C are vulnerable for Black. If White intrudes into these bridges, they threaten to connect to the edge through 10/12, so Black is forced to reply. White can therefore invade these points for valuable territory. Additionally, towards the end of the sequence, White obtained the stone (18), gaining more territory and forcing the reply (19). Lastly, the point E is also vulnerable for Black, if they want to keep b9 connected to the edge.

diagram20-26-01

Moves 20-26: Now White begins attacking the vulnerable points, starting at (20). After Black saves the connection, White moves to the other end to attack Black’s 5-5 stone in the obtuse corner, forcing a response there. White knows that after taking the territory at the vulnerable points, they will ultimately need to connect to their southwest edge somewhere in the lower half of it, so having 22 available strengthens this area to White’s advantage. With this secured, White returns to attacking Black in the west corner with moves 24 and 26.

diagram27_30-01

Moves 27-30: Clearly, White has been playing in sente for a while, dictating the direction of play ever since the attack that began on move 10. Black seems to have had enough, and rather than respond at b7 (and handing play back to White), Black tries here to take the initiative back with a block against the h8 stone. Here the play suddenly becomes a tactical affair. White first plays (28), because having these two stones parallel to the northeast edge will virtually guarantee their connection (thanks to the help of the white stones in the east acute corner). Next White plays (30). 

Here White begins to utilise that territory they gained through undermining. Since move 30 is connected to g4, White’s approaches have expanded considerably. (30) threatens to connect to f7, and g4 threatens to connect to e5. Before we look at Black’s response, it would be instructive to see what happens if Black tries to block the former with 31.g6. White might then respond at 32.f5. From here, a few lines to consider:

33. d6 e7 d8 d7 b7 (forced) c8 b9 and then c10 is a ladder escape fork for White, connected to the edge with Template A-3, and back to the main group by either c9 or e9.

33. b7 d8 (connected back by either f6 or d7) c9 d10 (d10 + d12 make for the edge template L-4, hence d10 is connected to the edge) d9 and now f9 is connected to the edge and threatens to connect to either h8 via g9, or to h5 via f8.

diagram31_42-01

Moves 31-42: Black attempted to block at (31) instead. The situation that follows is highly tactical. White first plays 32. d8. After Black blocks at 33. g6, White links up g4 to e5 with 33. f5. Black gains some free territory with a bridge intrusion (35-36). At this point, e5/f5 are connected to d8/f7 by either d7 or f6. If Black blocks at 37. f6, White’s connection is assured by 38. d7 (White can connect by either b7 with Template A-2 or c9 with Template A-3), so Black plays 37. d7. White connects up with f6 (although e7 would have been better, offering no intrusion points). Black takes a little more territory with move 39, but after move 41 White’s responds with 42. d10. As mentioned in the second variation above, this move (along with the stone on d12) is connected to the edge via edge Template L-4. If Black blocks at 43. d9, White plays 44. f9, which threatens either g9 or f8.

diagram43_46-01

Moves 43-45: With the southwest edge lost, Black must attempt to block the northeast edge. The odds aren’t good however. Presumably Black went all in on blocking White from the southwest because Black felt the chances were better there. Black didn’t gain much in the way of territory during that sequence that could help on this side of the board, with the possible exception of the stone on h4. 

The White stone on h5 isn’t yet connected to h7, but trying to block between them will just make things worse for Black (43. h6 i5 i6 and k4 can at best be held to a fifth-row ladder, heading towards the White stones in the east corner). So Black plays 43. j6. White connects up the smart way, at 44. i5. Unlike connecting via h6, this threatens the followup k4, which would start a fifth-row ladder, as well as the potential threats from the h7/h8 group. Black is forced to attempt to block both directions at once, with 45. k6. This cleanly blocks the potential of k4, but as we shall see, can’t hold off a White attack from h8.

Move 46: White bridges away from h8. This move is based on a simple concept: note that by placing the stone out so that there’s a clear line to the edge (shown by the arrows) it can’t be stopped with simple adjacent blocks (j9 j8 k8 k7 … ). This means Black will have to block this stone to a ladder, and that’s where those two white stones on l11 and k12 will come into play.

diagram47_50-01

Moves 47-50: All that remains is for White to finish off the connection. After 47. j9, White will ultimately play j8, after which a fifth-row ladder will begin (Black could hold White to either a fifth- or fourth-row ladder; generally you want to hold a player to the higher row). Before that, though, White sets up the ladder escape with move 48, which threatens to connect back via a bridge to the stone on i9. Black is forced to block (Black’s choice to play 49 at j10 as opposed to i10, is the stronger block since it leaves White with slightly less space underneath). Now White plays 50. j8, and the game is over. Although the final sequence wasn’t played, let’s quickly look at how it might have played out.

diagram_end1-01

The naive approach is just hold White to the fifth-row ladder. White easily connects with Template A-4.

diagram_end2-01

Black might instead jump ahead with move 55 and force a bottleneck, but after move 58 White connects to the bottom with Template A-3 and back to (50) via either A or B.

diagram_end3-01

Finally, Black might try to hold White to a fourth-row ladder instead, but after move 58 White’s stones are connected in the Trapezoid template, and Black has no means of blocking White from the edge. 

 

Y Sample Game: PCM vs Matthew Seymour

Next up we have a sample game of the Game of Y.  For those of you who don’t know Y, it’s actually even easier to learn than Hex:

  1. Two players, Black and White, compete to connect all three sides of a triangular board of hexagons.
  2. Players take it in turns to place one stone of their colour on any empty square on the board.  The first player to connect all three sides of the board with a single connected group of stones wins the game.

That’s it!  In Hex, players must connect two specific sides of the board that share their colour, while in Y all three sides are relevant to both players.  As we shall see, that fact can alter some of the tactics and strategies you may have learned from Hex, but broadly speaking your Hex knowledge is a great help in Y as well.

This game was played between PCM (Black) and Matthew Seymour (White) on iggamecenter.  The board is size-14, which is relatively small for Y but still big enough for a challenging game.  Matthew has annotated the game for us below:

Game of Y -- 14 -- mv4-01

Move 1: We’re playing with the swap rule, so Black (PCM) opens along the edge.

Move 2: White (Matthew) responds with a more central move.

Move 3: Connected left via the A-5 edge template, but the difficulty will be connecting to the bottom.

Move 4: Blocking Black’s stones from the bottom edge.

Game of Y -- 14 -- mv8-01

Move 8: Connected with the B-3 template.

Game of Y -- 14 -- mv10-01

Move 10: A blunder! e9 would have been better (winning I think) than f10, with template C-5 facing the left edge and move 4 helping guarantee the 8-2 group’s connection to the south. As it stands, 2-10 is connected south with C-5 and 2 isn’t fully connected to the left.

Game of Y -- 14 -- mv15-01

Moves 11-15: This block sets up a ladder with the bottleneck formation.

Move 16: Ladder escape. The plan here is that after b7, White plays d6 d7 f7, and now White is connected to all three edges.

Move 17: Counter-threat, threatening the connection between (8) and the edge.

Move 18: 16-18 is connected to the right edge through the M-4a template, and connected to the central group (14-8) via either d7 or the ladder on the left.

Game of Y -- 14 -- mv21-01

Moves 19-21: Black first blocks the d7 route, then blocks between the ladder and the escape on move 21.

Move 22: Here I blunder the game away! I was concerned the 20-8 group might lose its connection to the right that I had through either 8 or the 16-18 group. It looked like Black had blocked off the 16-18 group, so I had to save it via (8). I missed the winning move 22. a6.  Then, if 23. i10 I could simply play a5 and I would be connected to all three edges — in other words, it would have kept the double threat alive for connecting to the right, while also connected the group to the left.

Instead, I saved the connection to the right, but now Black can now cut me off from the left at a6. I missed this “obvious” move because (I think) I’m so used to playing Hex. 21 is connected to the left via A-2, and in Hex there’s no reason to ever invade A-2 because the two empty hexes are captured. But of course, in Y, the edge is shared by both players, so these hexes are NOT captured.

Game of Y -- 14 -- m23-01

Move 23: Forced. Black blocks White from the left edge.

Game of Y -- 14 -- m30-01

Moves 24-30: Ladder, followed by a break. The black group (1-29) is connected to the left and right edges. Black needs only to connect it to the bottom to win.

Game of Y -- 14 -- m36-01

Moves 31-36: 4th-row ladder, followed by a bottleneck. White has no hope however, as the 7-5 group will help escape the ladder.

Game of Y -- 14 -- m43

Moves 37-43: There are many ways to escape the ladder, but Black elects to go with this approach. More straightforward would have been e13 f14 f13 g14 g12 and then Black can play either h13 (with A-2) or j12 (with A-3). As played, (38) is the only reasonable reply to (37) (further left on this row, Black plays e11; further right on this row, Black plays g13; for plays on row 12, Black uses (37) as a second row ladder escape). (39) and (40) accomplish nothing but there’s no harm. After (41), Black can play either h13 (with A-2) or j12 (with A-3). White blocks the former, so Black plays the latter. White resigns.


So, there we have it — a quick but well-played game of 15×15 Hex, and a tricky game of Y that shows off some of the quirks of Hex’s cousins in the connection-game world.  We hope these give you some useful ideas about how to apply the core concepts of Hex strategy to your own play.

Let us know in the comments what you think, and if there are other subtleties to Hex (or Y, for that matter) that you’d like to hear more about, perhaps we may do some more posts in the future.

In the meantime, enjoy, and good luck with your journey toward becoming a strong Hex player!

 

 

 

 

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A Beginner’s Guide to Hex

Some time ago I talked a bit about Hex on this blog, discussing its history and how it kickstarted the entire connection game genre. Since then, a few readers have asked for a bit more detail on how to actually play Hex. So, for this post I have teamed up with Matthew Seymour, author of the brilliant Hex: A Strategy Guide, and we have put together this beginner’s guide to Hex strategy and tactics.

Below we will introduce you to basic tactics, templates, openings, and strategic considerations. Each section is very brief but will give you enough to get you started on improving your Hex play; after you tackle each section, please continue your studies with Matthew’s guide, which has much more detail and numerous examples of each critical concept.

Basic Tactics

The edges

Edge play in Hex is obviously critical, since in order to win we must connect our two edges across the entire board. Initially, connecting a chain of stones successfully to the edge seems like a baffling enterprise — an adept opponent can bend and twist your attempted connections away from the goal, and it can be difficult to understand how to set yourself up for a strong connection.

Edge templates are extremely useful tools for understanding edge play. In our previous discussion of Hex, we met the bridge, a configuration of two stones that proves to be virtually connected even though the stones aren’t adjacent.  Similarly, edge templates show us configurations of stones that, with correct play, are guaranteed to result in connect to the edge. Templates indicate patterns where, even if your opponent has the first move, you will always be able to connect successfully. Your opponent may intrude on your template, but so long as you defend your template at every step, you will succeed.

This means however that templates are always just a move away from breaking. If you have two overlapping templates, and your opponent plays a move that intrudes on both, you can only potentially save one of them.

Here are some examples of basic edge templates:

Our first edge template is the very basic A-2 template, consisting of a stone on the second row. If White tries to block at A, Black can respond at B (second diagram), and vice versa. Either way, White has no means of stopping black. This template is very similar to the bridge template.

One of the most useful templates is template A-3, consisting of a single stone on the third row. This template comes up very frequently. We’ll analyse the situation by considering Black’s possible threats. On one hand, he could play at A and connect to the edge with template A-2. Or, he could play at B, and connect by a chain of a bridge and template A-2. The important part here is that these threats don’t overlap. If White plays at A, or one of the two hexes below it, Black simply plays at B and connects by that route. And if White plays in any of the 5 hexes on the right, Black plays at A and connects by that route.

We can succinctly convey this information in what’s called a pivot diagram. The two small dots indicate Black’s alternative moves. We can see that the rightmost dot connects back to the top stone with a bridge. Both dots are connected to the edge by one of two possible moves (template A-2).

Lastly, let’s look at Template A-4, on the fourth row:

diagram5-01

Similar to A-3, Black has two threats: to play adjacent at A, connecting to the edge with A-3 (left), or to bridge to the side at B, also connecting with A-3 (right).

These alternatives can get around most possible blocks by White. But there’s one issue, the point C. Both the threats above overlap at this point. So Black needs a response to a block at this point. The solution is shown below (note that if White played (3) on the left side, Black could bridge to the right instead).

diagram8-01

There are a large number of edge templates. You can find an excellent catalogue here or here.

Interior templates: connecting chains

We’ve already encountered one interior template — a template for connections in the centre of the board, away from the edges: the bridge. As you might expect, other templates exist for more complex configurations of interior stones. Knowing these templates is very helpful indeed, as once you achieve such a configuration on the board and recognise that template, you can play elsewhere, knowing that you’ll be able to successfully defend that template against later intrusion.

Some well-known interior templates are the Wheel, the Crescent, the Span, and the Trapezoid.

Defending at a distance

We’ve talked a lot so far about connecting — positive, attacking play. But what to do if our opponent has us on the back foot, and a deadly connection is looming? How can we stop them?

First, we should remember that as satisfying as that positive, attacking play may be, Hex is what is called in combinatorial game theory a hot game. This means that it is always beneficial to make a move in Hex, and no stone of ours on the board is ever a detriment to us. On top of that, one player must always win in Hex, so if we successfully block the opponent from any possible connection between their edges, we’ve in fact won the game. So don’t neglect defensive play — in Hex, it’s precisely as powerful as attacking play, and will win you the game just as effectively! Defensive moves in Hex are also offensive moves.

Having said that, defence in Hex can be a delicate affair. As we’ve seen in numerous examples, stones can be connected even if they aren’t adjacent, and skilled players can move across the board at high speed, staying connected the whole way. Therefore, if we attempt to block simply with adjacent blocks — playing right next to opposing stones — a skilled opponent can easily bend around us. Likewise, if we block at a distance but misjudge the situation, the opponent may still get round us by using bridges to cover enough ground to do an end-run around our defences.

In practice we may need to combine adjacent blocks with more distant blocks in many cases. The adjacent blocks restrict the opponent’s options for bridging forward, while the distant blocks contain those advances:

The classic block short-circuits the opponent from afar, allowing the defender to respond whether the opponent advances directly forward or takes a more oblique approach:

In either case, in order to defend we need to evaluate the opponent’s options for onward connection, and place our stones in anticipation of those options. If we defend reactively, and follow the opponent around right at their heels, then we’ve no hope of survival. If we instead constrict their choices and contain their subsequent advances, then we may just keep them at bay.

Ladders

Often, when approaching an edge of the board, you’ll end up in a situation like this:

ladder1-alt-01

White wants to connect and Black can’t allow it, so Black blocks at (3). White can’t connect right away but can force Black to carry on blocking all along the edge. This series of back-and-forth adjacent plays is called a ladder. White is completely in control here; Black has to respond to every ladder stone White plays, otherwise White’s connection is assured.

Go players will be familiar with sente — the concept of maintaining the initiative, by making moves that force an immediate response from the opponent. When you have sente you are in control of the game; you are making profitable moves, and all your opponent can do is match you, stone for stone, unable to direct play to their advantage. Sente is just as important in Hex as it is in Go, and ladders are one common manifestation of it.

However, you have probably noticed that if White continues playing the ladder here, it’s Black that ends up connecting across the board:

ladder1-01

To make the ladder profitable for them, White needs to incorporate some additional tactical plays. If White had an additional stone in place to form a ladder escape, then when the ladder reaches that stone, they can connect to the edge with ease.

ladder1-escape-01

Of course, when a ladder is already forming, taking a turn to place a ladder escape stone simply dooms the ladder. So players will often place ladder escape stones during the opening phase of the game, to allow for profitable ladder play later.

Another option is to place a stone that is both a ladder escape and a threat to connect by another route. Your opponent will be forced to block either the threat or the ladder, and then you can connect by the other means. In the diagram below, Black plays a stone at 1. This can escape the ladder, but it also threatens to connect via A (with two bridges). White can’t block both approaches, so Black will connect. This is called a ladder escape fork.

diagram14-01

If you have no ladder escapes or forks available, you’ll have no choice but to “break the ladder”, as Black does with move 7 in the diagram below (note that 7 is connected with Template A-3). In the acute corner, this tends to reverse the roles: notice how now it’s White who’s the attacking player with a ladder.

diagram13-01

Strategic Considerations

Openings

The opening in Hex is an interesting moment, as the first player needs to consider not just what is the best move to play, but what is the best move to play that won’t get swapped. In Go or Chess, you can play your opening move without fear of that move suddenly becoming your opponent’s opening, but not so with Hex!

As the second player, you need to do the opposite calculation: has my opponent played a move that, with perfect play, would give them a winning advantage? If so, I should swap; if not, I can safely play on.

On smaller boards, Hex has been solved, meaning that we know the precise outcome of any given opening move. That leads to diagrams like these:

Above are three diagrams showing the ultimate winner, with perfect play, of opening moves played at every cell on the board. There’s an important trend to notice here — the winning openings for any given board size are not straightforwardly extendable to larger boards! While we can see a general theme that opening moves in the centre are stronger than those on the edges, the specific outcomes of those edge cells change as we change the board. That means that on the boards we humans play Hex on — from 11×11 upward — not only do we not have these convenient maps of what moves win or lose, but we cannot use the opening maps from smaller boards as a definitive indication of the outcome of any opening on the bigger ones.

Matthew’s guide focusses on the 13×13 game, and for openings on that board, he’s produced a swap map that can help guide you in the opening. The cells with black dots are Matthew recommendations for good opening moves for Black. When you are the second player, if your opponent opens anywhere in the shaded area, you should swap — those moves have the potential to give a winning advantage, so you’re better off taking that stone for yourself. If your opponent plays outside that shaded zone, let them carry on — you can possibly do better by playing your own opening.

swap-map-13x13-01

For larger board sizes, like 15×15 and 19×19, we don’t yet have enough games played at a high level to put together a reasonable swap map. However, we can make some reasonable inferences about good opening moves; in particular, opening in the obtuse corners seems a good way to go on all board sizes.

These are very simple principles, but should be enough to get you started. One thing to bear in mind is that we humans are far from perfect play, even on 11×11, so both sides are likely to make mistakes, not just in the opening but throughout the game. So our goal at this stage should be simply to ensure that our opening doesn’t obviously disadvantage us; we don’t need to fret too much about whether a particular move is 100% winning or losing.

Playing in the corners

The Hex board has two types of corners — acute and obtuse — that have different properties. Corners are the only parts of the board where your stones can both strengthen your own position and weaken your opponent’s, and for that reason, players tend to play stones in the corners early in the game. Typically you will want to play stones in at least one corner on each of your edges during the opening.

The corners being so important often leads to pitched battles to establish control over them, and so strong players may study corner patterns (think joseki in Go) to navigate these tactical scuffles. If you don’t have a presence in a corner and your opponent does, invading is useful in order to reduce their influence there, and corner patterns will help you to reduce that influence. Conversely, if your opponent invades your corner, you can use these patterns to settle the fight and maintain as much of your initial influence as possible. The challenge in these situations is judging when there is no more profit to be gained, and thus when it’s time to move on from the corner battle and establish yourself elsewhere.

There is a lot to discover in these corner patterns, but don’t worry too much about these early in your Hex journey; as you start to face stronger opposition and find your corner play is letting you down, refer to Matthew’s guide for detailed examples of how to fight for the corners.

Influence

We’ve alluded to this concept in the previous section, so now let’s expand on what influence means in Hex strategy. Stones in Hex are not just localised points — they have impact on the board around them and on other nearby stones. Every stone has the potential to connect to something or to block something else, and when placing our stones we need to consider the influence of the stones around our planned placement.

In the early stages of a Hex game, gaining influence is important. We would do well to place our stones around the board, to spread them out; this maximises the potential influence of each stone. Conversely, if we don’t spread our stones out, we may have a strong influence in a particular area but will be weak elsewhere. If we are struggling to find an effective place to play, we can look at our relative influence on different areas of the board; if we find some areas where we have low influence, those might be good places to play our next moves.

As you might expect, stones in the corners have a high degree of influence — the proximity to two edges means those stones are better able to restrict your opponent’s activity in that area and force them to work around you in a limited space. Placements in the corners also are tougher to block, and provide you with ladder escape stones for later in the game.

The edges are somewhat less intuitive. We might feel secure playing near the centre of our own edges, as this seems a useful way to block the opponent, but in practice these kinds of placements do not provide strong influence. Instead, we should play near our opponent’s edges — this forces them to work around you and makes it harder for them to connect.

Beginning Go players often play in a style referred to as Puppy Go, where they continually play very close to every one of their opponent’s moves, following them around the board like an excitable puppy. We can easily be tempted to play Puppy Hex in a very similar way. Unfortunately this is an adorable, but poor strategy; in a Puppy Hex scenario your opponent is dictating play completely, and since you are always one stone behind they will have free choice of where to establish influence and you will always be playing catch-up. Always keep an eye on the broader board situation, and try to take the initiative when the situation allows it — don’t let your opponent drag you around by the nose!

As you become more comfortable playing in an influence-oriented style, you can start to focus on making moves that serve multiple purposes. Gaining influence is good, but gaining influence and blocking the opponent is even better! This is a challenging step, requiring you to have both tactical and strategic vision, but as you gain more experience and become able to recognise common tactical motifs, you’ll be better able to keep these in mind as you seek to expand your presence across the board as well.

As a final note, we should remember that Hex is fundamentally a scalable game — we can play Hex on any size board we like without changing the rules, but the feel of play will change. Hex on larger boards is a challenging and rewarding affair, but specific tips on those epic battles is beyond the scope of this article. However, we encourage you to try larger boards, as they by necessity will make you play in an influence-oriented style. With so much additional empty space on the board, you’ll need to learn to anticipate where battles for influence and territory will rage, long before they actually happen. That experience can help you on the smaller boards too, training you to think globally more consistently.

Territory

Territory is a critical concept to understand in Hex strategy. Think of territory as the potential your stones create for future connection; the more territory you control, the more tactical options you have for later attempts to form connections between your stones.

As a starting point, we might say that each stone creates territory in the area immediately around itself; in other words, the empty hexes immediately adjacent to it. However, as we see below, this definition falls apart fairly quickly:

useless-stones-01

These intrusions by Black gain no useful territory. In both cases, White simply blocks any onward connections, so the ‘territory’ gained (the shaded cells) offers nothing that Black didn’t already have!

If we believe that stones create territory regardless of their disposition, then we will run into situations like the above, where our stone is effectively a wasted move, as it will never actually be able to connect to anything. Instead we should restrict the definition a bit more: the territory around our stones consists of the adjacent hexes that could in theory participate in a connection. If we want to invade somewhere and gain influence from that play, we need to be certain that the placement provides useful territory; if the stone does not gain territory, then we have simply placed a stone for no real purpose. Without territory we cannot claim influence, as the enemy can simply work around us at no real cost.

Taking the initiative

As in many other abstract games, in Hex gaining the initiative is of huge importance. Recall the Puppy Hex discussion earlier — imagine if we could force the opponent to play Puppy Hex. If we can place stones with aplomb while our opponent can do nothing but respond, we can dictate the pace of play and dominate the board at our leisure.

Here we will go in-depth into some Go terms we mentioned earlier: sente and gote. In Go, when we play a stone that forces the opponent to respond — because a group is threatened with capture, for example — we say that is sente, meaning we are gaining the initiative. Our next move after the sente move is essentially free; the opponent’s response is mandatory, so our next placement can be anywhere we like, and we can use that to gain influence or territory. Conversely, the forced response the sente move creates is gote — we are forced to be the puppy for that move and play where the opponent demands.

In Hex we also have sente and gote moves. For example, we may recognise that our opponent has an edge template in play, so we may choose to intrude on that template and gain some influence. That move is sente because it demands a response; the opponent must play to save the template, otherwise that connection is lost. At that moment our opponent’s move is gote, lending us the initiative.

As we gain more experience of Hex strategy, we will be better able to identify opportunities to gain sente. At the same time, we must be mindful of our opponent’s threats, and remember that playing gote moves to save a critical connection is vital too! We should try to avoid being the Hex puppy whenever possible, but sometimes there’s no escaping it.

Tenuki

Let’s look at another situation:

tenuki1-01

Here Black is threatening to cut the stone A off from the top-right edge, and the straightforward response would be for us to save the connection and take gote, such as by responding at L3. After all, by not playing there we lose the connection.

However, in this situation we can see that White has an opportunity to make an intrusion of their own, on the other end of the board. Black’s threat depends on using the stone B to connect to the bottom-right edge of the board. White’s board situation will allow them to make other connections, even if they sacrifice the connection under attack by Black, but Black’s situation is just as fragile. In cases like this we may elect to tenuki — to play away from the threat and allow our opponent to break the connection. Instead of defending against the threat we attack elsewhere, and now they must make a choice: either save their own template, or finish ours off. If they finish ours off, they must make a second move, giving us influence elsewhere; if they take gote to save their own connection, then we have regained the initiative.

In this game, White elected to attack Black’s B stone with move (2), rather than save the connection of A to the edge. Black elected to save the connection, playing out a standard joseki sequence, leaving White with the initiative.

tenuki2-01

Tenuki is an advanced concept, and often difficult to judge. In general, you will have more opportunities for playing away from threats in the early- and middlegame, when the board is less full and there will be opportunities for other connections. In the late game, typically both players will have committed many stones to particular connections, and there is inherently less flexibility; if we ignore a threat, we are more likely to hand the win to the opponent.

The Joy of Hex

We’ve covered a lot of ground in this post — over the course of these few sections we’ve gone from the basics of the board geometry through to advanced strategic play. Yet for all that, we’ve barely scratched the surface. From here, you can move on to Matthew’s detailed guide to Hex, and dig deeper into all of these concepts. While you’re there, be sure to try out his fantastic collection of 500 Hex puzzles (also available in PDF, in Hex style and Go style) to sharpen your tactical vision.  If you need help with openings, he also used over 6,000 online games on 13×13 to generate a very useful opening database.

Having said that, resist the temptation to power through all this material. Take some time with these concepts, apply them to your games, and move on only when you feel comfortable and confident. Remember too that Hex is perhaps the most famous modern abstract strategy game, but it is still very new in the grand scheme of things. Traditional games like Go, Chess and Shogi have had centuries for strategies to be developed, whereas in Hex we are all still beginners in some sense! So there is always more to discover and more to learn.

If nothing else, we hope this brief introduction will give you an appreciation for Hex’s incredible depth and nuance. Hex is a disarmingly simple game, so much so that a brand-new player may be tempted to ask ‘…that’s it?!’ when told the rules for the first time. But within that sparse framework lies a world of intricate tactical and strategic variety. This simplicity means Hex also has amazing flexibility — we can play lightning-fast blitz games on 11×11 boards, strategic masterclasses on 19×19, or mind-bending, baffling escapades as long as a game of Go on 26×26. Each one of these configurations is rich with possibility. Learning Hex also benefits you in other connection games — the tactics you learn here can transfer to other games, like the Game of Y (more on that in our next post).

Above all, we hope you have fun with the game! Go spend some time testing out your strategies online, entering tournaments, analysing games and writing about them. But alongside that, teach your friends and family (when Covid restrictions allow!), help them learn some basic tactical and strategic concepts, and show them why you love it. Every new player we bring to the game makes Hex’s future ever brighter, so the more we help others to see what the game can offer, the more enjoyment we’ll all have in the years to come.

Next moves

In the second and final part of our Hex mini-series, we will analyse a complete game of Hex in detail, and show how the concepts we’ve introduced here play out in a game between strong players.

Then we will analyse a brief game of Y, as well, to demonstrate how Hex concepts transfer to other, related games — and we’ll point out how some concepts change when we move to a different game.

Extra nerd stuff

Check out these papers if you’d like to know more about how the small-board swap maps above were generated:

SOLVING 7×7 HEX: VIRTUAL CONNECTIONS. AND GAME-STATE REDUCTION. R. Hayward, Y. Bjomsson, M. Johanson, M. Kan, N. Po, J. van Rijswijck. Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada.

Solving 8×8 Hex.  Henderson, Arneson and Hayward, IJCAI 2009.

9×9 Hex: Scalable Parallel Depth-First Proof Number Search.  Paulewicz and Hayward, Proc. Computers and Games CG2013, Springer LNCS 8427 (2014) 138-150.

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Quick picks: interesting abstract games in brief

As some of you will be aware, as a way of keeping myself occupied during the pandemic I’ve learned how to use Adobe Illustrator to design stuff.  A particularly enjoyable, if slightly odd, area of design I’ve gotten into is designing game boards for abstract strategy board games.  I’ve had a good time getting to know the software and experimenting with many different designs, and now that nice neoprene game mats can be custom-printed for affordable prices, I’ve actually gone ahead and had some of my designs printed out as well.  Hopefully, in some theoretical future where the pandemic is over, I can use these boards to introduce friends and colleagues to some of my favourite games.

I’ve made a lot of boards over the last year, so rather than wait until I can find the time and energy to write detailed blog posts on all of the games that go with them, I thought I’d share a few abstract strategy gems with you with just a few sentences about why they’re interesting.  Each brief review includes links to full-size images of the boards I’ve made for each game, which you can print if you wish.  Some of these games will get covered in detail in the future; for now, hopefully these short descriptions will entice some of you to give these games a try.

As a side note, I can output these designs in a huge number of formats — PDF, PNG, JPG, SVG, whatever — so if any of these strike your fancy but you need a different format, just let me know in the comments and I’ll upload it for you.

Catchup

Catchup is a wonderful game by Nick Bentley that I’ve mentioned briefly before, because the scoring system inspired my choice of scoring system for Permute.  This is a game I’ll definitely cover in the future, as it’s incredibly easy to learn, yet within moments of starting to play you’ll realise the core strategic dilemmas at the heart of the game.  Catchup is a really dynamic and exciting game, and personally I think Catchup is Nick’s best design by far.

Why it’s great: Catchup’s unique feel stems from its unusual movement protocol: each turn, you place two stones anywhere on the board, unless your opponent equalled or exceeded your score after their last move, and then you can place three stones.  The winner is the player who forms the largest group of connected stones at the end of the game, so the result is a tense back-and-forth where you absolutely must connect your stones to win, but each time your biggest group becomes equal to or larger than your opponent’s, they get a much more powerful move with which to fight back.

About the boards: The board on the top left above is a standard hexhex board, seven hexes on a side, with a scoring track where players can place a stone on the number representing the size of their current largest group.  The other five are variant boards with uneven sides, which an experienced Catchup player has suggested may generate more interesting play.

Chess: Supersized

These are simply enlarged chessboards — 10×10 squares and 12×12 — that I plan to print on mats and use to play large variants of Chess.  Many Chess fans over the years have attempted to transport the magic of the Royal Game to larger boards, and thankfully a number of them succeeded in creating some very enjoyable variants that feel like Chess, but still have a unique personality.  I’m planning to write an article in the future that will cover a bunch of large Chess variants and give you some detailed recommendations; for now, here’s a few worth checking out on both board sizes, should you fancy giving them a go.

Some recommended 10×10 Chess variants: Caissa Brittania (checkmate the Queen instead of the King!), Decimaka (hybrid of Chess and Maka Dai Dai Shogi), Elven Chess (hybrid of Chess and Chu Shogi), Grand Chess (Christian Freeling’s most famous Chess variant), Grand Shatranj (ancient Persian Chess brought to 10×10), Omega Chess (commercial variant with Wizards and Champions), Opulent Chess (Grand Chess but more my style — higher piece density, less wild tactically), Shako (Chess with Cannons and Elephants).

Some recommended 12×12 Chess variants: Chu Shogi (the best 12×12 Chess-type game, period), Gross Chess (mix of Grand Chess, Omega and Asian variants, very playable), Metamachy (fast-paced Pawns and crazy historical pieces give it a unique and fun feel), Zanzibar-XL (dense and diverse piece selection with a variable setup).

Exo-Hex and Iris

I briefly covered both these games before, but since then I’ve made some enlarged boards for myself, so I thought I’d share these here and urge you again to give them a shot.  Both these games are from Craig Duncan, and they are unique connection games that are centred on scoring points rather than being the first to make a single connection.  Both are rich and highly strategic, and well worth your time.

Why they’re great: Exo-Hex is essentially a distillation of Side Stitch into a simpler form, playable with a standard hexhex board with some extra stones around the edges.  The more straightforward rules and minimalistic look are great for beginners who may not yet be ready to graduate to Side Stitch and its endless variety of possible playing surfaces.  Exo-Hex is also much easier to construct with components you may already have around, so it’s more straightforward to pick up and play.

Iris, meanwhile, is part of the surprisingly small family of connection games with two-move turns.  Simple restrictions on placement — you may either place two stones on same-coloured spaces on the edge of the board that are directly opposite each other, or two stones in the centre on non-adjacent spaces — means that the game moves quickly and has a huge number of possible moves per turn (a large branching factor), yet structures you will know from Hex and other one-move games still work.  I’ve played Iris a lot against Ai Ai and I highly recommend it for any fan of connection games.

Lotus and Medusa

Lotus and Medusa are two under-appreciated territory games by Christian Freeling that are closely related — in fact Christian calls Lotus the ‘support act’ for Medusa.  Both centre around the use of a mechanic from a game called Rosette.  Over the years, numerous designers have tried to transport the game of Go to the hexagonal grid, only to find that the reduced connectivity of each point (from 4 adjacencies to 3) made it too hard for players to build stable groups of stones.  Rosette addressed this by allowing groups of stones containing a rosette — a formation that occupies all six points of a single hexagon — to be immune from capture permanently.  Lotus and Medusa adopt this clever tweak, while adding some fascinating additional touches.

Why they’re great:  Lotus takes the cool-looking board from the rather disappointing game of Kensington, and turns it into the basis for a compelling territorial contest.  Capture doesn’t just eliminate enemy stones, it flips them to your side, like in Othello, and occupying all six points of a hexagon keeps your groups alive forever, as in Rosette.  Medusa takes this further by removing hexagons from the playable area of the board to further reduce its connectivity, and allowing players to either place or move a group of stones already on the board.  Medusa also has the ‘Othellonian’ capture and rosettes of Lotus.  Both games have the satisfying tension of a good Go-like game, but with very different play styles; Lotus is quick and deadly, while Medusa is a longer epic that allows groups to flow sinuously across the board.  Both deserve more attention than they’ve received.

Nutty Shogi (and friends)

Nutty Shogi is here as a representative of the class of 13×13 Shogi variants.  The only historic 13×13 Shogi variant is Heian Dai Shogi, which is a very early form of Dai Shogi that is unfortunately not very enjoyable to play.  However, some modern Shogi variant fans have created some 13×13 variants that are worth your time, and given that 13×13 Shogi boards are not available anywhere, I decided to create one to print on a mat.

Why 13×13 Shogi is great: Nutty Shogi, designed by HG Muller, is a reduced version of Tenjiku Shogi, a 16×16 historic Shogi variant famous for its outrageously powerful pieces and extremely fast-paced and destructive play.  Nutty Shogi condenses Tenjiku’s armies of 78 pieces per player, with 36 types of pieces, down to 50 pieces of 25 types — still much more than Chess or Shogi, but quite manageable.  The selection of pieces is basically a Tenjiku Greatest Hits album, so the game retains the feel of Tenjiku in a more compact size.  HG Muller also created two other worthwhile 13×13 variants:  Cashew Shogi, a reduced form of Dai Dai Shogi; and Macademia Shogi, a reduced form of Maka Dai Dai Shogi.  While you’re at it, do check out Mitsugumi Shogi, a condensed form of Suzumu Shogi, which is a modern variant of Tenjiku Shogi (still with me here?).  All of these games pack a lot of action into that 13×13 area, so despite the large boards and starting arrays they are far from slow.

Odd-Y and Pex

Here we have two fascinating variants of the seminal connection games Hex and the Game of Y.  Odd-Y extends the core concept of Y to boards with more than three sides, while Pex transports Hex to a grid of irregular pentagons.

Why they’re great: Odd-Y circumvents one of the shortcomings of Y, in my opinion, which is that the triangular Y board gives different areas of the board very different values, which means some parts of the playing area go largely unused.  Odd-Y extends the goal of forming a Y — connecting three sides of the board — to boards of more sides, creating a more expansive feel.  The new winning condition is a bit complicated to explain on larger boards, but Odd-Y with five sides — 5-Y — is beautifully simple: connect any three sides to win, so long as all three sides are not adjacent.  This can then be translated to a six-sided hexagonal board by colouring the edges with five colours in a pattern like you see above (Craig Duncan came up with this idea).   5-Y feels very freeing — there are more winning connections available than in Y, creating more strategic complexity, and the entire board surface feels useful.

Pex was invented by connection game maestro David J Bush, world champion of TwixT and co-author of my post on that game.  He transformed Hex by placing it on the irregular pentagonal grid you see above, keeping all the rules the same (not that there are many rules in Hex).  The new grid forces significant changes in tactics, as cells now have different adjacencies, so standard Hex techniques won’t work.  Pex is a challenging and interesting variant, definitely intriguing for experienced Hex players, but also simple enough for newcomers to pick up and enjoy within minutes.

Snodd (and Xodd/Yodd)

Snodd is a variant of a pair of games by Luis Bolaños Mures called Xodd and Yodd.  Xodd/Yodd are mind-bending games in which players are assigned a colour, yet may play stones of both colours; Xodd is played on a square grid, while Yodd is played on a hexagonal grid.  On your turn, you may place two stones on the board, each of which may be either colour, and at the end of the game the player with the smallest number of groups on the board in their colour wins the game.  There’s a catch, however: at the end of any player’s turn, the total number of groups of stones on the board must be odd!  This single restriction is what makes the game so challenging and unique.  When you start to play you’ll soon realise how this parity restriction allows you to catch your opponent out in all sorts of clever ways.

Why Snodd might be great:  Snodd is my attempt to bridge the gap between Xodd and Yodd.  Xodd is played on a square grid, where each square has four adjacencies (diagonal adjacencies don’t count), resulting in a tight, tactical game where groups are often split apart.  Yodd is played on a hexagonal grid, where cells have six adjacencies, meaning groups stay connected more easily and the game feels more deliberate and strategic.

In Snodd I took the exact same rules and ported them to a snub-square tiling.  When you play on the points of this pattern, each point has five adjacencies, placing it right between Xodd and Yodd’s geometries.  In theory, this should make a version of the game with a nice balance between tactical fights and global strategies.  Test games against myself have been promising, but more investigation is needed.  Give it a try and let me know how you find it!

*Star and Superstar

*Star is another game I’ve covered before, but at the time I was a bit confused about the rules and had yet to try it.  Boards are also hard to obtain, as they can only be ordered from America, and shipping from America now is ludicrously expensive, so I made two variations of the *Star board to print myself.  Superstar is a predecessor of Starweb, a fantastic connection game from Christian Freeling; Christian says Superstar is no good now and fully superseded by Starweb, but he thinks lots of things are no good, so I wouldn’t take that to heart.

Why they’re great:  *Star is the final iteration of Craige Schensted/Ea Ea’s set of connection games built around the goal of claiming edges and corner cells, then connecting groups of those cells together.  *Star is a bit hard to understand at first, but once you get going, you’ll find a dynamic game of territory and connection, where both players writhe hectically around each other trying to weave their scoring groups together.  The resulting play is complex and challenging, and games of *Star often exhibit subtle and sophisticated strategies.  The *Star board also supports two excellent variants: Double Star, where players may place two stones per turn instead of one; and Star-Y, a pure connection game where players must connect three sides which are not all adjacent (just like 5-Y above).

Superstar’s relationship to Starweb is about more than the shape of the board — there’s a clear lineage here, where Christian was moving from Star/*Star toward what would eventually become Starweb.  Despite Christian’s misgivings, I enjoy this game — it has a remarkable diversity, in that multiple types of formations are available for point-scoring: stars (a group touching at least 3 edge cells); superstars (groups connecting 3 or more sides, worth many points); and loops (worth more points for enclosing more cells, and many more points for enclosing enemy stones within).  The feel in play is like a heady mix of Star and Havannah, where each player has incredible flexibility and must keep their wits about them to spot the myriad ways their opponent may be seeking to score.  The mix of connection and surrounding elements gives it a bit of a territorial feel as well.  For me it is a worthy entry in the Freeling canon, distinct enough from both Starweb and Havannah to have its own identity.

About the boards:  The two *Star boards above are equivalent — on the blue one you will play your stones in the cells, and on the other you will play on the intersections.  I made both since different players may find one or the other easier to parse visually, so I wanted to have both options available.  The Superstar board is very similar to the Starweb board, with the notable difference that the light-shaded cells are not playable, but instead are there to indicate the point values of cells adjacent to them.  The game would definitely be extendable to larger boards, but uncharacteristically I haven’t yet made one; I plan to write a full post on this game at some point (along with some other connect-key-cells games), so I will be sure to make a bigger board when that day comes.

Tamerlane Chess

Tamerlane-start-pos-01

Tamerlane Chess is a historic Chess variant from the 14th century; the game was allegedly invented by the Persian ruler Timur Lenk, but that may well be a myth.  Tamerlane is a large-board variant of Shatranj, the Persian form of Chess and direct ancestor to the Royal Game we know today.  This game takes the core of Shatranj and adds a bunch of unusual elements to the game, giving it a confusing and beguiling personality.

Why it’s great:  Tamerlane’s board immediately stands out — not only is it large and oblong, forming a 10×11 grid, but there are two extra squares sticking off the sides.  These squares are called citadels, and they serve a special purpose: if your King can reach the citadel on your opponent’s side of the board, you can secure a draw.  These little boltholes of safety are just one of the quirks of Tamerlane:

  • Several unusual pieces are added to the base Shatranj army, including two pieces that leap like the Knight but in different patterns (the Camel and the Giraffe)
  • The Pawns — shown above as tiny versions of the other pieces — promote differently depending on what column they start from, and the ‘Pawn of Pawns’ (on A3 and K8) can promote three times to become an extra King
  • The Pawn of Kings promotes to a Prince, which also must be mated to win the game, so each player may have up to three Kings on the board

The result of all this craziness is a remarkably exciting game, with varied tactics thanks to the diverse pieces and unusual endgame strategies resulting from the promotion rules and citadels.  Shatranj pieces are generally shorter-range than modern-day Chess pieces, and Tamerlane extends Shatranj with more leapers rather than long-range sliding pieces, so the feel is very different from Chess.  Tamerlane may be 600 years old, but it feels modern and creative.  I enjoy it a great deal, so I plan to do an article on this game once I finish writing about Courier Chess.

Trike and Tumbleweed

Unlike much of the rest of this list, these two games are extremely new — both Trike (designed by Alek Erickson) and Tumbleweed (designed by Mike Zapawa) were invented in 2020, and in fact are currently slugging it out to take the win in the yearly Best Combinatorial Game competition at BoardGameGeek.  Both are very modern designs — they have extremely minimal rules, and are built to do one thing and do it well.

Why they’re great:  Trike is an intriguing game in which players place pieces in their colour by moving a neutral pawn piece, then placing their stone underneath it.  As the board fills up, the pawn has less freedom of movement, until eventually it can’t go anywhere; at that point, the player with the most stones of their colour adjacent to the neutral pawn wins the game.  Trike is very tactically sharp and full of twists and turns, so despite its simplicity the play is complex and exciting.  This game reminds me somewhat of Tintas, a brilliant game of moving a neutral pawn to claim a majority of pieces of seven colours.  Trike has a quite different feel though and is inherently more flexible and scalable.

Tumbleweed is a game of territory based on a line-of-sight mechanic — on each turn you may place a stack of pieces of your colour in one cell on the board, with the height of that stack determined by the number of your pieces within unobstructed line-of-sight of that cell.  You may capture and remove an enemy stack in that cell if your stack would be larger, or you can reinforce your own stack in the same way.  At the end of the game, the player who holds the majority of the board wins.  Tumbleweed is gaining a lot of attention since its creation, because the simple line-of-sight stack placement idea immediately creates interesting tactical situations and strategic dilemmas.  Apparently the community of players is settling on hexhex-8 boards, but I prefer to play on the original hexhex-11 board.  Playing in real life is a bit challenging, mainly because you need a huge number of counters to potentially stack them six deep on numerous cells, but playing online or via Ai Ai is straightforward and very enjoyable.  My board above plays on the intersections rather than in the cells, which just intuitively makes more sense to me given the line-of-sight mechanic.

Volo

Volo is an innovative game of unification by Dieter Stein.  The game was inspired by the flocking of birds, as illustrated in the famous Boids paper by Craig Reynolds (read more about the game and its influences in this paper).  The Boids simulation was also seriously influential on me when I was young and first discovered the scientific field called Artificial Life, so I feel a certain kinship with this game.  Volo’s rules are fairly simple, but the mechanics are evocative of the theme: the board starts empty, and as you gradually place birds you will need to fly whole flocks of them around the board at once in an attempt to join them together into one giant flock.  Being able to move an entire line of pieces at once is fairly unusual in abstract games, so it feels quite satisfying.  The first player to create one unified flock including all their birds is the winner.

Why it’s great:  Volo is a creative game, and its inspiration comes through beautifully in its clever rules.  You will feel like you’re navigating your flocks through treacherous skies, trying to bring your birds together to safety.  Volo is also a fine example of the unification genre, which is surprisingly small; the most famous examples are probably Lines of Action, which is a brilliant game with an oddball movement mechanic, and Ayu, a compelling game playable on a Go board where every move is an approach move.  The unification genre is small but mighty, and Volo may just be my favourite of the lot; the ability to move lots of pieces in a single turn gives it a sense of freedom and allows for some highly creative moves.

About the boards:  The standard Volo board is a hexhex-7 board with corners and the center point removed.  In the spirit of experimentation I’ve been playing with larger boards, so you can see above I’ve constructed  hexhex-9 and hexhex-11 boards for more epic Volo games.  On all the Volo boards you place your birds on the intersections, rather than within the triangular spaces.

YvY

YvY is another forgotten connect-the-key-cells game from Christian Freeling, developed as a vision of a simplified Superstar, then refined into its final form in collaboration with David J Bush.  In YvY, players take turns placing one stone of their colour onto the oddly-shaped hexagonal grid, and attempt to occupy and join together the green ‘sprouts’ sticking off the side of the board.  At the end of the game, each player scores points equal to the number of sprouts they occupy, minus twice their total number of ‘live’ groups (live groups being those occupying at least one sprout).  So, as with Star and *Star, the scoring system forces you to try to connect your occupied sprouts with as few groups as possible.  Intriguingly, YvY also offers a ‘sudden-death’ victory condition: if either player forms a contiguous loop of stones of any size, they win immediately!

Why it’s great:  I’m a sucker for a connection game with multiple objectives, and YvY fits squarely into that category.  The need to connect groups across the board to score well gives the game a territorial feel, while the loop-formation win condition adds some tactical sharpness on top.  In play the game bears a certain resemblance to Havannah, and the need to score points via multiple connections encourages board-spanning play with great subtlety.  Christian views this game as obsolete, but I see it as another intriguing take on the connect-the-key-cells genre, alongside Star, *Star, Superstar, Starweb and Side Stitch.  For my money this category of games offers a lot of depth and intrigue, so I recommend trying several of them and seeing which one best fits your style of play.

About the boards: As per usual, I made a few different sizes of boards for this game, to allow potential players to choose a game length that suits them.  The YvY board is oddly shaped, with three of the sides being two hexes longer than the other three; as a consequence of this shape and the need to place sprouts evenly around the outside edges, the boards all have even-length sides.  As is typical with games like this, the larger boards produce longer games of greater strategic complexity; the size-12 board above has 330 interior cells and 33 sprouts for a total of 363 cells, almost exactly the same as a Go board’s 361 points.  The size-12 board is thus suited for intense strategic contests; the size-8 board is great for beginners and more casual games, while size-10 offers a nice balance between depth and brevity.  If you’re feeling particularly adventurous, have a go on the size-14 board, with a whopping 468 interior cells and 39 sprouts.

New boards for old favourites

Side Stitch

I’ve talked about Side Stitch before, of course, but in the last few months I’ve gone back and tidied up the boards I made previously, and added two new ones — the hexhex-11 with 15 colour-sides, and the 14×14 Hex board with 13 colour-sides.  Side Stitch is a favourite of mine not just for the actual game, which is great, but also the aesthetic — making boards for this game is really fun.

Why it’s great:  Side Stitch is a member of a class of connection games that I really enjoy — connective scoring games, where different types of connections have different values.  These games spice up the connection-game formula by allowing for a wide variety of winning connections, and the need to stretch across the board to connect key areas and score points gives them a dynamic flavour.  Side Stitch is even more dynamic than most, since players connect colours along the edges of the board which need not match up with the actual board’s sides, so there are a tonne of interesting board setups you can try.  I just wish Side Stitch was playable on more game servers, so that more people would get acquainted with this excellent game.

About the boards:  All of the boards above were based on designs originally uploaded to BoardGameGeek by the inventor of the game, Craig Duncan; I have simply replicated them in Illustrator and made them as clean and sharp as I can.  The ‘standard’ Side Stitch board is the hexhex-8 with 7 colour-sides (top middle in the above array).  The hexhex-7/9-colour board is great for quick games.  My personal favourites are the hexhex-10 with 9 colour-sides and the hexhex-11 with 15 colour-sides; note that I have two variants of the 11/15 board available, one with some repeated colours and another with all unique colours.  To my shame I have not tried the 14×14 Hex board version yet!

Star

Star is a classic game of connecting edge cells by Craige Schensted/Ea Ea, which I’ve covered before on this blog, so I won’t spend too long explaining it.  These boards are slight updates of previous ones that I have made, with slightly cleaned-up cell placement and updated fonts.

Why it’s great:  Star is an unfortunately overlooked game, I think partially because the published version in Games Magazine years ago was on a too-small board that didn’t adequately showcase its marvellous depths, and also because it was followed by *Star, which seemed to overshadow it.  I think Star deserves more recognition than it gets, as it an accessible game only slightly more complex than something like Hex or Y, but the introduction of scoring and a group penalty takes it into a more territorial, strategic realm.  On larger boards like those you see above, Star becomes a deeply challenging contest, and often a game will see much of the board filled with complex, winding connections.  I highly recommend it both on its own merits as a beautiful game, and as a first foray into the connect-the-key-cells genre.

About the boards:  My boards adopt the standard uneven hexagonal grid used by the original game, and simply extend that to larger sizes.  I should note that the designer felt the corner cells, which on these boards would be worth three points due to being adjacent to three exterior edge cells, should be adjusted to only score two points; I don’t have particularly strong feelings about this, but in the future I do intend to make versions of these boards with corners altered in that way.  Of course you can use these boards and simply adjust the scores accordingly when you play, but certainly having the scores clearly visible from the board geometry would be better.  The largest board above, Star-12, contains 363 cells, similar to the Go board’s 361 points.  Given that Star games often use most of the board, Star-12 is probably the largest size most players would be willing to use, and above that size the game is perhaps a bit too much of a marathon.

Poly-Y

Poly-Y is the ancestor to Star and *Star, and marks the first attempt by designer Craig Schensted/Ea Ea to impart a connection game with a bit of territorial flavour.  In Poly-Y, players strive to control more corners of the board than their opponent; in order to claim a corner, a player must form a Y-shaped connection, connecting the two sides adjacent to the corner with another non-adjacent side.

Why it’s great: Poly-Y takes the connection goal of the Game of Y and adds a territorial element, using that connection as a way to claim parts of the board and score points.  The addition of the point-scoring element gives the game an appealing strategic flavour, while adding minimal rules complexity.  The importance of corners in this game means that oddly-shaped boards with larger numbers of corners are particularly well-suited for Poly-Y play, which adds a certain quirky visual appeal.  If you want the depth of something like Star or *Star with simpler score calculations, Poly-Y is a great option.

About the boards: Out of the three boards presented above, only the middle one is for playing stones within the cells; on the other two, you should place your stones on the intersections.  Making these boards was a bit of a challenge due to the odd geometry, but the final result is quite visually pleasing.  All three boards are nine-sided, which seems to be the most-recommended shape by the designer, so they will play similarly; just pick the one that most suits your aesthetics.

Game of Y (Kadon-shaped)

Y-17-Kadon-01

As I mentioned in the Game of Y/Poly-Y/Star/*Star article, the published version of the Game of Y uses a board of 91 points with a distorted triangular shape, designed to balance out the in-game value of the centre, edge and corner points.  However, the board published by Kadon is simply too small, meaning that every opening move by the first player should be swapped.  A better option is to use the same board geometry but substantially larger, and that is what I have attempted with this board.

Why it’s great:  Y is the most elemental connection game, even more fundamental than Hex — in Hex the two players have asymmetric goals, and are attempting to connect different sides of the board, while in Y both players have precisely the same goal.  The need to connect all three sides of the triangular board can produce some interesting tactics, and it has a bit of a different flavour from Hex as a result.  For people new to connection games, or to abstract strategy games in general, Y is right up there with Hex as an instantly accessible gateway to the genre.

About the board:  The board above is 17 points long on each side, meaning that games will be substantially longer and more balanced than on the 91-cell Kadon board.  Besides being visually appealing, this board geometry helps balance the values of board cells.  The downside is that I haven’t yet found a straightforward way to extend this board in Illustrator without reconstructing large portions of it, so for now this is the only large board of this type that I’ve made.

So, that was a whirlwind tour of some of the games I made boards for over the past 12 months or so.  Over the coming months I’ll try to cover a few of these gems in more detail, but at least for now I hope this will give you some ideas if you’re looking to try out a new game.

Next up: more Courier Chess!

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Courier Chess, Part I: It’s like Chess, but Wider

As some of you may know, I’m a big fan of the large-board variants of Shogi, Japanese Chess.  These enormous games extend Shogi out from its normal 9×9 board with 20 pieces per player, up to Chu Shogi (12×12 with 46 pieces per player) and Dai Shogi (15×15 and 65 pieces per player), then through progressively more enormous boards and armies, all the way out to the ludicrous Taikyoku Shogi (36×36 with 402 pieces per player).  Not all of these games are particularly practical to play, at least not regularly, but the best among them use these large playing surfaces and diverse armies to create gargantuan strategic battles stay thrilling even over the course of hundreds of moves.

Large-Board Chess in History

Of course, Western Chess has a long history of variants.  A number of larger Chess games have been developed over the centuries as well, right from the earliest days of the game.  Shatranj, the ancient Arabic ancestor to Chess, was extended to the 10×10 board back in the 9th century to create Shatranj al-Tamma, or Complete Chess.  Inspired by Shatranj al-Tamma, Turkish Chess fanatics developed a family of enlarged ‘Turkish Great Chess‘ variants, ranging in size from 10×10 boards to 14×14.  Some other variants of Shatranj went off in some remarkably creative directions, such as Tamerlane Chess, where additional citadel squares hang off the 10×11 board and numerous new piece types appear.

At the time these games were invented, the pieces used in Chess were slower than today, with only the Rooks able to move unlimited distances.  That meant that on these larger boards the play tended to be rather slow, and while some may have appreciated the deliberate, strategic flavour this provides, some of these large-board games felt fairly ponderous.  Tamerlane was an exception, however; the piece density on the board was high and the board was shorter vertically as well, meaning that the opposing armies took less time to get into conflict.  The wide variety of pieces in Tamerlane also diversified play and provided some new tactical wrinkles compared to the smaller game.  Atranj and Indian Great Chess are also quite playable, largely because they include some powerful compound pieces (Bishop + Knight, Rook + Knight, Knight + Queen) that can range across the board very quickly and considerably speed up play.

Unfortunately, these more successful large variants still never quite established a significant foothold in the Chess-playing world, and most of these games have since disappeared and are now merely historical curiosities.  Tamerlane is still known to a degree, due to its unique character, but the others are long gone.  Generally speaking, historical large Chess variants came and went fairly quickly; clearly many players desired a larger game given the sheer number of attempts, but few games managed to maintain a following for very long.  Given that even the 10×10 variants had trouble finding players, none of the historical large Chess games were nearly as adventurous as the large Shogis, in terms of size, piece count or rules variation.  I suspect if these enlarged games had taken hold, we may well have seen Chess-based equivalents of the gargantuan Shogis.

Courier Chess

However, there is one large-board Chess variant that did have longevity — Courier Chess.   Courier Chess is believed to have originated around the 12th century, with its first known appearance being a tale written by Wirnt von Gravenburg in 1204 called the Wigalois.  Courier Chess is mentioned regularly in subsequent centuries, mostly in medieval German poetry, but its most famous appearance is in the painting The Chess Players by the Dutch master Lucas van Leyden in 1510:

Lucas_van_Leyden_-_The_Game_of_Chess_-_WGA12919

The gentleman on the left looks a bit chagrined, and he has every right to be — analysing the board position shows that the woman on the right will achieve checkmate in three moves!

Courier Chess -- painting game

As we can see in the painting, Courier Chess is immediately remarkable for its elongated board; the playing area is 12×8 (96 squares).  In order to fill in the 12 ranks in each player’s camp, some additional pieces are added to the lineup as well.  The Courier starting position looks like this:

Courier-Chess-start-pos-alt-01

The starting array for medieval Courier Chess.

Moving along the first rank from left to right, this is the piece lineup: Rook; Knight; Elephant; Courier (Bishop); Sage; King; Queen (Ferz); Fool; then we have the Courier, Elephant, Knight and Rook again.  In keeping with Chess convention, the second rank is filled with Pawns to protect our valuable pieces.

While there are clearly some pieces here that aren’t in the standard medieval Chess lineup, what is most remarkable about the Courier Chess piece assortment is that this game marks the first recorded appearance of the modern Bishop.  This piece actually gives the game its name — what we would call the Bishop is called the Courier here.  At the time, most Chess players would have been playing some medieval variant of Shatranj where Rooks were the only long-range pieces, so having these Couriers slicing diagonally all over this extended board must have been a thrilling change from the standard game.  Confusingly, what I have portrayed here as Elephants were actually called Bishops in the original Courier Chess, but given their moves match the Elephant of Shatranj, I am using that piece instead to prevent any mix-ups with the Courier.

In Courier Chess the most powerful pieces on the board are the long-range Rooks and Bishops, followed by the always-tricky Knight.  From there we have an array of short-range pieces of varying abilities.  This diagram shows the moves of every available piece type — yellow circles indicate a stepping move; red circles indicate spaces where a piece can only capture; solid arrows indicate a sliding move over any number of squares in that direction; and dashed arrows represent leaps directly to the square indicated:

Courier-Chess-moves-01

The pieces in Courier Chess generally follow the conventions of medieval Chess in place at the time:

  • The Pawn moves one square forward only, or may capture an enemy piece diagonally forward to the left or right.  Unlike modern Chess, Pawns only ever move one square — there is no initial double-move available, and therefore there is also no en passant capture rule.  When Pawns reach the opponent’s back rank, they promote to Queen (Ferz).
  • The Sage moves one step to any adjacent square, just like the King, but it’s just a normal piece — no worries about check or checkmate.
  • The Fool moves one step horizontally or vertically only; this move derives from the Shatranj piece called a wazir.
  • The Queen is far, far weaker than the ‘Mad Queen’ we are accustomed to in modern Chess — it moves only one square diagonally.  This move derives from a Shatranj piece called the ferz.
  • The Elephant (which again would have been called the Bishop in the original game) moves as an alfil in Shatranj, a diagonal leap of two squares, jumping over any pieces on the square in between.  The Elephant is thus colourbound — it will only ever be able to visit squares of the same colour it starts on.
  • The Knight moves just like in modern Chess — a leap of one square horizontally or vertically, followed by one square diagonally, jumping over any intervening pieces.
  • The Rook moves as in modern Chess as well, sliding any number of squares vertically or horizontally.  Note that there is no castling in Courier Chess.
  • The Courier moves as the modern Bishop, sliding any number of squares diagonally.  Like the Elephant, it is also colourbound, forever stuck on either the light squares or dark squares.

As in modern Chess, the goal is to checkmate the opposing King.  However, we do not know the precise rule for stalemate, where the King is not in check but has no legal moves; given the conventions of Shatranj and medieval Chess we might expect that stalemate in Courier is a loss for the opposing player, rather than a draw as in modern Chess.

Intriguingly, before starting the game both players would traditionally mvoe the A, G and L Pawns forward two squares, then move the Queen up just behind her Pawn.  These special Pawn moves were called ‘joy leaps’ and were not available during the rest of the game; these may well be the first known examples of a double Pawn move in Chess.  Presumably these initial moves were done so as to open up the position from the start and encourage the players to develop their slower-moving pieces.  So, before starting the game proper, the Courier board would look like this:

Courier-Chess-start-pos-medieval-01

Remarkably for a medieval Chess variant on a large board with many slower pieces, in actual play Courier is quite a lively game.  The pre-advanced Pawns mean the Rooks can be developed quickly, despite the lack of castling, and the forward Queen allows some cover for further Pawn advances to attack the centre.  The Knights and Elephants can leap into the action right away, while the Sage and Fool mostly hang back to protect the King from all these spiky Couriers swirling around the board.  A typical game of Courier will generally take longer than a game of Chess, but not as long as you might think; most of my games against the computer last about 60-70 moves per player, as opposed to around 40 for modern Chess.  However, two strong players of near-equal ability could easily end up locking horns for far longer.

Thanks to Courier’s interesting board shape, varied yet easy-to-remember set of pieces, and enjoyable play, the game was able to last for about 600 years in the parts of Germany where it was most popular.  The game did start to die off in the 19th century, however.  At that time, standard Chess had matured essentially into the form we know today, and the fast-paced action and compact game length of the 8×8 Royal Game certainly worked to its advantage.

Courier-Spiel

Despite the increasing dominance of standard Chess, some dedicated fans did want Courier to make a comeback.  In 1821, H.G. Albers of Lüneburg proposed an updated version of Courier Chess, which he dubbed Courier-Spiel (The Courier Game).  Albers cleverly updated the pieces and rules of the game to increase the pace and tactical richness, making it more competitive with standard Chess.

Courier-Spiel updates the classic Courier experience with some more modern rules and more powerful pieces:

Courier-Spiel-start-pos-01

Starting again from the bottom-left corner and moving to the right, this is our new starting lineup: Rook; Knight; Elephant; Bishop; Councillor; King; Queen; Sage; then completing the set with Bishop, Elephant, Knight and Rook once again.  Courier-Spiel thus has some new pieces and some changes to the old ones:

Courier-Spiel-moves-01

The moves of the pieces in Courier-Spiel.

  • Pawns move as in modern Chess — one square forward and capturing on the forward diagonal squares, but they may also take an initial two-step move from their starting square only.  En passant capture is now possible.  Pawns that reach the opponent’s back rank promote in an unusual way — they must sit on the back rank for another two moves, and then finally promote on the third move to any piece from the Pawn’s army that has been previously captured.  If no pieces have been captured from their army yet, then promotion is impossible, and the Pawn must sit on the back rank until a captured piece is available.  We are not entirely sure whether these Pawns are vulnerable while waiting for promotion, but modern players seem to have settled on making them immune to capture until promotion occurs.
  • The Sage moves the same as in Courier Chess — one step to any adjacent square.  The Sage is now next to the Queen rather than the King.
  • The Fool has had a significant upgrade, and now moves like a combination of the King and Knight.  This powerful new piece sits next to the King where the Sage used to be.
  • The Queen is no longer a ferz, but instead functions exactly like a modern powerhouse Chess Queen — moving any number of squares vertically, horizontally or diagonally.
  • The Elephant is stronger too, and now moves as a combination of alfil and ferz — it may move one step diagonally, or leap two squares diagonally.  They are still colourbound like the Elephants in Courier.
  • The King, Knights and Rooks move the same as in Courier Chess.
  • Rules-wise, of course the goal of the game as usual is to checkmate the enemy King.  I have not seen a definitive statement of the stalemate rule, but as far as I am aware modern players have stalemate as a draw in this game.  Courier-Spiel does not use the initial ‘joy leaps’ of the Pawns and Queen that were customary in Courier Chess.

Along with the modernised Pawns, players may now castle in Courier-Spiel.  As in modern Chess, in order to castle the path between the King and the Rook must be clear of any other pieces, and neither piece must have already moved.   Castling may not be done if either the King or the Rook is under attack by an opposing piece, or if any of the intervening squares are under attack.  To castle, the King will move to the C file (if castling with the A-file Rook) or the J file (if castling with the L-file Rook), then the Rook leaps over to the space adjacent to the King on the opposite side:

Courier-Spiel-castling-01

Castling example.

Taking all these adjustments together, Albers did a good job updating Courier for a more modern era.  The increased power of the Elephants, Sage, Fool and particularly the Queen significantly increase the pace of the game.  Tactical exchanges are more frequent than in the original as well.  The addition of castling prevents too many early wins by allowing the King a quick path to safety.  The removal of the initial ‘joy leaps’ of the A, G and L Pawns also allows the King further protection, and avoids a prematurely-developed Queen.  Cleverly, the newfound single-square diagonal move of the Elephant also serves to protect the B and K Pawns, which previously were unprotected and thus vulnerable to early attack in Courier.  Finally, the increased powers of the Sage and Fool provide some strong checkmating powers in the late game, and are also strong defensively, preventing the deadly Queen from completely dominating play.

The glaring flaw in Courier-Spiel is of course the promotion rule, which adds some serious rules complications while also significantly slowing down the process of Pawn promotion.  This leads to some weird pacing in the endgame, where the typical race to promote Pawns becomes a strange, cagey stand-off instead.

However, there is historical precedent here that likely encouraged Albers to adopt this strange promotion method.  In the version of Courier played in Ströbeck, Germany’s famous ‘Chess Village’, the Pawns must go through an odd ritual in order to promote.  Upon reaching the opponent’s back rank, the Pawn would have to make a series of three double-step jumps backward, each one taken on a separate turn (the Pawn’s controlling player did not have to do these jumps immediately or consecutively, but could do them whenever the board situation was convenient).  Pawns making these leaps cannot capture this way, but they can be captured.  After the third backward leap, the Pawn would have returned to its starting square and could then promote immediately into another piece (any piece, not just the Queen).

Given this odd promotion rule was in use in the past, perhaps Albers adopted a version of it to avoid altering the feel of the Courier Chess endgame beyond what Courier fans may have been willing to tolerate?  In any case, I suspect most modern players would prefer to replace these three-turn promotion rules with the simpler method of the original Courier Chess, and just allow Pawns to promote immediately upon reaching the enemy’s back rank.

Playing Courier Chess and Courier-Spiel

While neither of these variants are played widely today, thanks to the internet and powerful Chess-playing engines we need not be short of opponents.  Perhaps the most promising way to find human opponents would be to sign up for an account at the Chess Variant Pages, and then use their Game Courier (how appropriate) Play-By-Email system to invite someone to a game.  Courier Chess has a setup available on Game Courier, and a fair few games have been played, so probably someone will take you up on the offer.  Courier-Spiel has some fans as well.

Alternatively, if you would prefer to play against an opponent that is ready for a game 24 hours a day, you can download WinBoard and play Courier Chess against the FairyMax computer engine.  This is quite an enjoyable way to get to know the game, and FairyMax is a decent opponent.  WinBoard does not appear to have a Courier-Spiel setup available by default, but it is possible to define your own variants.  Winboard supports variants all the way up to Tai Shogi and its 25×25 boards, so feel free to experiment with your own wild expansions of Courier Chess.

If you are looking for a real challenge, download the Fairy-Stockfish engine, which also supports Courier (and you can define Courier-Spiel very easily, check the file ‘variants.ini’ under the ‘src’ folder in the GitHub repository at the link).  Fairy-Stockfish is based on Stockfish, one of the strongest Chess engines on the planet, so it is an absolutely brutal opponent!  Conveniently, Fairy-Stockfish also supports a tonne of other good Chess variants, although due to engine limitations it cannot play any game with a board larger than 12×10 (although this may change further down the line).

For playing Courier Chess on the go, you can grab the Chess Remix app for your Android phone or tablet.  This great little app contains over 100 Chess variants, including many of the major regional and historical ones.  Alongside Courier, Tamerlane Chess, Chu Shog and Dai Shogi are in there, too.  The piece graphics are little pixel-art representations of the moves of each piece, which is probably helpful for some but I personally am not a huge fan of that approach.  As a Shogi purist who loves Japanese calligraphy, playing the Shogi family without the kanji characters feels particularly wrong and gross, but I do enjoy having the ability to play all of these games on the go.  Chess Remix, true to its name, also lets you create your own variants or modify the included ones in all sorts of different ways, so it is a must-have if you enjoy mucking around with Chess.

Screenshot_20210207-113848

Playing Courier Chess against the AI in Chess Remix.

Over-the-board Courier play is a bit more challenging to arrange due to the lack of any 12×8 boards on the market, although some chessboard specialists may be able to make one to order.   There are some occasional reproductions available based on the Courier Chess set depicted in van Leyden’s painting, but these are handmade and the pieces are brass, so they are quite expensive!  A better option may be to buy a couple of inexpensive vinyl or neoprene chess boards, slice one in half and attach it to the other.  For pieces, a couple of regular Chess sets plus some variant pieces would be sufficient.

However, if you are willing to be a bit patient, the Chess Club of Ströbeck is planning to produce a run of Courier Chess boards and pieces sometime in 2021.  The boards will be handmade, and without a doubt these sets will be a fine collector’s item as well as being great for play.

Next moves

The second part of this series will go through a couple of sample games, one Courier Chess and one Courier-Spiel game.   These will provide some insight into how these games feel in action.  After that we will look at two present-day takes on Courier Chess: Modern Courier Chess, and Reformed Courier-Spiel.

In the meantime, please give Courier Chess and Courier-Spiel a try — in my opinion they are easily among the most interesting historical Chess variants, offering a unique feel and entertaining strategic dilemmas.  Courier’s distinct medieval feel and pacing is surprisingly absorbing, and while the modernised takes on it are probably more polished games, I still find myself returning more often to the 800-year-old original.  Certainly Courier will not appeal to everyone, but I feel every Chess fanatic owes it to themselves to experience this unique offshoot of the medieval game.

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Understanding Buddhism, Part I: The Diversity of Buddhist Practice

As I wrote in my critique of Todd May’s Death there are some misconceptions about Buddhism and its philosophy and practices that are widespread in Western sources.  Much of this is probably due to the works on Buddhism produced by Western scholars in the late 19th/early 20th centuries, which viewed Buddhism through a colonialist lens, with everything they perceived being positioned against a Judeo-Christian conception of reality.  These sources often viewed Buddhism as a nihilistic faith, a perception that would have been proven false had they engaged more deeply with Buddhist literature.  

Today, misconceptions of Buddhism have taken some additional forms, often inspired by a modern view of Buddhism as a ‘philosophy’ more than a religion.  There is a tendency to view Buddhists as largely secular, rational thinkers — introspective scientists probing the depths of the human mind.  Figures like the Dalai Lama present to us as benign, kindly monks promoting generally-acceptable ideas like the power of compassion, and they explicitly support other types of spirituality rather than positioning Buddhism as the One True Path.  As a consequence we believe that Buddhism sits comfortably within our Western materialist tradition, and some even go so far as to propose that core Buddhist concepts like rebirth and karma are metaphors rather than actual beliefs.  This way of thinking has led to the rise of Secular Buddhism, spearheaded by writers like Stephen Batchelor. 

Adding to the confusion, millions of people now practice Mindfulness-Based Stress Reduction — essentially Buddhist meditation stripped of all of its wider context; this further colours our perceptions, leading some to confuse these reduced practices with the whole of Buddhism.  In positioning Buddhism in this way we implicitly deny many centuries of Buddhist scholarship, the importance of esoteric practices and mysticism in Buddhism, and the deeply-rooted cultural influences that give each regional expression of the Buddha’s teachings their own vibrant traditions.

As another outgrowth of my own studies of Buddhist history, philosophy and practice, I decided to start putting together a summary of some common misconceptions about Buddhism found frequently in popular culture and Western scholarship.  I hope this may be useful for some of you out there who are interested in Buddhist traditions and practices, but mainly it will serve as a living reference document for myself, as my own understanding of Buddhism continues to evolve and deepen over time (hopefully).

Before I get started, a note about style.  When speaking of concepts drawn from the teachings of the Buddha as recorded in the Sutta Tipitaka, I will use terminology from the Pali language in which the suttas (sutras) were written.  When speaking of Mahayana and Vajrayana traditions, I will use terminology derived from Sanskrit, as these terms are more commonly used in these contexts.  This is primarily for my own convenience, so that on later readings and edits I can quickly identify what sources are being discussed in any given passage.

One more note about books on the Dharma (the teachings of the Buddha), since I recommend a number of these below.  Traditionally any book containing the Buddha’s words or any Buddhist teachings should be treated with particular respect.  Such books should not be placed on the floor or stepped over, have other books or objects placed on top of them, and they should be kept on high shelves and preferably away from non-Dharma books.  When reading them, you should only do so while sitting upright or standing.  Whether you do all this or not is up to you, there are no Dharma Police to arrest you and there are no gods in Buddhism around to punish you, but just bear this in mind in case you have visits from serious Buddhists someday, who may notice this kind of thing.

Before getting to the misconceptions themselves, in this first article I’ll quickly summarise the major Buddhist traditions and their differences.  I will provide much more specific details here than in my previous introductory article on Buddhist thought and meditation.  In the second part of this series, we’ll build on these foundations and explore some common misconceptions about Buddhism.

Just to lay out my position up front: throughout these articles, I will make an argument that capital-B Buddhism is built on a foundation of an incredibly comprehensive, internally-consistent philosophy, and that anything we call ‘Buddhism’ must include, at a minimum, a coherent subset of that philosophy.  The Buddha himself urged his followers not to be fanatics, and to test all his statements using their own critical faculties; so in that respect, there is nothing wrong with being a Secular Buddhist, or with being a Christian who practices mindfulness meditation, or whatever else.  Problems do arise when we claim that these patchwork Buddhist practices *are* capital-B Buddhism, or that our own interpretation of Buddhist thought is the correct one, and that we have some special insight into the Buddha’s teachings that 2,500 years of Buddhist scholarship somehow missed.  Ultimately I feel we need to re-examine how Buddhism is taught in the West; have more respect for the Buddhist scholars who precede us; and make more efforts to learn how Buddhism is actually practiced by the cultures in which it thrives, rather than simply presenting it as an abstract philosophical framework.

The Buddhist Path to Liberation

Many of us, Buddhist or not, are familiar with His Holiness the Dalai Lama.  The Dalai Lama is an incredibly charismatic person, and has single-handedly made the world aware of the fraught political situation in Tibet and has helped spread Tibetan Buddhism across the world.  His influence is so pervasive that many non-Buddhists perceive him as a sort of Buddhist Pope.

In reality, of course, there is no Buddhist Pope.  Buddhism takes many different forms in the numerous countries where it is practiced, and the Dalai Lama is connected only to Tibetan Buddhism.  Within the Tibetan context, the Dalai Lama comes from the Gelug tradition, which historically has been the most powerful and influential of the Tibetan Buddhist schools, but there are several other schools that have existed for just as long (or longer) and which have significant differences in how they practice compared to the Gelugpas.  

Before we dig deep into the complexities of Buddhist thought, we should start by clarifying what types of Buddhism exist, and develop some basic concepts of how each of these traditions view the teachings of the Buddha and the nature of existence.  In this way we can better appreciate the incredible diversity of Buddhist life in different traditions, and better understand how evolutionary steps in Buddhist doctrine have lead to very different approaches to practice.  Buddhism is traditionally divided into three ‘vehicles’, each of which builds on the foundation of the previous and extends it with new philosophical concepts and practices; below I will describe each of these vehicles in turn.

chaing-mai-buddha

A huge statue of the Buddha in Chiang Mai, Thailand.

Early Buddhism (previously called ‘Hinayana’):

The first ‘vehicle’ in Buddhism is Early Buddhism, formerly known as Hinayana (‘the Lesser Vehicle’), which follows the original teachings of the Buddha as laid out in the very extensive suttas (sutras, or discourses) given by the Buddha during his lifetime, and subsequently recorded in the Tipitaka, which were written in the ancient Pali language.  These suttas focus primarily on the Buddha’s fundamental realisations about the nature of suffering, which he codified in the Four Noble Truths, and his prescription for ending suffering, The Noble Eightfold Path.  The early Buddhist practitioner seeks to become an arahant, an enlightened being who perceives the true nature of existence, is free of the ignorance that leads to suffering, and will reach nibbana (nirvana) and thus ultimate freedom from suffering at the end of their life.

Core philosophical concepts:

The Buddha’s original teachings gave us the Four Noble Truths, the Buddha’s explanation of the nature of human suffering, and the Noble Eightfold Path, his prescription for ending that suffering and achieving nibbana (nirvana).  The Four Noble Truths can be expressed as follows:

  1. Suffering (dukkha) is an innate characteristic of existence in samsara.
  2. Suffering is due to attachment and desire — the desire for pleasure; the desire for existence; and the desire for non-existence.
  3. Suffering can be ended, by ending this attachment and desire.
  4. The way to end suffering is to practice the Noble Eightfold Path.

So, dukkha arises due to our desire for identity and constancy in a world that is constantly changing, and this desire and attachment causes us to perpetuate this suffering, in the form of continued existence in samsara — the endless cycle of life, death and rebirth that all sentient beings experience.  Samsara leads to endless suffering, as each rebirth is doomed to eventually age, decline, and die, only to start all over again.  By cutting off this desire and attachment, and by curing our ignorance of the nature of reality, we can end this suffering and free ourselves from cyclic existence.

The nature of each rebirth is determined by our kamma (karma), which is the only aspect of each life that persists to the next; in Buddhism each rebirth is a separate being and consciousness from the preceding one, as there is no soul or essence that transfers over (as would be the case in Hindu reincarnation, for example).  Kamma is understood as a cause-and-effect process; bad actions lead to suffering, good actions lead to a reduction of suffering.  Kamma is not a divine judgment on our behaviour imposed from outside, but instead exists in the outcomes generated by our actions that affect the world around us.  The only beings that may change our kamma are ourselves, by understanding the action of kamma and following the Noble Eightfold Path.

The Noble Eightfold Path provides the eight means by which we end craving and attachment:

  1. Right View — we must understand the functioning of kamma and the nature of dukkha (the Four Noble Truths), and avoid holding views of existence which enable attachment and craving.
  2. Right Intention — we must cultivate an intention of renunciation (abandoning craving), an intention of good will (metta, loving-kindness), and an intention of harmlessness (a compassionate wish that all beings be free of suffering).
  3. Right Speech — we must not lie, speak unkindly, or use our words to cause discord and suffering.
  4. Right Action — we must not kill or injure others, steal anything which is not ours, or engage in sexual misconduct (abuse, adultery, assault, etc.).
  5. Right Livelihood — we must earn our living legally, peacefully, without coercion or violence, and without trickery and deceit.  Our livelihood must not cause suffering for others.
  6. Right Effort — we must abandon our existing unwholesome mental states, and prevent the arising of other unwholesome mental states.  We must maintain and perfect our wholesome mental states, and generate wholesome mental states that have not yet arisen.
  7. Right Mindfulness — we must cultivate serenity and insight in the mind through the contemplation of the four foundations of mindfulness: the body; feelings; states of mind; and phenomena.
  8. Right Concentration — we must cultivate single-pointed mental concentration, progressing through four successive stages of increasing meditative absorption called the jhanas.

Note that the Noble Eightfold Path contains three elements focussed on meditational practice — Right Effort, Mindfulness, and Concentration — but the rest of the path consists of actions we must take in everyday life and in our relationships with other people.  So the image occasionally presented of the Buddhist as a detached, cold, robotic meditator is not accurate; Buddhists must cultivate positive actions and qualities in all aspects of life, as well as within their minds.  Part of the path is to demonstrate good will and compassion for others, as well as refining our internal mental states.  The Noble Eightfold Path must be practiced in its entirety if one wants to achieve liberation.

The truth of suffering in Early Buddhism leads us to the three marks of existence: dukkha (suffering), anicca (impermanence), and anatta (not-self).  Dukkha is the concept that all existence leads to suffering, due to our fundamental ignorance of the nature of reality and our grasping for solidity and changelessness in a world forever in flux.  Anicca is the concept that everything is impermanent and subject to decay and dissolution; on a human level we experience this as the reality of mortality, that all of us are born, will age and decline, and eventually die.  Anicca extends this to all things, including our own thoughts, which continually arise and disappear again from moment to moment.  Finally, anatta denies the existence of a permanent self.  This means not only that humans, and all sentient beings, do not have a permanent, changeless essence like a soul, but also that our perception of self is fundamentally illusory.  We perceive single unified selves, but in fact each of us is a constantly-changing bundle of perceptions interacting with the world, and on a fundamental level all phenomena are dependently arisen — they are the consequences of the interactions of various causes and conditions, rather than singular entities with an independent, absolute existence.

In modern times some Western scholars choose to believe that the Buddha talked about rebirth symbolically, but this is definitely not the case.  The suttas are nothing if not scrupulously clear, and whenever rebirth is mentioned it is described carefully and precisely, often with the phrase ‘after death and upon the break-up of the body, [thing happens]’.  Rebirth is very explicitly discussed throughout the suttas as a real process.  Some have argued that the Buddha included rebirth in the suttas simply because that was the default position in India at the time; this is also incorrect, and part of the reason rebirth is described so carefully and extensively in the suttas is that the Buddha’s position was novel and controversial.  Kamma likewise is often misinterpreted as a system of supernatural reward and punishment, but in the suttas it is simply portrayed as cause and effect, a spiritual equivalent to gravity or electromagnetism.  Kamma is determined only by our own actions and is not imposed by outside agencies or deities.   

In the early days of Buddhism, there were 18 schools of Buddhism with varying interpretations of the suttas.  Today only the Theravada tradition remains.  Theravada is widely practised in Thailand, Sri Lanka, Burma, Cambodia, and in the West.  Mahayanists used to refer to Early Buddhism as Hinayana, which literally translates as ‘the Lesser Vehicle’, but today this term is considered derogatory because all three Buddhist ‘vehicles’ are capable of achieving enlightenment for their practitioners, and therefore none can really be characterised as inferior.  I will use the term ‘Early Buddhism’ to refer to the general category of traditions focussing purely on the Pali Canon, and ‘Theravada’ to refer to Early Buddhism how it is actually practiced today.  According to various sources, about one third of all Buddhists in the world today are Theravadins.

Within the Theravada tradition, there is a fairly widespread belief that achieving enlightenment is almost impossible unless one chooses to become a monk or nun.  As a result, in countries dominated by Theravada traditions like Thailand, lay practitioners are extremely reverent of the monastic community, and go to great efforts to pay them respect and help out with donations and so forth.  Many lay Theravada Buddhists focus on cultivating good karma so that they may be reborn as someone who is in a position to become ordained, and thereafter can focus on achieving enlightenment.

However, in the suttas there are prominent lay practitioners who are portrayed as arahants, or at least on the path to arahantship, which suggests that enlightenment is very much still achievable for laypeople with families, homes and jobs.  Naturally, becoming a monk and devoting onself to constant, unceasing practice of the Dharma makes achieving enlightenment much easier, but the suttas do suggest that laypeople can become enlightened as well.  This is also very much the case in the Mahayana sutras and the tantras; the Mahayana sutras feature numerous laypeople who are portrayed as just as wise as enlightened monks, and the history of Buddhist tantra is littered with lay yogis who are revered as enlightened beings.

Recommended Reading: 

In the Buddha’s Words, by Bhikku Bodhi: a complete, detailed and readable introduction to the core of the Buddha’s teachings in the Pali Suttas.  Perhaps the best introduction to the Pali Canon available today.

The Pali Canon, by the Buddha: the Pali Canon, or Tipitaka, includes three parts:

  • Vinaya, a collection of teachings outlining the conditions under which monks and nuns should live.  The Vinaya justifies each rule of conduct in detail, and in essence aims to be a comprehensive document illustrating how a spiritual community should function. 
  • Sutta Pitaka, a huge collection of discourses delivered by the Buddha during his 45 years of teaching.  These are subdivided into various collections called nikayas.  Together they form an extremely clear and internally consistent statement of the core of Buddhist philosophy, and taken as a whole the suttas provide a complete path for liberation from cyclic existence.
  • Abhidhammaa collection of seven books that systematise the principles outlined in the suttas into a staggeringly complex and ambitious framework for analysing all conscious experience.  Reading commentary on these is absolutely essential in order to develop a useful understanding of the dense theories contained here.

All of these texts are freely available to read on Access to Insight or Sutta Central, or in hardcopy form in the series of fantastic hardcover volumes from Wisdom Publications.

Mindfulness in Plain English, by Ven. Henepola Gunaratana: the best guide to insight meditation (vipassana) practised in the Theravada tradition, but equally usable and applicable in all traditions.  The author’s related books on samatha, or single-pointed concentration (Beyond Mindfulness in Plain English), and metta, or loving-kindness meditation (Loving-Kindness in Plain English: The Practice of Metta) are equally excellent, and owning these three books will give you a very comprehensive and practical guide to some of the most important meditation practices in Buddhism.

Teachings of the Thai Forest Sangha:  The Thai Forest tradition is quite popular in the West, and at the link you will find a huge collection of free ebooks with teachings from a number of monks in that tradition.  Ajahn Chah is particularly popular, but there’s tonnes of good stuff in there.  I recommend checking out some of these books to get a sense of modern Theravada practice.

Teachings of Thanissaro Bhikku:  Another treasure-trove of Theravada books and essays, including complete translations of the Vinaya and the Sutta Pitaka.  Thanissaro Bhikku is a very good communicator, so again I highly recommend these for some very readable explanations of Theravada philosophy and practice.

For more on Early Buddhist history, check the Buddhology section of the library at A Handful of Leaves, which includes a huge number of free downloadable books.

Tofukuji-Sanmon-M9589

Tofuku-ji, one of the five great Zen temples in Kyoto, Japan.

Mahayana Buddhism:  

Mahayana, like Early Buddhism, evolved in India and is believed to have first arisen around the 1st century CE.  The Mahayana traditions accept the entirely of the Early Buddhist teachings, but add to these numerous additional teachings in the form of the Mahayana Sutras.  The name ‘Mahayana’ means ‘Greater Vehicle’ in Sanskrit, and refers to the fact that Mahayana traditions go beyond seeking purely individual liberation and becoming an arahant.  Instead the Mahayanist strives to become a bodhisattva, a fully-enlightened being that remains in the suffering of cyclic existence (samsara) to help others, until all sentient beings are likewise liberated.  This altruistic motivation was seen by adherents as being of higher aspiration and quality than the individual liberation promoted in Early Buddhism, hence the name Mahayana (and the subsequent disparagement of Early Buddhism through the ‘Hinayana’ label).  In modern times most Mahayanists avoid such statements, and view Early Buddhism/Theravada as a valid path to liberation, and acknowledge the Pali Canon as being central to all Buddhist traditions.

Core philosophical concepts:

The Mahayana sutras build upon the foundations laid by the Tipitaka and incorporate some additional concepts that end up substantially evolving the Buddhist view of reality and mental factors.  However, the Mahayana traditions include a wide range of views, so here I will only outline a couple of critical concepts, and leave some of the finer doctrinal distinctions up to the reader to discover.

The Buddha outlined the concept of dependent origination in the Tipitaka, in which all phenomena arise through the interaction of causes and conditions.  The Mahayana texts extend this concept significantly, and explore the metaphysical consequences of this framework.  The resultant concept of shunyata (emptiness) is hugely important in the Mahayana literature, and has lead to the development of two major interpretations:

  • Madhyamika: Meaning ‘the Middle Way’, this school is largely credited to the incredibly influential texts written by Nagarjuna, great Buddhist scholar and sage (150 – 250 CE).  Nagarjuna used dependent origination to systematically refute any theories that proposed an inherent existence to any phenomena, including the Buddha and the Dharma themselves.  What makes this the ‘Middle Way’ philosophy is that the inherent emptiness of all phenomena does not mean they do not exist at all, but instead proposes that they have no inherent independent existence.  This concept is often presented as a dichotomy between relative existence — for instance, my sofa relatively exists because I can see it with my conceptual mind — and absolute existence, where we cannot find any specific property that absolutely defines a sofa, since they exist only as a confluence of causes and conditions, labelled by our conceptual mind.
  • Yogacara: Attributed to the Indian philosophers Asanga and Vasubandhu, Yogacara proposes that all conditioned phenomena have no inherent existence but instead are simply outgrowths of the dependently-originated course of mental phenomena arising and falling.  In other words, external objects only apparently exist, but are in fact generated by mind alone.  For this reason Yogacara is often called the ‘mind-only school’.  This is a significant simplification of course, and numerous alternative interpretations have been proposed.  A ‘mind-only’ approach to existence has some fascinating repercussions when discussing other aspects of Buddhist thought and practice, such as karma and nirvana, so I highly recommend reading more on the topic.

Mahayana also introduces the concept of the tathagatagarbha (lit. ‘essence of the Thus-Gone one’), or the Buddha-Nature.  This idea asserts that all sentient beings share a fundamental nature which allows all of us to become Buddhas.  This stands somewhat in contrast to the Madhyamika philosophy, which focusses so directly on the emptiness of all phenomena, and some have proposed that tathagatagarbha edges perilously close to endowing all sentient beings with an independently-existing ‘self’ of sorts, which of course would go against the word of the Buddha himself.  In practice the tathagatagarbha serves more as a positive and hopeful expression of the capacity for all beings to achieve Buddha-hood, and suggests that we all may glimpse this fundamental purity of all beings when we clear our minds of defilements and obstacles.  Key sutras for further reading include the Tathagatagarbha Sutras, Nirvana Sutra, and Uttaratantra Sutra. 

Prominent Mahayana traditions:

Perhaps the most well-known Mahayana tradition for most Westerners is Zen Buddhism, a Japanese school of Buddhism that originated from Ch’an Buddhism in China, which was heavily influenced by Daoist philosophies.  Zen practice emphasises rigorous meditational practices, namely zazen (seated meditation) and shinkantaza (‘just sitting’, a form of meditation aimed at emptying the mind and not using any meditation object), and challenging one’s perceptions via koan practice (stories or questions designed to test a student’s understanding).  Zen practitioners generally value examination of mind and the nature of existence through direct experience above all;  encyclopaedic knowledge of doctrine and sutras is often de-emphasised in Zen practice.  Zen is said to be one of Japan’s largest cultural exports, and has had significant influence on Western popular culture. 

These days we tend to use ‘Zen’ as a term expressing a sort of ‘going with the flow’, but in reality Zen practice is very disciplined and often heavily ritualised (at least this tends to be the case in Japanese Zen centres, less so in Western ones).  Zen appears in two varieties: Rinzai, a school of Zen that focusses more on zazen, koans, and is known for being quite severe (as in, expect to be hit with a stick if you don’t sit properly); and Soto, which emphasises shinkantaza and is generally more accessible and a bit less formalised.  The experiential and minimalist approach of Zen has made it remarkably popular with Western practitioners, and its undeniable results lead to it being highly respected by other Buddhist traditions as well.

Of particular note is the Plum Village community of globally famous Vietnamese Buddhist monk Thich Nhat Hanh.  Plum Village is a community of engaged Buddhists who reinforce the importance of expressing loving-kindness for others through charitable works.  Thich Nhat Hanh is very good at communicating the Buddha’s words to Westerners; in particular his book on the life of the Buddha Old Path, White Clouds, and his summary of Mahayana principles The Heart of the Buddha’s Teaching are worth reading.  Plum Village is of course inspired by Thich Nhat Hanh’s Vietnamese Zen (Thiền) background, but has adopted its practices very skilfully to make them more compatible with Western lifestyles.  Some argue that Plum Village is perhaps too Western-friendly, and honestly I agree to an extent, but Thich Nhat Hanh’s expressions of Buddhist thought, mindfulness and compassion are superb even if I differ with him on some finer points.  

Alongside Zen and its variants, there are numerous Mahayana schools that developed in China, Korean, Vietnam and elsewhere; far too many to name here.  My experience of the Mahayana is largely defined by my experience of Zen and Zen-adjacent practices, so I will refrain from saying too much about other traditions.  Tibetan Buddhism is often referred to as Mahayana, but generally is classified separately as Vajrayana due to the focus on tantric practices.

Recommended Reading:

Mahayana Buddhism — The Doctrinal Foundations, by Paul Williams:  This excellent book summarises all the key points of Mahayana Buddhist doctrine and practice in detail, with exhaustive notes.  Highly recommended as a broad overview of the core of these traditions.

Mahayana Sutras:  There are hundreds of Mahayana sutras, and many of them are exceedingly long, so I do not recommend necessarily trying to read all of them unless you are seriously motivated.  However there are a few categories of sutras that are very valuable in terms of understanding Mahayana doctrine, and also are full of fascinating imagery and astounding cosmologies filled with Buddhas, bodhisattvas and their Buddha-fields.  For background on the bodhisattva ideals and the six virtues, check out the Prajnaparamita Sutras.  The Lotus Sutra is widely considered one of the most important sutras in East Asian Mahayana, and states that all paths in Buddhism eventually lead to Buddha-hood.  The Yogacara Sutras are critical for understanding the Yogacarin view of reality (unsurprisingly).  The Tathagatagarbha Sutras expound on the Buddha-Nature inherent to all sentient beings.  The lengthy Vimalakirti Sutra expresses numerous critical concepts in the Mahayana, including emptiness and the non-dual nature of phenomena, and explores them via debates between various powerful beings and the lay practitioner Vimalakirti.  This is possibly my favourite sutra.  A close second would be the Surangama Sutra, which is well over 400 pages long but covers an enormous amount of ground, from Buddha-Nature to 50 mental states that interfere with meditation and all kinds of other stuff.

Zen Mind, Beginner’s Mindby Shunryu Suzuki:  This was one of the first books I read about Zen proper, and I still believe it’s an excellent first book on Zen thought and practice.  This book to me epitomises the Zen approach — austere, minimalistic, and focussed on developing wisdom through the practice of zazen.

Shobogenzoby Eihei Dogen (1200-1253):  The Shobogenzo is the masterwork of Eihei Dogen, father of the Soto Zen school.  This is a very long (1100+ pages) and deeply challenging work, so perhaps not for Zen beginners, but certainly should be read at some point by anyone with a substantial interest in the tradition.  Numerous commentaries and teachings on the text are available as well.  Dogen’s work is dense, poetic, and challenging, but it also expresses non-dual awareness and the experience of impermanence better than anything else I have read.  Well worth reading and contemplating.  Many Shobogenzo experts prefer the Gudo Nishijima translation, which is available in hardcopy or as 4 free PDF volumes from BDK America.

Vajrayana Buddhism

Vajrayana, also referred to as Mantrayana or Secret Mantra, is the third ‘vehicle’ of Buddhist practices for achieving enlightenment.  The vajra is a powerful, mythical weapon found in the ancient Indian vedas, and is said to be indestructible, so Vajrayana is sometimes translated as ‘the Diamond Vehicle’ or ‘Indestructible Vehicle’.  Vajrayana is most associated with Tibetan Buddhism, though it also appears in other traditions such as Shingon Buddhism in Japan.  The Vajrayana builds on the foundations of the two previous vehicles — Early Buddhism and Mahayana — and incorporates all of their core ideas, but further extends on these concepts, particularly in relation to the tathagatagarbha (Buddha-Nature).

Practitioners of Vajrayana follow the Four Noble Truths and the Noble Eightfold Path (like Theravadins), and they aspire to be a bodhisattva and take vows to achieve enlightenment for the benefit of all sentient beings (like Mahayanists), but they add to this a substantial, intricate body of esoteric ritual designed to achieve Buddha-hood far faster than the Theravada or Mahayana.  Indeed, Vajrayana is said to be able to lead to enlightenment in a single lifetime, whereas becoming a bodhisattva in a Mahayana context may take ‘three incalculable eons’ (Buddhism loves talking about extremely long periods of time).  Vajrayana practitioners achieve this by following the teachings of the tantras, Buddhist texts laden with symbolism and unusual, often transgressive practices.  Tantric practices diverge from more traditional Buddhist practices by embracing mental states and behaviours normally considered negative — anger, desire, intoxication — and harnessing those states to generate realisations.  As stated in the Hevajra Tantra:

“Those things by which evil men are bound, others turn into means and gain thereby release from the bonds of existence.”

Origins of Tantra

The true origins of tantra are shrouded in mystery.  The earliest Buddhist tantras appeared in around the 7th century CE, with most of those early texts focussed on the use of mantras and rituals to generate useful real-world consequences.  In the 8th and 9th centuries, the tantras developed toward higher ends, aiming to harness our innate Buddha-Nature and reach enlightenment at breakneck speed.  The Kalachakra Tantra, an incredibly comprehensive text that includes detailed descriptions of mystical cosmologies and astrological practices along with tantric ritual, appeared around the 10th century.  The Dalai Lama has given numerous initiations into Kalachakra Tantra practices for very large audiences.

According to Tibetan Buddhist scholars, Vajrayana was actually taught in secret by the Buddha himself to his closest disciples, and was kept hidden from the wider world until Padmasambhava, also known as Guru Rinpoche, revealed the tantric teachings in Tibet in the 8th century.  Some Tibetan historians claim that the appearance of Padmasambhava was foretold by the Buddha; others claim Padmasambhava was himself a reincarnation of the Buddha.  Academic historians question the veracity of these claims, of course, and propose that the Buddhist tantras emerged gradually from around the 1st century CE as an evolution of earlier Vedic practices.

Some Buddhist scholars have developed a narrative for how the Buddha may have taught the tantras during his lifetime.  They claim that the concepts and methods outlined in tantra likely derived from earlier practices, which the Buddha would have experimented with during his long search for enlightenment.  Tantra by nature is esoteric and kept secret by practitioners, and while Tibetan tantric practices are widely known today, some tantric practices are still highly secretive and virtually unknown to outsiders (as in Shingon Buddhism).  This suggests that the Buddha’s disciples may indeed have been able to keep tantric teachings secret for centuries after his death.  So if we accept these premises, perhaps it is possible that the Buddha may have developed tantric methods, transmitted them secretly, and left his later disciplines to determine when the time was right to reveal them.  Textual evidence is hard to decipher and nearly impossible to date, so quite possibly we may never be able to prove or disprove this account or the academic historical account.

In any case, there are numerous tantric texts and systems in evidence today, with around 3,000 tantric texts currently in the Tibetan canon.  Tantra remains a hugely active area of study and practice, and with Tibetan Buddhism having now spread across the globe, it is quite possible there are more tantric Buddhist students and practitioners now than at any other time in history.

Tantric practices

Tantric practices and texts are esoteric, meaning that many of them are not accessible to the average student of Buddhism.  Aspirants must be initiated into these practices by qualified teachers, gurus, who hold direct connections to lineages of tantric transmission going back centuries.  Traditionally these practices are kept secret so as to avoid damaging unprepared minds; tantric practices are considered very powerful, and require in-depth knowledge of complex symbolism and difficult philosophical concepts in order to be practiced correctly.  If someone practices tantra without the appropriate instructions and guidance, they may inadvertently create bad karmic results for themselves or others, including their guru.  Tantric texts themselves are typically very dense and cryptic, and often intentionally obscure their meanings with coded statements and metaphor, making them incomprehensible without the guidance of a guru.

Secrecy in tantra is further upheld by the vows taken by initiates called samaya.  Samaya requires that initiates undertake specific practices transmitted by the guru during the initiation in order for the practice to stay effective, and further demands that the initiate maintain strict spiritual and ethical discipline in perpetuity.  Breaking samaya is said to lead to severe karmic consequences for both the initiate and the guru, so gurus tend to be cautious about giving initiations to students they feel may not be able to keep samaya.  Typically samaya is only required for the two highest levels of tantric practice (there are four levels); for the lower two levels the initiate must take the bodhisattva vows.

Some specific lower-level tantric practices are fairly accessible, and may be practiced by even novice Tibetan Buddhists.  Typically these practices are mantra recitations, visualisation practices, or varieties of deity yoga.  In deity yoga, practitioners visualise themselves as specific enlightened beings in an effort to cultivate characteristics of enlightened beings in themselves.  Initiated tantric Buddhists may conclude these practices by visualising themselves taking the form of the deity directly (‘self generation’), whereas the uninitiated will be restricted to visualising the deity in front of them or on the crown of their head (‘front generation’).

A common question about deity yoga is whether Tibetan Buddhist deities are ‘real’ deities — do they really exist out there, ready to help us refine our minds and achieve liberation?  When we call them to being in our visualisations, are they really appearing in some way, or are we just fooling ourselves?  Most who ask that question end up being dissatisfied by the answer, given that producing an answer requires us to determine what is ‘real’ in Buddhism in general, and for Buddhists all things, including ourselves and the deities, are empty of inherent existence.  Asking if the deities are ‘real’ implies a materialist, dualist framework in which things are either fundamentally existent or non-existent, but Tibetan Buddhist thought doesn’t really support that view.  So perhaps we might just say that the deities are as real, or unreal, as the yogic practitioner — both are empty of inherent existence.  Of course there is a lot more to say on this topic — this is always the case with any topic in Buddhism.

Tantric practices also focus on the visualisation and manipulation of the ‘subtle body’, a complex psycho-spiritual ‘map’ of the body which includes numerous channels that direct energies throughout the body, and points of focus for these energies known as chakras.  The form of the subtle body varies widely between different tantras and practices, and sometimes has the seven chakras we may know from yoga and sometimes not, but in any case it’s not seen as a concrete map of our spiritual form, but instead a collection of useful symbols for aspects of phenomenal experience/consciousness that the tantric practitioner wishes to apprehend and manipulate.

Tantra in Tibetan Buddhism

Tibetan Buddhism is the most known and most developed tradition of Vajrayana Buddhism, with each major Tibetan school incorporating numerous tantric texts and practices.  The intense imagery associated with the Tibetan traditions is derived from tantra, including the trappings used in rituals at all levels of practice, and devotional art like thangkas (detailed images of tantric deities used as an aid to visualisation) and mandalas (maps of the celestial dominions of tantric beings).

For the newcomer to Tibetan Buddhism, first encounters with the intensive ritual practices can be quite intimidating.  We are accustomed to the Dalai Lama and his extremely calm and light-hearted demeanour and his simple robes, so we can quite easily find ourselves taken aback when confronted with imagery like this:

dandapani-mahakala

“Hey what’s up? Don’t mind me, I’m just chillin’, wearing a crown of skulls and a belt of human heads, standing on a fresh corpse, surrounded by an aura of flames. You know, the usual.”

Couple these scary deities with rituals involving intensive chanting, lots of smoke and drums and bells, people waving daggers around, and drinking wine from skulls (yes, really), and it can all come across pretty weird and cult-ish.  But the imagery and ritual objects are not just intended for shock value — they are dense with layers of symbolism, and are all defined in reference to core concepts of Buddhist philosophy.  So in the image above, the deity’s crown of five skulls represents mastery of the Five Buddha Families; his flaming aura represents the light of the Dharma (the Buddha’s teachings); the corpse under his feet represents his conquering of attachment; and so on.  By visualising oneself as this being, with precise and detailed knowledge of all the qualities it represents, tantric practitioners believe we can cultivate these enlightened qualities within ourselves.  Similarly, mantra repetition cultivates states of mind that are receptive to the Dharma; prostrating ourselves repeatedly in front of symbolic deities generates humility, and so on.

All told, Tibetan Buddhism is quite a bit more Extreme Death Metal Buddhism than most outsiders commonly expect — ‘I just wanted a chill meditation session, what’s with all the skulls?!’  But this transgressive imagery and practice is the core of the tantras, where enlightenment can be reached not only by cultivating knowledge of suffering and non-self and the nature of emptiness, but also by harnessing our afflictive emotions and redirecting them in a positive way.  The tantras have in turn influenced the everyday practices of Tibetan Buddhism, even those that do not require initiation.  Thus, in the Tibetan traditions, we see the influence of tantric themes: meditation on death using very direct and visceral imagery is very common; many Tibetan meditation practices are highly ritualised and involves mantra recitations, dedications of merit, and prostrations; and rich visualisations are used much more than in other traditions in practices like guru yoga and tonglen.  Whether one is explicitly practicing tantra or not, Buddhist practice in the Tibetan traditions is often rich with vibrant colours, powerful imagery, intricate ritual objects and complex procedures.

This intense take on the path to enlightenment has appeared in Tibetan Buddhism since its early days.  Tibetan legends have long portrayed Buddhist practice as powerful but at times risky, compassionate but sometimes fierce.  Padmasambhava’s biography makes for incredible reading; according to Buddhist historians he was essentially an ancient Dharma sorcerer, flying all over Tibet like a yogic Superman, subjugating the local spirits and demons and swearing them into service of the Dharma.  Milarepa, another Tibetan Buddhist saint, began his life by using black magic (!) to murder his aunt and uncle for stealing his family’s fortune, along with numerous other people, only to later achieve enlightenment through Vajrayana practice.  In the Tibetan view, enlightenment is something fought for with intensive, powerful methods, and these practices are so powerful that even murders and black magicians can still use them to achieve enlightenment (assuming they also stop murdering/evil-wizarding, of course).  In taking on these commitments we also take greater risks, but the payoff is significant if one can truly reach enlightenment in a single lifetime.

The Effectiveness of Tantra

As we have seen, Vajrayana practitioners believe that these powerful tantric rituals enable them to potentially reach enlightenment in a single lifetime, as opposed to the three incalculable eons of following the bodhisattva path in standard Mahayana practice.  There are a number of arguments out there for why tantric practice is considered so effective, of which two in particular seem to recur in numerous sources.

First, tantric practices are transgressive — they use visceral imagery with images of corpses, skulls and severed heads; tantric deities are frequently depicted in sexual union with other deities, and visualisations of ritual sex are part of some high-level tantric practices; and other behaviours that go against the usual Buddhist moral precepts, like ingesting alcohol and meat, are also seen in some rituals.  This is not only because the tantras advocate the harnessing of afflictive emotions and behaviours for positive ends, but also because the very act of transgressing moral codes in this way promotes non-dual awareness.  We are conditioned to think of existence in terms of dualities: this thing exists or doesn’t exist; this behaviour is good or bad.  In tantra, flagrantly violating those categorisations forces the practitioner to abandon dualistic thinking, and in this way move closer to the pristine, clear light of the Buddha-Nature, which knows no such divisions between phenomena, as they are all empty of inherent, absolute existence.

Second, tantra is said to ‘take the result as the path’, as opposed to sutra Mahayana, which focuses on causes.  In sutra Mahayana, practitioners focus on developing the causes of awakening — the Thirty-Seven Factors of Awakening, the Six Perfections, and following the Bodhisattva Path.  In tantra, practitioners assume they have already achieved the goal of the path — they contain a Buddha-Nature, as do all sentient beings.  Visualising oneself as an enlightened deity and developing ‘divine pride’, in which the yogi sees themselves as inseparable from the deity and hence fully awakened, aims to remove the obscurations that hide their inherent Buddha-Nature from view.  Thus, the tantric practitioner makes Buddha-hood part of their practice directly, and in that way they ‘take the result [of Buddha-hood] as the path [to enlightenment]’, rather than patiently developing karmic seeds to allow that nature to ripen over many lifetimes.

Of course there is much more to say about all of these aspects, but I leave that to the experts who are capable of studying these arcane texts and unraveling the tangled history of tantric practice.  Weirdly, Buddhism studies at the turn of the 20th century largely ignored tantra, as biases in the Western scholarly community considered it in a way ‘impure’ compared to the crystal-clear, logically-consistent framework for enlightenment developed in the Pali Canon.  As a result, the academic study of tantric Buddhism is actually quite new, only really becoming a serious area of enquiry after the Dalai Lama’s escape into exile in 1959 and the subsequent spread of Tibetan Buddhism across the world.  If you want to learn more about the fascinating history of tantra, and about the evolution of these practices over the centuries, Buddhist Thought by Paul Williams has a concise summary of Vajrayana history and practice in the closing chapters, and The Origins of Yoga and Tantra by Geoffrey Samuel goes into intense detail on the development of tantra from its earliest appearances to the 13th century.  

Recommended reading:

Tibetan Buddhism is packed to the brim with complex imagery and symbolism, and has a seemingly endless supply of mind-boggling esoteric literature to study, so it’s a real joy to dive into if you like such things.  

Indestructible Truth and Secret of the Vajra World, by Reginald Ray: This two-volume set of detailed, yet approachable summaries of Tibetan Buddhist history, doctrine and practice are essential for the newcomer to the subject.  Reginald Ray has been a practicing Tibetan Buddhist for a very long time, worked with many of the most famous lamas and teachers, and is an excellent source in general.  Check out his podcast and other stuff too.

The Lotus-Born: The Life Story of Padmasambhavaby Yeshe Tsogyal: this spiritual biography describes the incredible life of Padmasambhava, AKA Guru Rinpoche, who brought tantric Buddhism to Tibet.  His life story as depicted here is filled with fantastic deeds and the demolition and subjugation of ornery spirits and demons.  Guru Rinpoche’s influence on Tibetan Buddhism today remains prodigious, so understanding his life and teachings can be very insightful for the student of Vajrayana.

The Library of Wisdom and Compassionby His Holiness the Dalai Lama and Thubten Chodron:  This remarkable series is intended to provide a comprehensive introduction to the whole of the Buddhist path, from the basics in volume 1 through to deep and complex investigations of core Buddhist philosophical issues in the following seven volumes.  Books 1 through 5 are available now, and book 6 is coming next summer.  The detailed academic investigation of Buddhism is broken up by chapters from both the Dalai Lama and Thubten Chodron sharing quite personal reflections on their own experiences in Buddhism, which gives the books a personal touch and a strong connection to real-world practice.  Highly recommended.

Library of Tibetan Buddhist Classics:  This series of books collects new, comprehensive translations and commentaries on crucial Tibetan texts ranging across a variety of traditions.  The texts include foundational commentaries for all the major schools of Tibetan Buddhism, and tantric texts previously unavailable in English.  Just be aware that some volumes will contain material and rituals that should not be practiced without the guidance of an experienced teacher; indeed, some will insist that one should not read them at all without receiving the appropriate tantric empowerments from a guru.

Three Turnings of the Dharma Wheel

Hopefully now you can see that the three main ‘vehicles’ of Buddhism are connected, with each subsequent vehicle building directly on the previous one.  Throughout the many Buddhist traditions, at a minimum they share the original teachings of the Buddha, as laid out in the Pali Canon — the Four Noble Truths, the Noble Eightfold Path, and the Three Marks of Existence, among other things.  The Mahayana extended this foundation, developing the Path of the Bodhisattva, sunyata (emptiness), and tathagatagarba (Buddha-Nature).  Vajrayana extended this further, with deeper examinations of the concept of emptiness, and working directly with the fundamental nature of mind and the innate Buddha-Nature of all beings.   

This three-part hierarchy of the Buddhist path to enlightenment is further reinforced by the common expression of these three vehicles as being Three Turnings of the Dharma Wheel.  Each turning corresponds to one cycle of teachings by the Buddha, each revealing extensions to the core teachings of the previous turning.  The Dalai Lama in Approaching the Buddhist Path defines the critical concepts the Buddha taught in each Turning of the Dharma Wheel as follows:

  1. The First Turning (Early Buddhism): defining the nature of suffering (the Four Noble Truths), the path to eliminating suffering (the Noble Eightfold Path), the Three Marks of Existence (dukkha, anicca, anatta), and the Thirty-Seven Aids to Awakening.
  2. The Second Turning (Mahayana): the Prajnaparamita Sutras (Perfection of Wisdom Sutras), revealing that all phenomena are empty of inherent existence; defining the Six Perfections (generosity, ethical conduct, fortitude, joyous effort, meditative stability, wisdom) and the Bodhisattva Path.
  3. The Third Turning (Vajrayana): further interpretation of emptiness in all categories of phenomena; the pure, ‘clear light’ nature of mind, and the Buddha-Nature.

We can see from the clear connections between the three vehicles/turnings that while the Buddhist traditions differ hugely in their practices and approaches to enlightenment, there are core teachings common to all of them that all Buddhists accept, and these lie in the original teaching delivered by the Buddha.  For practicing Buddhists of any tradition these elements are essential to all paths to enlightenment.

amitabha-statue

A statue of Buddha Amitabha.

Pure Land Buddhism

Pure Land Buddhism is somewhat hard to categorise in the typical three-vehicle structure, and is practiced in a very different way than the other traditions I have outlined above.  Many Mahayana and Vajrayana traditions have practices related to the Pure Lands — these are celestial realms linked to Buddhas and Bodhisattvas.  These practices can allow one to aspire to rebirth in a Pure Land, rather than the human world, which makes practice of the Dharma in that future life much easier, thereby accelerating the path to enlightenment.

However, Pure Land Buddhism takes this idea as the sole focus of practice.  In Jodo Shinshu, one of the most popular Buddhist traditions in Japan, adherents believe that the human world is simply too corrupt for any of us to have any hope of practicing enough Dharma to achieve enlightenment.  Therefore, our only salvation is to be reborn in a Pure Land where there is no such corruption, and at that point we can focus entirely on practicing the Dharma and achieving Buddha-hood.  As a consequence, Jodo Shinshu adherents do ‘the practice of no practice’, where they do not practice anything other than the repeated recitation of the mantra of Buddha Amitabha — namu Amida Butsu or ‘I take refuge in the Buddha Ambitabha’.  They believe that Buddha Amitabha made a Primal Vow to allow any beings that recite his mantra with true intentions to be reborn in his Pure Land, and thereafter practice Dharma in a pristine environment.

Essentially, this tradition is a kind of ‘faith alone’ form of Buddhism, in which meditation, the Noble Eightfold Path, and so on are left aside, and one simply relies on the grace of Buddha Amitabha to save them from this corrupt world in the next life.  This idea became very popular with people who did not want, or were not able, to practice intensive Buddhist activities like meditation, or those who had committed serious crimes and could see no way to redeem their karma in this life.

Jodo Shinshu and similar Pure Land sects can be considered Mahayana traditions, as they do believe that the Dharma is effective (just not here), and they certainly believe in the Buddhas, Bodhisattvas, and Pure Lands found in the Mahayana Sutras.  But then, they do not actually practice anything else in those sutras, or in the Pali Canon for that matter.  Also, the Buddha was very explicit that blind faith was to be discouraged, and one should test all Dharma teachings (and teachers) for themselves and determine whether they were effective; this is of course impossible with Pure Land traditions like Jodo Shinshu, since the effectiveness of these beliefs cannot be determined until after death, whereas practices like meditation have benefits in this life that can be experienced and tested.  With all that in mind, to me Pure Land Buddhism of this type is a very different animal from anything present in the three vehicles, and is more akin to Christianity than any of the other forms of Buddhism.

I have to admit to a personal bias here, of course.  What attracts me to the teachings of the Buddha is that the practices they outline are accessible to everyone and described in a coherent and clear way, and they are testable and are subject to our own discernment and critical analysis.  While the truth that ‘everything is suffering’ sounds bleak, the Buddhist is ultimately empowered to change this state of affairs, and can do so without relying on any external teacher or authority if they so wish.  Not only that, but human existence is seen as very fortunate, even though many of us suffer immensely, because we have opportunities to improve ourselves and to end that suffering for ourselves and others.  In Jodo Shinshu the outlook is far bleaker, as even the Dharma cannot save us, since the world is simply too corrupt for us to be able to practice it successfully.  We have no power at all to change this — in fact, the tradition explicitly lays out a distinction between ‘self power’ and ‘other power’, and only other power can save us from suffering, in the form of Amida Butsu’s vow.  So in essence, Pure Land traditions eliminate the most meaningful element of Buddhism to me, which is the practice of the Noble Eightfold Path, and that means I tend not to engage with them. 

I hasten to add though that many Pure Land practitioners are heavily engaged in the study of Buddhist philosophy, and supplement their faith in Amida’s Vow with additional study of Buddhist principles in preparation for that future life in the Pure Land.  I also fully understand the difficulties Buddhist practices present for many people; not all of us are capable of meditation, or have the time and resources available to study the Dharma.  Across all Buddhist traditions there is broad agreement that practicing and studying the Buddha’s teachings to even the tiniest extent is better than not doing it at all, and one should simply try to do what they can in this life according to their own limitations.  So in that sense, even the ‘practice of no practice’ is still striving to create the conditions for future study of the Dharma, and is providing a connection to the Buddha’s teachings that is accessible to everyone, regardless of their circumstances.

The whole concept of Pure Lands in general is valuable to Theravada/Mahayana/Tibetan Buddhist practice, too.  In Tibetan Buddhism, Pure Land elements exist as part of the typical framework of Buddhist practices — meditation and visualisation.  Visualising the Pure Lands reinforces the power of the Buddha’s teachings, by portraying planes of existence where Buddhas and Bodhisattvas have transformed reality into blissful reflections of pristine Buddha-Nature.  Some Pure Land practices also function as ‘karmic parachutes’, where one can perform them at the time of death to shunt your mindstream off to a Pure Land if enlightenment has not been reached.  If there’s one thing Tibetan Buddhism loves, it’s optimising their practice to achieve powerful results, so Pure Land practices fit right into that.  

dalai-lama-gifu-soto

His Holiness the Dalai Lama joins two Soto Zen monks in paying respects to the Buddha, before addressing a meeting of 1,600 Soto Zen priests in Gifu, Japan in 2015.

A Note About Sectarianism

A natural question that may arise after reading all this is: what happens if someone follows the Buddha’s advice, studies the teachings and investigates everything for themselves, and discovers that none of the traditions out there completely match what works for them?  Alternatively, what if they want to participate in multiple traditions at once?

I’ll defer here to Drubwang Tsoknyi Rinpoche, a Tibetan Buddhist lama of the Driking Kagyu tradition:

Seen from my point of view, the Buddha taught what we call Three Vehicles. Each of them contains a complete path for sentient beings to eliminate their negative emotions—desire, hatred, ignorance, pride, and envy—with all their 84,000 proliferations and variations. It is therefore entirely possible when someone practices free of laziness and procrastination any of these three paths to attain the same level as Buddha Shakyamuni.

Moreover, it is possible for any person to practice all three vehicles in combination without any conflict whatsoever. This is often the case in the Tibetan tradition of Buddhism, where many practitioners have practiced the three vehicles either separately or unified into a single system.

In the present time, when we see a growing interest in Buddhist practice all over the world, I find it important that people come to understand the primary emphasis and special qualities of each of these three vehicles. Free of bias, and with clarity, each person is then free to adopt what is closest to their inclinations — whether one of the vehicles alone or the three in combination.

In other words, Buddhists believe that all three vehicles can lead to liberation, and thus each is a worthy path to take.  As a consequence, Buddhists are welcome to partake of elements of some or all of the vehicles simultaneously.  There is no issue with going to a Zen temple for zazen one day and a Tibetan Buddhist puja on the next.  Buddhists often say that the Buddha taught 84,000 versions of the Dharma, each one adapted to the needs of a different audience.  He adapted his teachings to ensure that the truths of existence he offered could be put into practice, and made accessible to as many people as possible; he speaks in the suttas as well of the importance of testing all teachings we receive with our own experience and critical faculties, and not engaging in fanaticism.  With all that in mind, we might imagine that the Buddha himself would have had little patience for sectarianism.

Of course, if you venture into Buddhist forums around the internet and social media, you will certainly see infighting between traditions, and seemingly interminable debates on finer points of doctrine.  But when you venture into real-world Buddhist centres of all stripes, you are likely to find Buddhists being quite accepting of varied points of view.  When I attended three days of teachings by the Dalai Lama in Glasgow in 2004, I saw monks in the yellow robes of the Thai tradition, in the red and orange of Tibetan traditions, and the austere black and grey of Zen.  The Dalai Lama has been a strong supporter of unity across Buddhist traditions, and speaks often of the need to pay equal respect to the teachings of all three vehicles.  

The quote above comes from the foreword to a book by Ajahn Amaro called Small Boat, Great Mountain, a series of talks comparing the Tibetan teachings of Dzogchen, the Great Perfection, with similar concepts in Theravada Buddhism.  This book is a nice example of a fascinating dialogue between Buddhist traditions.

Next Steps

So, now that I have outlined some of the core elements of the three main Buddhist pathways to enlightenment, in the next article I will examine some of the more common misconceptions about Buddhist practice one tends to find in the media and popular culture.  Over time I will add more to this article, although it is already so long that I will try to avoid extending it to ridiculous levels.  At present I am planning to add some details on the Bodhisattva Path to the Mahayana section at some point, and after that I will see where it goes.  

 

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A critique of Todd May’s ‘Death’

Death (The Art of Living): Amazon.co.uk: May, Todd: Books

UPDATE 11 Dec 2020: I added a piece of Buddhist artwork depicting death meditation, and some details on the very significant role that mortality and impermanence play in various Buddhist traditions and practices.

Recently my wife and I re-watched the excellent series The Good Place, a comedy centred around the misadventures of four souls marooned in a confusing and flawed afterlife.  In addition to being simply funny and enjoyable, with great characters, the show stands out due to its surprisingly nuanced depictions of key concepts in ethics and moral philosophy.

One of the central characters of the show, Chidi Anagonye, is a professor of ethics and moral philosophy, and ends up teaching the other characters about ethics in an effort to help them become better people.  Throughout the show he makes reference to numerous well-known works in ethics and moral philosophy.  I have read some of these already, but at one point he mentions the book Death by Todd May, and after having that on my reading list for some time I finally picked it up off my e-bookshelf last night and read through it.

I want to start by saying that the book, considered as a whole, is a highly readable reflection on the reality of human mortality, and manages to be at once both gentle and disarming.  This balance is hard to strike, and I’m genuinely impressed that the author was able to thread that needle so successfully.  I also applaud Todd May for expressing these concepts so clearly, and for translating difficult concepts into a form that’s highly accessible for non-philosophers.

The book consists of three parts: first, an investigation of the problems death presents for the human condition; second, a discussion of the problems that would be created by immortality; and third, an attempt to synthesise a point of view that accepts death as the central fact of human existence, without being overwhelmed by it.  The first part coalesces around the four central characteristics of death as outlined by Heidegger in Being and Time:

  1. Death is final — it marks the end of human existence and conscious experience.
  2. Death is not an accomplishment or a goal to reach, and dying is not a form of closure for our lives — it simply is an end.
  3. Death is both inevitable and uncertain, in that we cannot avoid it, and we can never know for sure when it may happen to us.
  4. These three facts about death lead us to search for meaning in life.

These four points provide a framework for Todd May to confront his readers with the grim reality of human mortality.  They underline his central thesis, which is that death is not merely an intruder that appears at the end of our lives, but in fact it is the most important defining element of human experience.  Everything that humans do — the relationships we form, the projects we undertake, the passions we indulge — are shaped by the fact that we are mortal, our time in this Universe is limited, and therefore we must try to make things happen before that time ends. 

May places this perspective, a frank assessment of the facts of human mortality, against the more typical response many of us have to thinking about death, which is to avoid it. He discusses Christian theology as an example, in which the terrifying reality of death is soothed in the minds of believers with the idea that death is not an end to their experience, but that the soul, the self, continues beyond death. He points out that this may be comforting even if one believes in Hell, because at least even in Hell there is no cessation of existence; Hell-bound souls continue to be, even if they do so in abject suffering.

From there he offers Buddhism as another example of the avoidance of the reality of death in religious thought, and here is where I must part ways with May’s take. He presents Buddhism as avoiding the final cessation of death via reincarnation:

When you’re reborn, it is into a different body.  It is your mind or your soul – again as in Christianity – that is. reborn. If your karma consists in what you have made of yourself in a particular life, your rebirth situates you in a particular karmic state in your next one.

In the past I have written extensively about Buddhist thought, and Buddhism has been an object of study for me since I was a teenager.  The characterisation of reincarnation May offers above is fundamentally at odds with the Buddhist concept of life, death and rebirth.  What he describes is reincarnation as in Hinduism, and indeed later in the book he explicitly conflates the two.  But in reality, Buddhist thought defines itself in opposition to Hinduism in this regard.

In Buddhism, the concept of anatta — non-self — is one of the three marks of existence, alongside anicca (impermanence) and dukkha (suffering).  The word anatta itself stands in opposition to the Hindu concept of atman, that within all of us lies an essence, a soul, which transfers from one life to the next.  In Buddhism, there is no eternal soul, and there is no essential self that transfers between existences.

May attempts to sidestep this a few pages later in the text:

There are those who study Buddhism who will want to take issue with the interpretation I have offered here. After all, they point out, for Buddhism the self is a myth. There is no self, only the ever-changing process of the cosmos. This is true. All Buddhist doctrine denies the idea of a distinct self. The significance of this denial, though, depends on one’s interpretation of Buddhism. For those who do not embrace the doctrine of reincarnation, it is easy to see how there is no self.

The central thrust of this paragraph is flawed, however; there are, by definition, no Buddhists who embrace the doctrine of reincarnation.  Buddhists believe in rebirth, which is not the same thing.  Reincarnation does rest on the concept that souls transfer between lives; one’s current life ends, and our essence moves on to another life, and there is a continuity of our essential self between those lives.  But that does not apply here, since Buddhism does not include reincarnation.

In Buddhism, the end of one’s current life is an actual end.  When I die, Eric Silverman will cease to exist; my consciousness and all my experiences will vanish along with my corporeal body.  My karmic actions, presuming I have not achieved enlightenment, will create the conditions for a rebirth, but that rebirth will be a different life.  Rebirths are linked by the causal processes of kamma (karma), not by a soul or identifiable, independently-existent self.

The central problem here is that May has dismissed anatta as if it were a quirk of interpretation, rather than the centrepiece of an extensive and coherent belief system.  Anatta is not a concept one can separate from the Buddhist view of the cosmos and our place in it; since the time of the Buddha this concept is central to Buddhism, and many of its practices rest on apprehending and experiencing the absence of self and the emptiness of existence.  Without anatta, we are no longer talking about Buddhism.

To further reinforce this point, I would stress that Buddhists of every stripe — Theravadins, Mahayanists, Tantric practitioners — all agree that anatta is a central component of Buddhist thought.  In 1967, a historic meeting of representatives from every major Buddhist sect agreed on a set of common beliefs: 

The Buddha is our only Master (teacher and guide)

  1. We take refuge in the Buddha, the Dharma and the Saṅgha (the Three Jewels).
  2. We do not believe that this world is created and ruled by a God.
  3. We consider that the purpose of life is to develop compassion for all living beings without discrimination and to work for their good, happiness, and peace; and to develop wisdom leading to the realization of Ultimate Truth
  4. We accept the Four Noble Truths, namely duḥkha, the arising of duḥkha, the cessation of duḥkha, and the path leading to the cessation of duḥkha; and the law of cause and effect.
  5. All conditioned things (saṃskāra) are impermanent (anitya) and duḥkha, and that all conditioned and unconditioned things (dharma) are without self (anātma).
  6. We accept the thirty-seven qualities conducive to enlightenment as different aspects of the Path taught by the Buddha leading to Enlightenment.
  7. There are three ways of attaining bodhi or Enlightenment: namely as a disciple (śrāvaka), as a pratyekabuddha and as a samyaksambuddha (perfectly and fully enlightened Buddha). We accept it as the highest, noblest, and most heroic to follow the career of a Bodhisattva and to become a samyaksambuddha in order to save others.
  8. We admit that in different countries there are differences regarding Buddhist beliefs and practices. These external forms and expressions should not be confused with the essential teachings of the Buddha.

Note point 5, which explicitly includes anatta (written here in the Sanskrit as anatma) as a core belief common to all Buddhists.  Point 8 is also important, as it acknowledges that other forms of Buddhism may exist, but these must not be confused with core Buddhist principles.

So, in other words, the moment May proposes an interpretation of Buddhism which includes a soul or self, he has ceased talking about actually-existent Buddhism and begun talking about something else.

Ultimately, if we introduce reincarnation to Buddhism instead of rebirth, the whole edifice no longer functions, and the core concepts of mind and existence that define it no longer make sense together.  Reincarnation requires a soul to be transferred from one life to another, and anatta makes this impossible, so these two elements are mutually exclusive.

May continues along this line of reasoning, further conflating reincarnation and rebirth:

Things are more complicated with the doctrine of reincarnation, however. If, in a way, the self is an illusion, in another way it is not. As with the Christian doctrine we discussed, there must be something that survives death in order to get reincarnated. And that something must be continuous with the previous life, or else the nature of one’s reincarnation would be entirely arbitrary. We might put the point this way: the self is an illusion that only dissipates when one achieves nirvana.

Again this logic does not hold, although there is some room for argument here.  As described briefly above, in Buddhist thought the thread that links different lives is not an independently-existent soul or essence, but instead the karmic actions of one life create the causes and conditions for the next.  To expand a bit on this I will quote myself from that post of a few years ago:

It is this kamma that continues beyond death.  The Buddhist belief, at its core, is that once we die, the consequence of our kamma is that another birth takes place, and our little bundle of karmic pluses and minuses determines what kind of birth that will be.  This cycle is inevitable, and eternal, unless we are able to break free of this cycle via liberating ourselves from clinging to this world and become enlightened.

This cycle can be hard to conceptualise, so it’s often described using an analogy.  Imagine my life as a burning candle, with the flame representing my consciousness.  Right as the candle is running out, I use that flame to light the next candle.  The next candle lights up right as the old one burns out.  So my consciousness directly causes another, subsequent consciousness to arise in the next life, but my original consciousness burns out — the new one is a different consciousness, existing in a different body (which may or may not be human).  Kamma is what lifts the old candle to the new and causes the new one to light up.

The philosophical difficulty for Buddhists in this context is that logically we might expect that some causal agent would need to exist that creates the causes and conditions for the reborn consciousness to arise, rather than a mind arising from nothing yet still somehow being linked to a previous mind.  Kamma is posited to be the agent in this case, but how does a formation of karmic aftereffects lead to the creation of new mental events, a new consciousness?

There are several approaches to this, but the most common one I’ve seen in the Buddhist community is the concept of one’s existence as being a mindstream, a continuous stream of moment-to-moment sense impressions and mental events which continue across lifetimes, but like anything else has no inherent independent existence.  This stream is affected by our positive and negative actions during our various lives and is the ‘stuff’ that transfers the karmic ‘seeds’ one has planted in previous lives into that next existence.  In that sense, there is a continuity of mind at a fundamental level, but again this is not a soul or essence, and while my mindstream may continue after this life, Eric Silverman will not.  My death will be an end to my life, and only my karma survives me. 

Part of the source of confusion here may be that, as with any other conditioned thing, consciousness in Buddhism is actually a confluence of numerous causes and conditions.  Consciousness exists in different forms, and at different levels of subtlety, and these interact in different ways with the physical aggregates that form our body.  In Western theology we think of the mind as a singular entity, whereas Buddhism does not; this can lead us to think that the mindstream indicates a continuity of consciousness from one rebirth to another, whereas in Buddhism the continuity occurs at the subtlest levels of mind.  Since my lived experience as a human is defined by the grosser forms of consciousness as well as the subtler one, and those grosser forms interact inextricably with my physical form, in a fundamental sense my different rebirths are different existences, despite sharing at a deeper level a subtle continuity of mind.  This means that even though there is a link between this life and the next, that next life will be different from this one, with a different mind and experience, linked by kamma and the subtlest levels of mind.*

On that basis I reject May’s contention that Buddhists avoid the finality of death.  While there is a continuity of existence between lives, at the core this is not reincarnation, and does not require a self or soul to be transferred. 

In practical terms, Buddhists do take death as an end to life, and there are numerous traditional practices that confront this directly: Thai forest monks meditate in dangerous and scary places to contemplate the impermanence and eventual dissolution of all things; and monks of various traditions sometimes meditate in graveyards or near decaying corpses to confront the reality of our eventual death.  This practice is as old as the Buddha himself, and can be seen depicted in Buddhist art:

Tibetan Buddhists in particular view meditation on death and dying as a supremely important aspect of their practice.  Beyond the meditating-in-charnel-grounds stuff, which was recommended from the earliest days by the Buddha himself, there are other common practices of death meditation practiced in Tibet:

Another powerful technique for developing awareness of death involves visualizing oneself lying on one’s deathbed, with life slowly ebbing away. All one’s friends and relatives are gathered around, weeping and lamenting, and one’s body progressively degenerates. The glow of life fades from the face, and the pallor of death replaces it. Breathing becomes shallow. The lips dry up, slime forms on the lips, and the body becomes like a lump of flesh, unable to move freely. Bodily temperature drops, eyesight, hearing, and other senses lose clarity, and one becomes aware of past negative deeds…. Through cultivating this meditation one should develop a sense of urgency regarding religious practice and a poignant awareness of death. (John Powers, Introduction to Tibetan Buddhism, p 331)

These practices are considered so important that in some cases Buddhist teachers recommend they be practiced daily:

Atisa is said to have told his students that for a person who is unaware of death, meditation has little power, but a person who is mindful of death and impermanence progresses steadily and makes the most of every precious moment. A famous saying of the school he founded, the Kadampa, holds that if one does not meditate on death in the morning, the whole morning is wasted; if one does not meditate on death at noon, the afternoon is wasted; and if one does not meditate on death at night, the evening is wasted. (Ibid., p 326)

The Tibetans also produced the Tibetan Book of the Dead (Bardo Thodol, lit. ‘Liberation Through Hearing at the Intermediate State), a detailed description of the processes the mind undergoes at the moment of death and during the intermediate state between lives (the bardo).  Tantric practices in Tibet go into exhaustive detail into the process of death, and view it as a vital opportunity to momentarily touch the subtlest aspects of mind and the Buddha-nature that pervades all of us.  

The bardo concept is also applied to the moment-to-moment deaths we all experience, as our consciousness changes, adapts and reforms itself continually:

Each moment is said to give us a glimpse of the bardo, the intermediate state between death and rebirth, since every moment of mind passes away and is replaced by a successive moment. Reflection on one’s own mental processes graphically indicates the fleeting nature of consciousness: thoughts flow along in unending succession, each one giving way to its successor. Cognitions and emotions change in response to our experiences and perceptions, and even our most cherished ideas and aspirations are subject to change. Thus, for a person who has awareness of death, every moment becomes a lesson in death and impermanence. (Ibid., p 328)

Buddhists as a whole, and Tibetan Buddhists in particular, encourage continual awareness of death and its finality, and have developed detailed practices aimed not at avoiding death, but using its power to progress further on the path to liberation.  These practices are not particularly obscure; the Tibetan Book of the Dead is widely known through The Tibetan Book of Living and Dying by Sogyal Rinpoche, an international bestseller.  Death meditation in the traditional form outlined by the Buddha is still practiced in Thailand, and the original sutras on death and impermanence are freely available in English.  That being the case, I struggle to understand how Buddhism can be characterised as a religion that avoids death; even a brief look at Buddhist literature on the topic shows that Buddhists confront death and mortality very directly, and specifically encourage adherents to develop a continual awareness that death stalks us all.**  

Unfortunately, this erroneous presentation of Buddhism’s attitude toward death is a continuing thread in the book, and at times presents what seems to me a rather colonialist view on Buddhism.  A vibrant and complex system of thought is lumped in amongst ‘Eastern religions’ with no attempt made to distinguish it from other, equally nuanced approaches to these critical human questions: 

In Eastern religions , as with the monotheistic tradition, death is ultimately something that is avoided. It’s not just that it can be avoided. It is essentially avoided. If we can put it this way, it is unavoidably avoided. Whatever happens to your body (or your bodies), you continue to exist.

This passage positions Buddhism — and all ‘Eastern religions’ — as avoiding death, and not only that, but forcing one to exist continually.  The core concept of Buddhism centres on breaking out of that cycle, so death is not ‘unavoidably avoided’ — the whole point of Buddhist practice is to achieve enlightenment, and thereby break the cycle of death and rebirth.  While it is true that one may be stuck in samsara forever if no action is taken, the moment one becomes a Buddhist, one is attempting to avoid this endless loop.

May goes on to contrast Buddhism with Taoism, claiming that Taoism is more consistent in its beliefs than Buddhism:

Taoism, like Buddhism, takes the concept of the self to be illusory. There is simply the unfolding process of the cosmos, and what appears to be a self is nothing more than a moment in that cosmic unfolding. But, unlike those Buddhists who believe in reincarnation, Taoism is more consistent in this regard. Reincarnation has implicit in it the idea of a self. That self may disappear again when it reaches nirvana, but at least it remains throughout a series of lives.

Leaving aside this additional wholesale dismissal of centuries of Buddhist thought on these issues, again the description of Buddhist beliefs here is not accurate.  As we know by now, Buddhists do not believe in reincarnation, and there is no independently-existent self or soul that remains throughout our numerous lives.  The elements of mind that continue to the next life do not include the grosser consciousnesses and physical aggregates of our previous lives, and therefore do not represent a continuation of the same existence in the way that a transference of self or soul would imply.

Taken as a whole, the overriding impression is that May has taken a view of Buddhist thought that seems quite common among Western thinkers.  Buddhism is a highly developed and systematic philosophical system, encompassing enormous numbers of sutras, commentaries and analytical works investigating the nature of the mind, consciousness, the nature of reality and the Universe.  Perhaps due to the systematic approach Buddhism takes to these questions, we have a tendency to view Buddhism as more of a ‘scientific’ take on these topics than other religions, and that leads some to conclude that we can carve off and recombine bits of Buddhist thought in whatever way suits our argument.

This is true to an extent, in the sense that Buddhists do not believe in a God or gods, or a system of divine judgment that sorts us into Heaven or Hell.  We must reap the consequences of our actions due to kamma, but kamma is more of a law of nature rather than a divine system of accounting.  Therefore, one can do whatever one likes with Buddhist thought from that point of view, since no one is watching, so if you don’t care about suffering or the conditions of your next rebirth, then there is nothing stopping you.

But there are certain aspects of Buddhism that cannot be separated out without dismantling the whole belief system.  Kamma (karma), dukkha (suffering), anatta (non-self) and rebirth are among these; without these concepts, little of Buddhism remains.  Without kamma there is no need to practice the Noble Truths, and no next life for which to plant the seeds of good actions; without dukkha there is no need to seek liberation; without anatta we lose the balance between concerns of this life and the next that define the approach of Buddhism to human existence; and without rebirth there is no samsara to escape or dukkha to eliminate.  So when May denies anatta, he denies Buddhism, and presents instead a caricature which suits his argument but does not reflect the reality of Buddhist thought and practice.

Speaking more broadly, I wish that Western thinkers in general would examine why they feel able to dismantle Buddhism in this way, in a way that we do not see as often in relation to Western monotheistic traditions.  Taking anatta out of Buddhism is like taking Jesus Christ out of Christianity — self-evidently ridiculous, and in doing so we would no longer be talking about the same system of thought.  Yet we often see Buddhism approached like a menu of disparate concepts to be recombined at will.  I suspect that Buddhism being more distant, more ‘alien’ to us allows us to pry it apart without feeling we must maintain the integrity of these concepts. 

However, Buddhism has been highly accessible in the West now for decades, and one can easily find native Westerners who are serious Buddhist practitioners and monks/nuns throughout our hemisphere.  So why do so many thinkers not even take the step of contacting these practitioners to check their understanding?  To me it feels disrespectful, and dismissive of a way of life that defines existence for many millions of people.  To say we can extract what we like from Buddhism and discard the rest unmakes the hard work of not just the Buddha himself, but untold thousands of scholars and monks who succeeded him.  When discussing Christianity, we consider it as a system of thought and respect its great scholars of theology like St Augustine, St Thomas Acquinas, and Martin Luther.  When discussing Buddhism, why do we instead break it apart, and ignore great minds like Nagarjuna, Vasubandhu and Buddhaghosa?   This disparity particularly stands out in this book, where ancient philosophers like Marcus Aurelius get their due, but Buddhist scholars of India existing at the same time bear no mention.  

What particularly disappoints me in this case is that May’s search for a synthesis, a viewpoint on death that accepts its finality while not being consumed by it, is what actually-existent Buddhism attempts to offer us.  The Buddha explicitly denies nihilism, which denies a purpose to existence and excuses numerous bad actions in one’s short life, and the existence of a soul/afterlife, which distracts one from the import of this life.  In Buddhism, when one dies, one’s existence in that form is over, so we must make the best use of our limited time; but that existence affects subsequent ones through kamma, so a single-minded focus on only our moment-to-moment struggles is not enough to achieve liberation.  Buddhism says that this life matters, death is an end, and yet we are not consumed by that thought; our karmic actions take root beyond this momentary existence, and though all things are impermanent and must end, we all have the ability to contribute to freedom from this suffering, not just for ourselves, but for all sentient beings.

Now I do not mean to suggest that May should take this view, or agree with this synthesis as the best one.  Nor does he have to present a detailed critique of Buddhism as a whole, particularly given just how dense Buddhist thought is on these questions.  But I would have liked to have read a version of this book that addresses the perspective of actually-existent Buddhism on a basic level, and apprehends it with the same sensitivity and care that he provides for other ways of thinking about death and mortality.  

At its core, May’s project is a worthy one.  I agree with him that avoiding the reality of death is problematic, and in doing so we deny the essence of what it means to be human.  I would even say that our experience of coronavirus this year has underlined the hazards of pushing death to one side; we have a well-developed ability to ignore death that does not actively affect us, and so we find ourselves shockingly adept at ignoring the hundreds of thousands of needless deaths we have caused due to the wilful incompetence of many of our governments.  If we sought not to ignore death, but to embrace it as a motivator for human existence, then perhaps we would have a wholly different reaction to the tragedies unfolding all around us.

My objection to May’s take is simply that, as a student of Buddhism, I would have liked to see its approach critiqued accurately in the context of this project.  Instead, we are given a version of Buddhism divested of its core concepts, and the incoherent result is dismissed as unhelpful and illogical.  For me, this seriously damages what is otherwise an accessible, empathetic and powerful take on the central importance of mortality in human existence.

——

*I should note here that I’m providing a very basic explanation, and one coloured by my study of Mahayana traditions like Soto Zen and Tibetan Buddhism; for a more complete picture that includes other strands of Buddhist thought, the Stanford Encyclopaedia of Philosophy has a nice article summarising concepts of mind in Indian Buddhism/Theravada.  For Mahayana/Vajrayana concepts, accessible works by His Holiness the Dalai Lama (Approaching the Buddhist Path), Vietnamese Buddhist monk Thich Nhat Hanh (The Heart of the Buddha’s Teaching) are good starting points; alternatively, the brave may wish to start with Nagarjuna and go from there!

**Just to reinforce the point, here is a sample death meditation from the Dzogchen preliminary practices in Tibetan Buddhism (translated from Heart Essence of the Vast Expanse, by Jigme Lingpa):

Second, meditate on the impermanence of the beings that inhabit the universe. Even the sages and gods, with their eon-long life spans and majestic brilliance, cannot escape their own mortality. What, then, of those of us on earth, born as we are at the end of an age in a place where the life span is indefinite? We too will soon be dead.

What were once thriving villages and monasteries are now empty and deserted. Once inhabited by great individuals, they are now home to nothing more than birds and mice. Just look at your own parents, friends and relatives, fellow villagers, neighbors, pets, and so on. Of those that you can recall, most of them are now gone. Some of them were alive just last year, but this year they are no more.

More specifically, in your present circumstances you feed your body good food, dress it in the finest clothes and jewelry, and maintain a healthy lifestyle. Despite all this, your life is getting shorter with each passing day. Death will arrive before long, and when it does, your breathing will become labored and your face will grow pale. Your limbs will twitch and your mind will grow delusional. In the end, you will end up a corpse, your body tied and covered with cloth. Cast naked into a charnel ground, your limbs will be hacked apart and eaten by vultures and wild beasts, with even your hair and bones torn apart and scattered here and there. When all this happens, your loved ones and possessions will not go with you, yet leaving them behind will seem unbearable. Your karma alone will dictate what happens. Such a time could even arrive today or this evening. You can’t be sure!

With a sense of urgency, think about how unbearable this actually is. As you continually familiarize your mind with this idea, when you move, sit, or lie down, you can even say to yourself, “This is my very last act in this world!”

This is but one of many examples of such practices.  Having seen how disarmingly, brutally direct these meditations are, how can we say that Buddhists avoid the reality of death and mortality?

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Permute Update: Now available in Ai Ai!

Since my first post on my game Permute, there’s been a very exciting development.  Thanks to the efforts of Stephen Tavener — thank you, Stephen! — Permute is now playable in his wonderful abstract-gaming mega-package Ai Ai!

Ai Ai is a fantastic, and free, collection of many dozens of excellent abstract games, all playable online or against various strong AI opponents.  I’ve talked about it in my Connection Games series a few times, but I can’t emphasise enough how essential it is if you have any interest in this category of games at all.  Ai Ai includes everything from classics like Go, Chess and Draughts, to modern legends like Amazons, Havannah, Symple, and Catchup.

Ai Ai is particularly great if you like to experiment with games.  The platform is incredibly robust, and with some simple modifications to the MGL files that define the parameters of each included game, you can try out ludicrous variants of your favourite games and Ai Ai takes it all in stride.  As you can see in my post on Symple, you can play games on ludicrously large boards if you like, or modify starting positions, and so on.

Even better, Ai Ai is festooned with super-interesting analysis functions that you can use to investigate all the included games.  You can generate opening books and endgame puzzles, produce detailed statistics on game complexity, create detailed reports on branching factors throughout a typical game, and much, much more.  I used Ai Ai to generate a full report on Permute, which Stephen has uploaded to the Ai Ai website here.

A big part of the reason I was so excited to have Permute in Ai Ai is because of these analysis functions.  While my initial testing of Permute showed that the game is fun and allows interesting strategies to develop, there were a couple of lingering questions:

  1. Draws are theoretically possible on the recommended even-length board sizes (12×12 and 16×16).  How likely are draws in typical play?  Is it possible that high-level Permute play could become infested with draws?
  2. Permute does not use a balancing protocol like the swap rule we use in many other games like Hex or Havannah.  Is the game balanced enough as-is, or does the first or second player have an advantage?  Should I add a balancing protocol?
  3. Is it possible that symmetric playing strategies might break the game?

The Ai Ai report helped alleviate my concerns on these three aspects.  While of course these results shouldn’t be taken as gospel, I’m comforted by the fact that in 88,891 games played by the AI, not a single one was drawn!  On top of that, the winning chances for each side across all those games was 49.99% for Orange and 50.01% for Yellow — nearly perfectly balanced.  Finally, Ai Ai attempted to win with various mirroring strategies, but lost every game in those instances.  Permute might still prove to have issues on these fronts when attacked with superhuman neural-net AI, or super-strong humans, but at least I can rest assured that the game doesn’t break too easily.

Playing Permute in Ai Ai

When you load up Ai Ai, you can find Permute in the ‘Combinatorial 2020’ category, which you can find in a folder if you go to the File menu and click ‘Choose Game…’.  Once it loads up you’ll be presented with a dialog box to choose a few options:

  • Resign when hopeless?  This means that the AI will determine when it has no chance to win, and will resign at that point rather than playing on.  This is a very convenient feature, though for new players it might be worth playing a few games without it on, so that you see games all the way through to the finish.
  • Alternate setup?  This allows you to choose the alternate starting position with a 2×1 chequerboard pattern rather than the standard chequerboard.
  • Board size:  Here you can choose the size of the board, ranging from 8×8 to 24×24.  The default is 12×12, which is a good size to start playing on.  When you want a deeper, longer game, I’d go for 16×16.

After choosing your options, you’ll see something like this:

permute-screenshot1

Here I’ve loaded up a 16×16 game with the standard chequerboard setup.  If this is your first time starting Ai Ai, you may find the default will be for you, the human player, to play as Orange and the AI to play as Yellow, but you can change this to Human vs Human or AI vs Human or AI vs AI using the AI menu.

Stephen has implemented a very handy system for making moves in Ai Ai that uses mouse-dragging to determine which direction your twists will go.  To make a clockwise twist, locate the 2×2 face you want to twist, and click and drag from the top-left of that face to the bottom-right; to make a counterclockwise twist, drag from the bottom-right to the top-left.  After that, just click on one of your just-twisted pieces to bandage it, and there you go — your first Permute move!  If at any time you need a reminder of how the moves work, just click the Rules tab on the right side of your Ai Ai window.

Once you get used to the input method you’ll find Ai Ai is an incredibly convenient and flexible way to play the game.  By changing the AI thinking time in the AI menu, you can tailor your opponent to your skill level.  Beware, Ai Ai can be very strong if you give it lots of time!  To give you an idea of what Ai Ai plays like on higher thinking times, here’s a sample AI vs AI game played with ten seconds of thinking time per move:

This game was quite a good one, a close back-and-forth battle.  As is typical from the AI, the game was fought initially in the corners, and once territories took shape there, both sides extended into the centre to battle for dominance there.  This seems a good way to open a game of Permute in general — territory is easier to secure along the corners and edges with fewer bandaged pieces required, and once some gains have been made in those areas the protected groups can be used as a base to stake a claim on the centre of the board.

Just for kicks, here’s another sample game played on a 24×24 board, this time with 5 seconds of thinking time per move:

As readers of this blog will know, I generally love playing abstract games on larger boards anyway, but I particularly love playing Permute on big boards.  There’s something extremely satisfying about seeing these huge chequerboard patterns gradually coalescing into interestingly-shaped blocks of colour.  On the larger boards there are tantalising hints of fascinating strategies lurking in the distance; as you’ll see in the game above, the AI battled itself across the whole board, and intriguing local battles eventually linked together into larger contests as the game evolved.  Playing on a physical board this size might be a bit challenging, not just in terms of space but also in terms of keeping track of group sizes, but since Ai Ai takes care of both those problems, I highly recommend trying some bigger boards when you have time!  In truth 16×16 will stay my recommendation for tournament play, but I can say for sure that 20×20 and 24×24 have real potential, and the resulting games still take less turns than a game of 19×19 Go to play out, given that each move affects a decent-sized chunk of the board.

What’s next?

I hope the info above might convince you to give Permute a try using Ai Ai.  This program is essential for any fan of strategic games regardless, and the implementation of Permute is just perfect.  The AI plays a tough game, and you can easily experiment with larger board sizes and the alternate start position.  As you can probably tell, I’m hugely excited to have Permute available on Ai Ai, and I’m enormously thankful to Stephen Tavener for taking the time to implement it!

Hopefully this won’t be the end of exciting news for Permute.  I’ve been speaking with some very talented designers about the game, and earlier today I received a beautiful concept for a purpose-built physical game set for Permute that just blew me away.  Abstract games are a bit of a risk for publishers compared to more accessible, flashier board games with fancy bits, but nonetheless I do intend to keep investigating if this game could be realisable physically.  In the worst-case scenario, perhaps we could offer 3D-printed game sets for fans to purchase, if publishers don’t want to take a chance on it.

In any case, I hope you’ll download Ai Ai and give Permute a shot!  Let me know how you get on with it.  Keep an eye on these pages for more updates on the game, and hopefully some strategic tips and tricks as I gradually become less awful at it 🙂

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Permute: A Game About Twisting Things

As some of you are aware, one of my hobbies besides games is solving twisty puzzles, also known as 3D rotational puzzles.  The most famous example is the legendary 3x3x3 Rubik’s Cube, but since that set the world alight some decades ago a fascinating community of twisty-puzzle designers has emerged, producing some truly outrageous puzzles.  Here’s a few examples from my collection: 

So, as challenging as the Rubik’s Cube is, these days you can get puzzles that quite simply put it to shame.  I love the challenges presented by these amazing puzzles, and in recent months I’ve been trying to develop a way to bring the joy of twisty-puzzling into the world of abstract strategy gaming.

A new core behaviour: the twist

The key properties of twisty puzzles that makes them so challenging is the way in which the twistable faces of the puzzle interact with one another.  Any time you twist a face on the Rubik’s Cube, or any of the monstrosities above, you are forced to disrupt some of the work you’ve already done.  This creates a feeling of tension and danger when you’re first learning to solve a new puzzle; you’re acutely aware that at any moment, a wrong move or two could re-scramble the puzzle and essentially send you back to the beginning of the solve.

I wanted to capture this feel in the form of a two-player abstract game, so I began to cast about for examples of games that used twisting mechanics to shuffle pieces around.  Probably the most famous example in abstract games is Pentago:

Pentago Game from Mindtwister USA, Black-Natural/Solid Birch: Amazon.co.uk:  Toys & Games

In Pentago, players place marbles on the board and rotate the clever 3×3 sub-boards in an attempt to build a line of five of their pieces before the opponent.  The board rotation does create an enjoyable feeling of chaos in the game, but I had to immediately dismiss this idea for my game.  In a Pentago-type game with rotatable sub-boards, the sub-boards don’t actually disrupt one another; the relationships between stones can shift as they rotate around, but the sub-boards can’t actually scramble each other, as the faces do on a Rubik’s Cube.

I soon realised that the best way to replicate the behaviour I wanted would be to allow the players themselves to define the axes of rotation.  This wouldn’t really be possible with a physical board, though — how could you build a board where any sub-board of a certain size on it could twist?  

Instead, players would select an area on the board — a 2×2 or 3×3 subsection — and rotate the pieces within it, as if the board section below them had rotated like the face of a Rubik’s Cube.  This would capture exactly what I wanted: rotations could overlap with one another, allowing pieces to get twisted around and then re-twisted and scrambled up in other newly-created ‘faces’!

Then I embarked on a series of experiments to work out how best to implement these face-twists.  My first impulse was to allow players to rotate 3×3 sections of pieces, since the 3×3 Rubik’s Cube is so iconic.  However, I soon found that, while it was definitely fun, for a serious game 3×3 twists were simply too confusing.  The board state changed so much on each turn that trying to build strategic plans felt a bit fruitless.

I finally decided on 2×2 faces as the sweet spot — four pieces were still moving every turn, creating interesting situations on the board, but there wasn’t so much disruption that calculating future moves became impossible.  The core twisting behaviour of Permute was born:

Permute-twist-demo

Here Yellow selects a 2×2 ‘face’ of pieces and twists them 90 degrees clockwise.  At the start of the move, neither player had orthogonally-connected groups on the board; at the end of the twist, both players have two groups of three.

This behaviour would allow for the possibility of disrupting groups with further twists, which was another key concept of the game for me:

Permute-twist-demo response-01

After the move above, Orange strikes back by twisting a face just to the south of Yellow’s last move.  By twisting that face clockwise, Orange wrecks Yellow’s bottom-right group and boosts his own upper-right group from three connected pieces to six!

From here the overall shape of the game fell into place in my head almost automatically:

  • I wanted the players to focus on permuting pieces around the board, without additives like placing additional pieces or removing them through capture.  That meant the board should start already full of pieces.
  • The most interesting task to do with 2×2 twists would be to connect groups, and this would also mirror the act of ‘solving’ coloured pieces on a Rubik’s Cube.  I could keep the game tactically spicy by restricting connectivity to only horizontal or vertical; this would ensure that players could slice groups in two with twists that changed connectivity to diagonal only.
  • If the goal of the game is to build the largest orthogonally-connected group of pieces, then the fairest start position would be one where not a single piece of either side is connected orthogonally — a chequerboard pattern.
  • To ensure that players had to keep the whole board in mind and not just fight over the biggest chunk of pieces, the Catchup scoring mechanism — where if the largest groups are tied, then the player with the biggest second-largest group would win; and if those are tied, then check the third-largest, etc. — would be perfect.  That would ensure players would also need to build and preserve secondary groups, in case scoring went to the wire, and would prevent the game descending into a non-stop back-and-forth slap-fight over the largest group without opportunities to play distant strategic moves.

The game already felt nearly done!  I tested out the chequerboard starting position and twisting mechanics on my Go board with some colourful plastic pieces, and I found it was easy enough to play even with physical components.  Everything felt right so far, but I still had a problem:  how to get players to stop twisting?

Bandaging

A clear issue with the game at this point was a lack of termination.  Players could endlessly twist pieces back out of position, preventing their opponents from making any serious headway.  I needed a way for moves to have some finality, and create permanent changes in board state.  That’s when I decided to take a break and play some Slyde:

slyde16-10s-1

In Slyde, players take it in turns to swap one of their pieces with a horizontally or vertically adjacent neighbour of their opponent’s colour.  After the swap, the active player’s piece becomes pinned in place and can’t move for the rest of the game (and the opponent can’t swap with it). 

This was exactly the kind of thing I need for Permute!  Since a twist moves four pieces, and up to three of them could be of the active player’s colour (twisting four would be meaningless so I excluded that as a possibility), then a player’s move could consist of two parts: a twist in either direction, followed by fixing one of their pieces in place permanently.

That would accomplish what I needed — each move would have some finality, but since only one piece would be fixed in place, groups would still be in constant danger of disruption without further moves to shore them up.  Giving players a choice of which pieces to fix in place added an additional strategic element to the game, enabling players to try to optimise their twist/fix combo to achieve the best result in terms of securing territory and/or denying territory to their opponent.

With this final element now in place, I had a complete game — the initial position, goal, end condition and moves were all set.  I decided to call the piece-fixing ‘bandaging’, a term derived from twisty puzzles.  Bandaged puzzles have certain pieces glued together so that in some positions certain moves would be blocked; the term also refers to states in some puzzles where twists in certain directions are blocked.  The term comes from the fact that bandaged puzzles were made in the early days by using Band-Aids to stick pieces together on the Rubik’s Cube.

Playtesting

Now that the rules were set, I started playtesting the game, first with trial matches against myself.  The game seemed roughly balanced in my tests on 9×9, 10×10 and 12×12 board setups.  The core twist/bandage dynamic was enjoyable and gave each player’s turn a couple of interesting decisions to make, and each move felt like a tradeoff between securing territory and sacrificing future mobility, which was just the kind of feel I wanted.

The final test was a playtest match against Phil, which we did via a convoluted setup involving sharing my Adobe Illustrator screen over Google Meets.  Phil is quite good at most games he tries, so I felt confident he’d be able to tell if the game was obviously broken pretty quickly.  We had an enjoyable match, and true to form, Phil took a convincing win:

Phil told me that while it took a bit to get used to the twisting aspect, he could see that there was room for interesting strategies to develop, and he felt engaged by the action throughout the game.  At that point I felt it was an appropriate time to share the game with the wider world and get some more feedback, so I typed up the final rules and put together a thread on the BoardGameGeek Abstract Strategy forum.

The Rules

Here are the final rules, as presented on BoardGameGeek (well, tided up a bit):

The basics: Permute is a game about twisting things, inspired by twisty puzzles like the Rubik’s Cube. The name comes from one of the two main things we can do with pieces in a twisty puzzle: permute them (shuffle their positions); or orient them (change their facing). In this game players take it in turns to rotate 2×2 sets of pieces (‘faces’) on the board, in an attempt to bring pieces of their colour together in larger groups. Once a face has been twisted, part of it is locked in place (‘bandaged’) and can’t be twisted again. When no more twists are possible, the game is over and the players’ largest groups of pieces are scored. To win the game, you must permute your pieces so that they form the largest connected group, and deny your opponent the chance to do the same!

The rules: Play proceeds on a square board with a 9×9 grid (or larger). At the start of the game, all squares are filled with alternating Yellow and Orange stones in a chequerboard pattern.

Definitions:

Face: a 2×2 subset of the board surface. A face may not extend off the board.

Bandaged Stone: a stone with a token, sticker, or other marker on it that indicates it may not be twisted again.

Bandaged Face: a face containing one or more bandaged stones. A bandaged face cannot be twisted.

Twist: a move in which all the pieces in a face are translated around that face simultaneously 90 degrees in either a clockwise or counterclockwise direction, as if rotating the face of a 2×2 Rubik’s Cube.

Group: a group is a set of same-coloured stones connected orthogonally. The value of a group is the number of same-coloured stones it contains.

Orange plays first. The swap rule can be used – after Orange’s first move, Yellow may choose either to play their first move or change their colour to Orange.

Players then take it in turns to twist one non-bandaged 2×2 face containing at least one of their colour stones 90 degrees clockwise or anticlockwise. Once a face has been twisted, the player who twisted it must select one of their stones in that face and place a token on it, thereby bandaging it.  Faces containing a bandaged stone cannot be twisted.  Faces consisting entirely of one colour cannot be twisted either, so this is not a way to pass a turn (but mono-colour faces can be disrupted by twists of neighbouring faces, of course).

The game ends when no more twists can be made. At this point scores are compared. The player with the highest-valued group wins; if both players’ largest groups are equal in size, then compare the second-largest, then the third-largest, and so on until a winner is determined.  If the board is even-sided and the scores are somehow equal all the way down, then the game is a draw, but this should be very unlikely (and outright impossible on odd-length boards).

Translation for non-gamers

That looks like a lot of rules, but really it’s a pretty simple game!  There are two players, Orange and Yellow; Orange plays first.  Each turn, the active player must select a 2×2 sub-section of the board (a ‘face’) and rotate the pieces in it 90 degrees clockwise or counterclockwise, just as if they were rotating the face of a 2×2 Rubik’s Cube.  Once the twist is done, they must choose one piece of their colour in that face and bandage it; once a piece is bandaged, it can’t ever be twisted again.  

As the players make more and more twists and bandaging moves, gradually the board will get more and more constricted.  Since faces with bandaged pieces in them can’t be twisted, moves will be blocked and players will start to have secure territories built up.  Once no more moves are possible at all, players count up their largest groups of pieces of their colour; a group is a set of pieces that are connected horizontally or vertically, diagonal connections don’t count!  See the pictures from the game between Phil and myself for a scoring example.

The player who built up the largest group of their colour wins the game.  If both players’ largest groups are the same size, then compare the second-largest groups of each player, and the largest of those two groups wins.  If those are still tied, then check the third-largest, and so on.  

So, winning a game of Permute means you have to bring your pieces together into connected groups, but because twists can disrupt so much of the board, you have to work hard to protect them!  That means bandaging pieces strategically, to hopefully prevent your opponent from tearing apart everything you’ve worked so hard to build.  Once you play for a bit, you’ll start to see ways to build your groups while simultaneously blocking or disrupting your opponent, and that’s when you’ll start to really enjoy what Permute has to offer.

Alternate starting positions

The default chequerboard starting position works well, which is why I chose that as the ‘official’ starting position in the rules.  However, during testing, Phil had suggested the possibility of an alternate starting position that might be easier on the eyes.  We worked out that a chequerboard pattern of 2×1 blocks could work well, and had another advantage in that early-game twists would immediately create some bigger connections, which could be helpful for new players who may have more trouble seeing groups right away:

In the discussion on BGG, Steven Metzger pointed out that playing on a 13×13 board would forbid the possibility of draws, and would also mitigate a possible first-mover advantage by giving the second player a stone advantage:

F2L-13x13 -- NEW start position --Orange-Yellow-01

Ultimately I’m not sure that draws will be much of a problem anyway, as maintaining precise parity across every group down the size order would be pretty unlikely, but it’s good to have the option.  Plus in a matchup between two players of uneven strength, giving the weaker player the side with extra stones on the board in this setup could help them be competitive.

However, it’s not immediately clear how to replicate the alternative 2×1-chequered start position on an odd-length board; Phil had some ideas about this which could work, but the setup would be more awkward on a physical board.  We’ll keep trying though, eventually we’ll find a good alternative.

Permute on MindSports

I was generally pleased by the reaction on the BGG forums; most posters seem interested in the game, and had some good suggestions about the visuals.

Most exciting for me was that Christian Freeling, a designer I’ve spoken about quite a bit in these pages, was immediately positive about the game.  This meant a lot to me, not just because I’m a fan of several of his games, but also because he’s got a very strong intuitive sense about whether a game will work or not; for him to say that he felt “it is immediately obvious that it works (without endless modifications)” gave me a big boost in confidence.  

Christian is also the proprietor of MindSports, a website that hosts all of his games for online and AI play, as well as some games from outside contributors.  Lucky for me, Christian and Ed van Zon decided to implement Permute on MindSports, so now anyone can play Permute against the AI or against other people (via the MindSports Players Section)!

This was tremendously exciting for me — not only is Permute now playable easily in a digital format, but it’s sat in the MindSports website right below Catchup and Slyde!  As I described above, these two games gave me inspiration I needed to get Permute to its final form, and both are really excellent games, so I feel privileged to be sharing a page with them.

I’ve spent the weekend making some YouTube videos about Permute and writing this post, so I haven’t yet dived into online play, but I did have a couple of matches against the AI.  The AI isn’t super strong but it’s still a fun time and a great way to learn the game:

Now that my first promotional push for the game is completed, I’m happy to accept challenges for games on MindSports, so please let me know if you fancy a game 🙂

Where next?

I’m really happy with how Permute turned out, and as people are playing it here and there I’ve had some great feedback on it.  That being the case I’m not planning to make any further changes to it, beyond perhaps adjusting the starting position if computer analysis finds a strong advantage for either player or something.

However, the core twisting mechanism does have lots of potential for future development.  I have two new twisty experiments I’m working on right now: a four-colour twisty game on a hexagonal grid; and a square-grid game where players only twist, and no bandaging happens.  The latter is a difficult design challenge, so if you have thoughts about it feel free to air them in the BGG discussion thread on the topic!

Twisty experiment -- game 1-01

The initial test of the idea in that thread (shown above) has some potential, but definitely needs some work.  In this game, players only twist 2×2 faces, and pieces become fixed in place (‘solved’) when they join a group of pieces connected to three or more neutral edge pieces.  There are some other ideas in the thread that I think are worth investigating too, and ultimately I think some synthesis of these concepts will produce a good game.  However I’m going to let all this simmer in the back of my head for awhile, and keep most of my attention on enjoying Permute for now.

In the meantime, I hope some of you out there will give Permute a try!  Go check out MindSports, have some games against the AI, and get in touch if you want to have a game with me.  I hope that some more strong players will have a go at the game, and that soon we may see some interesting tactical and strategic concepts develop.

I’ll do some follow-up posts on Permute in the future and show off some sample games with interesting play, so please look forward to that.  At some point too I’ll reveal Permute’s other twisty siblings once they’re in good shape 🙂 

If you’re dying for more Permute content, please do check out my YouTube videos: I have a short intro to Permute with some sample moves; a longer intro with a full sample game against the AI; and finally a video introducing Catchup and Slyde alongside the wonderful Ai Ai game-playing platform.

So, give the game a shot and let me know what you think!  Perhaps I’ll see you on MindSports.  Before I go, I wanted to say another heartfelt thanks to Christian and Ed for putting Permute up on MindSports, and to Nick Bentley and Mike Zapawa for creating Catchup and Slyde respectively, without which Permute might have just stayed as a weird twisty concept in my head and never become a playable game.  

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