Tag Archives: Abstract Games

Reviewing (almost) all the games on MindSports

UPDATE 6 Nov 2021 — Oust review updated, thanks to finally having a breakthrough!


Christian Freeling’s MindSports site is an essential destination if you want to play some good abstract strategy games.  Christian’s own games take centre stage, of course, but numerous other games, both traditional and modern, are also featured.

During the pandemic I’ve taken the time to try out most of the games on MindSports, either against AI or using my collection of various printed boards.  I was keeping my impressions in a little text file, mainly as a reminder of what to focus on in future blog posts, but have decided to put them up here in case they might help anyone looking for something to play but perhaps lacking the time to try everything until they find a hit.

Before I start I’m going to do something I wish other reviewers did, which is provide a summary of my general perspectives on games.  Hopefully this will give you an idea of where I’m coming from, and will help you interpret my mini-reviews in that light.

  1. I value games with tradition, that have survived centuries of scrutiny, and that have a culture that has grown around them.  However, I also love experimenting with new rules, and with variants of existing games.  So in that sense I probably would annoy both the traditionalists and the cult-of-the-new types.
  2. Simple rules are nice, but as a regular player of very complex board games,  I tend not to consider rules simplicity a particularly important factor in my evaluations of games.  A good game is good regardless of how long the rules document happens to be.
  3. I have dabbled in game design but above all I’m a player.  With that in mind I’m trying to avoid terms like ‘arbitrariness’ or ‘inelegance’, which are ill-defined terms that relate to mostly to rulesets and not gameplay.

And my scoring system, which uses the entire 0-10 scale:

  • 0-2/10: I do not like this.
  • 3-4/10: There are other similar, and better options available.
  • 5-6/10: Good but not earth-shattering.  Worth a try if you like that sort of thing.
  • 7-8/10: Very good games that deserve your attention, even if you’re not normally into the genre.
  • 9-10/10: Games that are either modern classics or traditional classics.  Potential lifestyle games.

While I’m here, a disclaimer: these opinions are intentionally brief, to-the-point, and somewhat flippant.  I don’t claim any particular authority here, so do yourself a favour and don’t take these overly seriously!

With that out of the way, let’s start with the games in The Arena.

The Arena

Christian’s six essential games

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Grand Chess Christian’s 10×10 Chess variant adding the Cardinal (Bishop + Knight) and Marshal (Rook + Knight) to the traditional lineup.  On the whole this is a decent variant, but I have some issues with this game — the Cardinal/Marshal were first used by Pietro Carrera in 1617 and at this point are not very exciting; the initial position allows Marshals to be traded off too easily; the removal of castling is unnecessary in my opinion; the presence of three power-pieces of similar value dilutes the excitement of the game somewhat; and the piece density is too low for my taste, making for a big game that doesn’t actually expand Chess’ strategic/tactical landscape as much as I would like.  What really bugs me is the promotion rule, which needlessly punishes early promotions and leads to the awkward rule forcing Pawns to remain in suspended animation if no captured pieces are available.  I don’t like that rule in the historical variants that include it, and I don’t like it here either; just let me promote stuff, promoting stuff is fun!  Honestly I would probably score this game higher, except that in its wake this promotion rule appears to have become more popular, which is a problem for me.  In any case, Grand Chess is fun but there are other 10×10 variants I prefer over this one, and I still plan to feature some of these in a future post eventually (a recent favourite of mine is Expanded Chess).  4/10.

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Dameo Christian’s highly-regarded Draughts variant, often touted as a replacement for 10×10 International Draughts.  Unfortunately, this game doesn’t quite work for me.  The linear movement aspect feels out of place in a Draughts game, and the kings are a bit too strong for my taste.  Various people have told me I’m wrong about this, but I can’t shake the impression that breakthrough is the critical factor in this game, and that getting a king first is a very strong indication that player will win.  I can, however, see why people like this game, so I give it a good score on that basis; certainly opening play will be varied, and the draw rate is low.  Personally I’d rather play Croda or Turkish Draughts though.  6/10.

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Emergo Here Christian boils down column checkers variants like Bashni and Stappeldammen to their essentials.  The result is a frantic tactical game characterised by a somewhat confusing placement phase, followed by a violent explosion of captures in all different directions.  The game is most definitely unique and at times feels brilliant, but I’m not much for placement phases in Draughts (or Chess, for that matter), and I do find myself missing the incessant forward motion inherent in Bashni and Stappeldammen.  Definitely worth a go if you haven’t tried it.  If I can ever get past the placement aspect, I feel this game could become a favourite of mine.  7/10.

Sygo A Go variant that uses the Symple move protocol combined with Othello-style toggle-capture.  I started out a bit skeptical of this game, given my love for Go itself; most Go variants are a fun distraction at best.  Sygo however does have a distinct personality, and the Symple protocol is a slice of genius.  As Go variants go, it’s better than most, but given the choice I’ll take Symple every time.  7/10.

Symple — Formidable.  Once I sunk my teeth into this game I was blown away by how singularly unique it feels.  In Symple one can either place a single stone on its own to start a new group, or grow every group of yours on the board by one stone; the goal incentivises building small numbers of large groups of stones.  The game creates a feeling of constant tension that builds until the endgame, where precise calculation is required to squeeze out the last few points, or to force your opponent into bad placements.  Symple is one of the most remarkable and exciting discoveries to be found in modern abstract gaming, in my opinion.  10/10. (read more here)

Storisende — An extremely unusual game of territory, featuring pieces that move and split, and walls that form, and there’s just a lot going on here.  I’m not sure I can really rate this game properly, as I simply don’t understand it.  Christian has made various valiant efforts to explain this game, but I still find it confusing.  I trust his judgment, generally speaking, so I believe something interesting must be happening here, but I just can’t find it yet.  Note that Christian has written quite a lot about this game and its strategic complexities, with another article forthcoming soon; I plan to study these articles and revisit the game again in the future.   5/10.

The Arena: The Other Seventeen Freeling Games

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Yari Shogi — A 7×9 Shogi variant that uses pieces with lots of Lance-like forward movement.  Any Shogi variant is a tough sell for me, because the historical variants are so incredibly interesting.  In contrast to something like Tori Shogi or Wa Shogi, Yari feels a bit pedestrian.  Also, only one piece type can move backward at all, meaning many more games of Yari will end in an impasse as compared to standard Shogi, as the King will be very safe from attack if it enters the opponent’s camp.  I also admit to a certain dislike for attempts to ‘Westernise’ Shogi; Shogi is a Japanese game made by Japanese people, and it bothers me that we so often try to strip its Japanese-ness away, rather than meet the game on its own terms.  4/10.

Dragonfly — This game is reasonably fun, but if I’m going to play a 7×7 game with drops I’ll stick with Tori Shogi.  Dragonfly also has a hovering unpromotable Pawn thing that’s similar to the promotion rule I dislike in Grand Chess, and the Pawns can’t be dropped, which diminishes the excitement somewhat.  I understand why that rule exists in this particular game, but Christian’s claim that Chess Pawns aren’t suitable for drops is odd to me — they work perfectly well in Crazyhouse, Bughouse, Chessgi, etc.  3/10.

Chess+ I appreciate the design goal of this game, which was to create a version of Chess which eliminated opening theory without requiring some external list of starting positions like Chess960.  Unfortunately it doesn’t work that well, in my opinion.  The opening protocol adds significant cognitive load for the new player.  Messing up is very easy, and early losses can happen because the long-range power of the Chess army makes it relatively easy to punish bad placements quickly.  If you want to play Chess with placement, I recommend the traditional Burmese variant Sittuyin; this game works better, in my opinion, as the pieces are weaker and bad placements are less immediately dangerous thanks to the fixed Pawn structure.   4/10.

Chad, Rotary — I haven’t played these.

Hexdame A direct translation of International Draughts to the hex board.  Quite enjoyable, although a lot of the play seems to bunch up around the edges; granted, that happens in other Draughts variants too, but I notice it more here for some reason.  The tactics are enjoyable, and I wouldn’t turn down a game of this, but it’s perhaps a bit *too* tactical.  6/10.

Bushka — A Draughts-adjacent game inspired by the classic Fanorona.  Here pieces capture by approach rather than by leaping.  This game also originated the linear movement mechanic which made its way into Dameo.  The idea is intriguing, but in actual play I find it a bit confusing.  The games I’ve played also ended surprisingly quickly, which was a bit disconcerting given the size of the board and the number of pieces.  Colour me skeptical, but interested to learn more.  6/10.

Pit of Pillars — haven’t played this yet.

Io — An excellent showcase for the under-appreciated one-bound, one-free opening protocol.  Io is an Othello variant that starts with a placement phase, but the innovative one-bound, one-free procedure ensures that the pieces of both sides are placed in interesting ways and tends to create balanced positions for the subsequent capture-fest.  A very good game that deserves more attention.  8/10.

PhalanxThis game has several elements not usually seen in combination, bringing together placement, movement, capture, movement of whole groups, all in service of a territorial goal.  The result is complex and intriguing.  I’m intrigued by the capture mechanic, which ends up creating impassible walls around the board that gradually constrict and focus play until the inevitable conclusion.  I can’t pretend to have a good grasp on this game yet, but so far I like what I see.  8/10.

Mu VeloxThis game scares me, so I haven’t tried it yet.

InertiaThis game is a rare example of the unification genre, in which players strive to be the first to bring all their pieces together into a single connected group.  While reminiscent of the venerable Lines of Action, Inertia feels quite different due to the variable opening position produced by the one-bound, one-free opening protocol, and the movement mechanics which are easier to grasp than in LoA.  Enjoyable.  7/10.

KnightVision This very recent creation melds the classic goal and rhombic board of Hex with a focus on a hexagonal version of the Knight’s leap.  Christian’s pitch says ‘it adds drama to an incredibly deep game without affecting its depth’, but I slightly disagree; the Knight’s-move placement pushes more locality on a game that thrives on global strategy.  Having said that, the chucking of axes is very fun, and the game overall is a good experience.  But if someone breaks out a Hex board I’m going to play Hex on it over this every time.  7/10.

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Havannah — I respect Christian enormously, but his decision to exclude Havannah from his ‘games that matter’ list is forever baffling to me.  A classic by any measure, Havannah is easy to understand yet blessed with bottomless depth.  The multiple goals create a sense of limitlessness that few games can muster.  I can understand the impulse to push his fans toward his later games, and certainly he’s produced many great games after Havannah.  But equally, there’s nothing wrong with getting it right the first time.  Brilliant.  10/10. (read more here)

Starweb — A game of connecting corner cells together, with point scores growing rapidly as groups encompass more and more corners.  A beautiful melding of connective and territorial impulses, this game has been a favourite of mine since I first heard of it.  I continue to hope more players will discover the strategic delicacy that emerges on this unique star-shaped board.  I like this game so much that I asked Stephen to add even bigger boards to Ai Ai, so that I could immerse myself in the game for even longer sessions (in the collage of sample games above, the top left one is playing on the standard size-10 board, the others are on the bigger size-11, 12 and 13 boards).  Essential.  10/10. (read more here)

Scware — Here we find a noble attempt to combine the Symple protocol with a connective goal.  There’s fun to be had here; however, the restrictions in place feel rather *too* restrictive to me in the context of a connection goal.  In the sub-genre of connective Symplistic games, I think SympleHex just squeaks past this one.  6/10.

The Glass Bead Game — I’m not much of a mancala player, so I haven’t played this one yet.

The Arena: Other Contributions

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Chess — Still the greatest source of drama available on an 8×8 square grid.  This game has captured the gaming world’s imagination to such an extent that it has birthed an entire global genre of checkmate-based games and variants.  I learned this game in my youth, like many people, but only truly learned to appreciate it in my old age.  Now it’s a fixture of my daily life.  10/10.

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Shogi — Possibly the greatest game ever invented by humans.  The rules, piece movements, and aesthetics marry perfectly to create a glorious experience — a game of delicate beauty and intricate manoeuvre, combined with vicious tactics and constant aggression.  I love everything about this game, and my Shogi board and traditional pieces with Minase calligraphy (pictured above) are perhaps my favourite gaming item in my home.  If I could give this 11/10, I would.  You know what, I’m going to, this is my blog, dammit!  11/10. (read more here)

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10×10 Draughts As a kid I played Checkers, Anglo-American style, and like many other kids I played it incorrectly (with optional captures instead of mandatory).  Years later I found out that A) Checkers is unbelievably better when you play it properly, and B) a 10×10 version exists with long-range kings and backwards captures!  Boy did I feel silly once I realised I’d been playing Checkers fundamentally wrong all that time.

Incidentally, since that embarrassing realisation I’ve been somewhat relieved to find that apparently a huge number of other people also never played Checkers correctly.  Here are a few reviews of the app All-in-One Checkers on Android:

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So, on the plus side, at least I figured out my mistake eventually!  I feel for all these people who never had that moment, though.  So far as I’m aware there’s not any established Checkers/Draughts variants out there with optional capture, and thank goodness for that, because from that rule comes all kinds of tactical excitement.

Anyway, the discovery of 10×10 International Draughts was quite a moment in my gaming life.  I fell in love with this glorious game of spectacular combinations.  Christian often criticises the game for being drawish at the high levels of play, and while that’s completely true, I’m not good enough for that to be a major problem.  10/10.

Constitutional Draughts This variant of 10×10 Draughts reduces drawishness by restricting kings, forcing them to avoid crossing squares where they could be captured.  For me this substantially screws up my endgame tactical vision, and feels more awkward than Killer Draughts’ simple restriction, which also has predecessors in historical Draughts variants.  The constitutional restriction reminds me of Caissa Britannia, a Chess variant invented in 2003, which is where I first saw this concept; perhaps unfairly, Constitutional Draughts feels weirdly un-Draughts-like to me as a result.  6/10.

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Frisian Draughts — Frisian Draughts massively expands the tactical craziness of 10×10 Draughts by allowing pieces and kings to capture orthogonally as well as diagonally.  The result is very hectic, with spectacular combos appearing frequently, and often in surprising ways.  Initially I found this game too confusing, but recently it finally clicked; I played a game against a strong AI (on Lidraughts), and suddenly I found myself seeing patterns and creating robust structures that I had never thought of before.  I’m now convinced this is an excellent take on Draughts, and the tiny 5% draw rate in competitive play is a great bonus as well.  Download this 59 page guide for a great intro to the game.  9/10.

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Stappeldammen — 10×10 Draughts extended into verticality.  Like Bashni or Emergo, here pieces build stacks as they capture, and subsequent captures can re-expose stacks, leading to frequent changes in ownership.  A unique element here as that there is no promotion, meaning stacks can get stuck on the last rank until freed by the appearance of an adjacent capture target.  This seems weird at first, but I agree with Christian that it adds an interesting strategic wrinkle.  Bashni is more fun though.  7/10.

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Oust After numerous attempts, I finally had a breakthrough moment with this game.  Oust is a game with the unusual property that each game both starts and ends with an empty board.  Players may either place a stone anywhere, so long as it’s not adjacent to their own stones, or grow one of their groups on the board in order to capture an adjacent opposing group of lesser size.  The winner is the player who completely annihilates his opponent’s pieces.  Critically, each capturing move must be followed by another placement, which means that wins can appear in sudden and shocking fashion as one capture chains into another.  I found the game utterly impenetrable at first, but at last I figured out some basic strategic principles and could begin to place my pieces on the board in some sort of structured way.  Now I find the game innovative and surprising, rather than confusing and opaque.  However, I probably played about 30 games to reach this point, so be aware that you may not ‘get it’ right away.  Whether it’s worth it to you to face that learning curve is another question; in any case I would say the game deserves a few tries so you can judge that for yourself.  7/10.

Many people praise this odd game of placement and elimination, but I find it utterly baffling.  Some other games have boggled me in the past, but something kept me motivated to try again until a lightbulb eventually went off.  Here, for whatever reason, that didn’t happen for me.  I’ve no doubt this will be intriguing for others, and the uniqueness is obvious, but for me it’s an alienating, confusing experience.  Nick Bentley’s Bug is similar to Oust, and that game confuses the heck out of me too!  I played both games a bunch of times and never got the sense I was unlocking any additional understanding or improving my play in any meaningful way.  3/10.

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A treasured part of my gaming collection — a Go board made from Japanese Kaya, with the lines drawn via a sword dipped in black laquer (yes, really). The stones are the traditional slate and clamshell.

Go — The quintessential game of territory, one of the oldest games on the planet, and perhaps the most revered.  What can I say about this game that hasn’t already been said?  Go is staggeringly deep, tactically complex and strategically varied, and capable of making hours fly by as you end up completely absorbed in the infinite possibilities in front of you on that 19×19 grid.  Many people praise it for its simple rules, but I tend to stay away from that characterisation; in theory, the rules are simple, but the learning curve is steep, so it feels anything but simple as a beginner.  Go can take a while to reveal its character and richness to the newbie; beginners are often urged to dive in and lose 100 games as quickly as possible, as it takes a lot of bitter experience to grasp the basic concepts.  But if Go does end up hitting the mark for you, you may well find it takes over your gaming life.  10/10. (read more here)

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Rosette Go on a hex board has been a goal for many a designer, and Rosette makes it work through a wonderfully simple mechanism: if a player occupies all six points of a single hexagon, that group of stones cannot be captured, ever.  In a single stroke this rule compensates for the reduced number of liberties on the hex board, and allows a Go-like intricacy to flourish on the hexagonal grid.  Yes, I know it’s played on the intersections so it’s actually the dual of the hex board, but it’s hexagonal enough for me, and a great game besides!  8/10.

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Stigmergy This game started life as a Tumbleweed variant, and has subsequently branched off into its own thing.  I actually came up with the name, which apparently everyone hates, but as yet no one has come up with a better one.  Anyway, Stigmergy is a good game, substantially easier to play OTB than Tumbleweed, but also feels a bit more sterile.  I’ve yet to play the Stigmergised connection game that recently appeared on MindSports, but I suspect that might suit me a little better.  7/10.

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Ready to play a quick game of Ayu on my 9×9 Go board.

Ayu Another example of the underserved unification genre, Ayu (‘attach your units’) forces the game toward inevitable unification via an easy-to-understand movement restriction.  I’m very bad at this game but I still love it, which in my view is a clear indication that a game has something special about it.  Strongly recommended.  9/10.

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Playing 19×19 Hex on a board of my own design.

Hex — The game which looms so large in the world of modern abstract games that any connection game is inevitably compared to it.  Hex is incredibly simple to explain — take turns placing a single stone of your colour, win by being the first to connect your coloured sides with a continuous line of stones — but in play one finds endless intricacy and an innate focus on global strategy.  The more I play Hex, the more I admire it, and unlike some other games I admire, I actually thoroughly *enjoy* it as well.  I strongly recommend starting on 13×13 boards, then progress to 15×15 and 19×19, where the territorial aspects become significantly more important.  A must play.  10/10. (read more here)

The Pit

There are many games on this page, so I’m going to simply skip over those I haven’t played, to save some space!

Chess Variants

I like my Chess variants expansive and with unusual pieces, and most of these games don’t hit that mark for me.  Loonybird is fun, but divergent pieces are pretty common in Chess variants, so I didn’t stick with it for long.

Chess960 — Christian hates this game, and his complaints about it from a design perspective are reasonable, but as a player I don’t find them to be a problem.  FischerRandom/Chess960 had as its goal the elimination of opening theory, and it succeeds admirably at this without much in the way of rules changes, and now with official FIDE backing it’s easily the most important Chess variant on the planet (not the best, but the most impactful).  I’d quite like to ditch castling from FRC/960, which is awkwardly implemented in my opinion, but otherwise it’s a simple variant that allows interesting Chess to happen without 20 moves of opening prep needing to happen first.  8/10.

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Xiangqi — China’s traditional form of Chess, virtually unchanged over the last 900 years.  Played on a larger 9×10 board, yet is more tactical rather than strategic.  The feel is substantially different from FIDE Chess, in part because the concept of material value here is much less important than positional advantage.  I very much enjoy playing Xiangqi, but I prefer Janggi, which removes the river and allows the Elephants to roam free (plus they have a more interesting move).  Xiangqi deserves additional credit for gifting us the wonderful Cannon piece, which is extremely interesting to use and is an excellent addition to numerous large Chess variants (like the superb Shako and its larger relatives Zanzibar, Maasai, Gigachess, and Terachess).  The downside for me is the relative lack of Pawn structure and promotion (except for slightly stronger Pawns); however, I must admit the game works fine without these, thanks to the confinement of the King in the palace, which allows checkmate to occur even when little attacking power is left on the board.  If you want to learn more about Xiangqi, Jim Png’s excellent XQ in English site has everything you need; do check out his excellent introductory books and translations of ancient Xiangqi texts as well.  8/10.

Games of Annihilation

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Turkish Draughts — For some reason, despite having played Checkers in my youth I never considered the idea of an orthogonal version, so seeing this game for the first time was a real eureka moment.  In Turkish Draughts, players start with 16 pieces each on the 8×8 board, and men may move one square straight ahead or in either sideways direction; kings move like Rooks in Chess and capture via the long leap.  Unlike Draughts, pieces are removed as soon as they are jumped rather than at the end of the sequence, which can allow some spectacularly long capturing sequences.  The tactical problem above (White to move and win) is a great example; the final move captures 12 checkers at once!  I love this game and play it constantly on my phone, and I feel it should be just as revered as Draughts and Checkers. 10/10.

Armenian Draughts This variant of Turkish Draughts spices things up by allowing men to move diagonally.  This seemingly small change actually completely alters the gameplay, removing the concept of opposition.  For fans of Draughts this is worth a try.  Kings are strong as in Dameo, but men here are also more mobile, which feels a bit better in my opinion.  However, I’m a little unsure about the rules reported in the English-speaking world; in Russian sources, it is said that pieces are removed at the end of a capture sequence, rather than immediately.  I’m trying to find Armenian sources to get a definitive answer, but as yet have been unsuccessful.  Most of the Russian-language information seems to come from the book Checkers: 60 Unusual Games on a Classic Board by Alexander Pavlovich, so I’m working on obtaining this book.  8/10.

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Bashni — The columnar version of Russian Draughts, where captured pieces are continually stacked under the capturer.  Stacks can be unveiled again by re-capturing the top piece off a stack, leading to amazingly complex combinations and exciting back-and-forth action.  Promoted stacks capture with the long leap, too, adding to the hectic nature of the game.  An absolute blast.  Abstract Games Magazine featured this game in a number of articles, and included numerous useful tactical and strategic tips, as well as some nice problems like the above (White to move and win).  10/10.

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Croda — This ingenious Draughts variant takes Turkish Draughts, replaces the sideways moves of the men with diagonal ones, but keeps capture orthogonal only… then stuffs the 8×8 board with 48 pieces.  The result is an action-packed game with lots of opportunities for exciting combinations.  Dameo was inspired by this game, but I actually prefer Croda; the lack of linear movement and the weaker kings produces a simpler game that feels more balanced to me.  Admittedly the average Croda game will be much longer than a typical Dameo game, but all other things being equal I usually prefer longer games to shorter ones.  A viable alternative to 10×10 Draughts, if you’re worried about drawishness.  9/10.

Fanorona A traditional elimination game that uses contact capture, and that later inspired Freeling’s Bushka (see above).  Very fun to play casually, as the action starts immediately, but as with Bushka I find it quite confusing.  I like a more subtle opening phase, and as any reader of this blog will know, I always like larger boards.  Still, well worth a try!  There’s no denying it’s a unique game that’s packed with excitement.  7/10.

Killer Draughts — An attempt to alleviate the drawishness of Draughts, Killer forces kings to stop immediately on the square just beyond the piece it captures at the end of a capturing sequence, but only if that piece was also a king.  This simple change, derived from a similar rule in Thai Draughts, allows two kings to win against one in the endgame (as compared to four kings being required in the standard game).  The rule is simple to understand, and large endgame tablebases have already been calculated for this variant, making it possible to adjust one’s endgame knowledge through study.  In my view, a straightforward and effective option for tightening up the Draughts endgame.  9/10.

Lasca — The famous Chess player Emanuel Lasker invented this game, which is the columnar adaptation of English Draughts (or Straight Checkers, for my American compatriots).  Sadly the result is too constrained and dull, lacking all the verve and vitality of Bashni.  Still better than a kick in the head, and I imagine this game could be substantially improved if someone with design chops spent some time with it.  5/10.

Loca This tricky little number flips one’s Draughts expectations around, allowing men to capture like kings.  The result is a weird experience, with carnage starting very quickly.  I’ve only played this twice, and I don’t think I could possibly take this game seriously, but it was pretty fun.  7/10.

Territory Games

Amazons — This is one of those games that I admire, but don’t actually like playing that much.  Players move their Amazons around the board like Chess Queens, blocking off an adjacent square after each move; the last player to move wins.  In play the game becomes a territorial battle, and there is ample scope for delicate strategic play.  I just find it a bit dull in practice; the interaction between the Amazons is indirect, and slightly unsatisfying for me.  An amazing invention and clearly a great game, just not one that suits my temperament.  7/10.

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Cannons and Bullets — This clever game allows players to place pieces on vacant hexes, but only if that hex is directly visible to a friendly piece; if a piece is visible to three or more friendlies, you may place a double-stack, which then can be fired as a cannon to capture enemy pieces.  I find this game easy to get into and remarkably fun in play; games are quick, generally speaking, but there is scope for some cute tactics.  Recommended.  8/10.

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Desdemona — This odd combination of Amazons and Othello is actually more fun for me than Amazons itself.  The addition of toggle-capture adds some much-needed interactivity to the game that I find enjoyable.  Desdemona has been through a few revisions to avoid degenerate play, but the final version works well and is recommended if, like me, you find Amazons just a little bit sterile.  8/10.

HexSygo — One of the few, elite members of the hexagonal-Go-games-that-actually-work club.  A straight-up translation of the Sygo rules to the hexagonal board results in a game with Go-like territorial vibes but a very unique tactical feel.  I haven’t played this game all that much but it’s on my list to study more deeply.  8/10.

Keil — I don’t like to be this negative, but I really, really dislike Keil.  Keil takes Go, known for its minimalistic visuals and high clarity, and transforms it into a game that makes no visual sense, where links between cells and stones are obscure and hard to follow.  In essence, in my opinion it takes Go and removes virtually all of the clarity and aesthetic beauty.  This is perhaps the only abstract game I’ve tried so far that actually upset me when I attempted to play it.  0/10.

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Lotus I mentioned this game in a previous post as an under-appreciated gem, and I stand by that assessment.  The odd board and Othello-style capture give this game a unique impression, and it’s certainly a better use of the Kensington board.  Check out the other post for more.  8/10.

MacBeth — Not much to say about this game other than the fact that it’s a translation of Othello to a hexagonal grid, and it works great.  I’ve had a few games of this, one of which ended in a last-second victory for me that had all the thrills of a close scrape in its parent game.  I liked this enough to program it for Ludii, so clearly I like it a lot.  9/10.

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Medusa — Another unusual territory game with an unusual board, Medusa again features in my other post with brief reviews of cool abstracts.  Medusa is like Lotus’ big brother, with a more deliberate, strategic feel.  Both games make fine use of Rosette’s clever conceit of granting eternal life to hexagonal formations of a single colour.  Give it a whirl!  8/10. (read more here)

othello1

Othello This game is of course a classic, present in millions of homes throughout the world, and is particularly popular in Japan.  Othello is one of the rare modern-ish abstracts to actually have a robust tournament scene, with regular world championships and ample high-level online opponents available.  The flip-flopping capture mechanism can be a bit opaque at first, but Othello is so instantly accessible and fun that it’s easy to break this out with non-gamers and have a good time.  My only lament is that the 10×10 version is so hard to find anywhere; I still occasionally trawl Japanese auction sites looking for a copy, and someday I hope to grab one at last.  This game often gets denigrated in the abstract community for some reason, but there’s a lot of depth here and it’s absolutely possible to take up Othello as a lifestyle game.  9/10.

tumbleweed-sample

Tumbleweed A rare example of a game birthed on the BGG forums that has gained some kind of community around itself, thanks to the herculean promotional efforts of the creator Mike Zapawa and superfan Alek Erickson.  Tumbleweed is a territorial game centred on a line-of-sight placement mechanic and the use of stacks of counters.  I initially was excited about this game, as it felt novel while still being comprehensible, but in subsequent play something bugs me about it.  I haven’t quite worked out what that is, but I suspect a few factors play into it: it’s hard to justify expending lots of effort on another territory game when I’ve invested so much in Go; OTB play is tough to organise due to the need for hundreds upon hundreds of counters; and large board sizes produce a much more interesting game, IMO, but most players prefer smaller sizes.  However, it’s definitely a significant and enjoyable game and I would recommend trying it; plus it has a tournament scene, which is a rare and precious thing.  8/10. (read more here)

Largest Group Cascading

Catchup-new-attempt-hex9-01

My order-9 Catchup board design.

Catchup — Easily the best game made by Nick Bentley, which regularly gets criticised by the BGG abstracts community, and Nick himself, because of the need to keep score.  This is unjust in my view, as the Catchup mechanism, in which players may place 3 stones in a turn instead of 2 if the opponent matches or exceeds their current score, is a brilliant innovation that gives this game an immediately apparent uniqueness and flair.  For a very long time it was only played on order-5 hex boards, which means games were so short that there was not much room for strategy.  Despite my love for this game I don’t enjoy playing it on the order-5 board.  Thankfully, now people seem to be playing on order-7 boards more often, which is a significant improvement.  I printed an order-9 board for myself, and I sometimes play at even larger sizes using Ai Ai.  In any case, I consider this one of the finest modern abstracts, and in a more sensible world it would have been published and would be getting played by millions of adoring fans.  10/10. (read more here)

Migong-test1

Migong — Here’s part of a post I wrote on this game in the BGG abstracts forum, in relation to the game captured in the screenshot above: “That was pretty fun. Shutting down opposing groups is enjoyable and there’s a lot of back-and-forth fights. I’m curious what high-level Migong would look like, and what sort of strategic play might develop.  Weirdly, I think I’d enjoy this much more as a physical game than as a MindSports app. It’d be visually satisfying on a clean board with acrylic pieces, and it’d be appealing to people who might not normally engage in a combinatorial territory game. There’s a satisfying ’embed the rules’ thing going on here that I think makes for a good candidate for a physical product.”    To add to that, I’m not normally a big fan of tile-laying games, but this one I enjoyed, not least because the patterns produced during play are visually attractive.  Digging up that post made me want to play again, which is a good sign.  Let’s call that a solid 7/10.

Permute 12x12 -- move40 -- Ac6d7-d7-01

Permute This is my game, and I like it, and I’m good at it.  But I’m not going to give it a numerical rating on my own blog post, because people do that on BGG sometimes and give themselves 10/10 and say their game is better than Go, and every time I see that I roll my eyes so hard I need to go see an ophthalmologist.  So instead I’ll just say it’s a fun game, inspired by the Rubik’s Cube, in which players build up groups of pieces by rotating them like the face of a twisty puzzle.  I’ve written a long post about this game which took a huge amount of effort, so please go take a look.  12×12 is the ‘beginner’ size, I recommend the 16×16 game for a deeper strategic battle.

Qascade — The sole member of the exclusive games-inspired-by-Permute club, Qascade adds the twisting mechanic to a placement game on the hex grid.  Combined with Christian’s one-bound, one-free opening protocol, we get a nice game of group-building with some tactical surprises due to the twisting element.  Fun to play, but in my extremely objective, not-biased-at-all opinion, Permute is more purely about twisting and therefore has a stronger identity.  7/10.

slyde16-10s-1

Slyde — One of the inspirations for Permute, this game tasks players with building up groups of pieces on the square grid by swapping them.  Each swap locks a piece in place, which was the mechanic I later used in Permute to ensure termination.  The game seemed to be doing relatively well at attracting players, until the creator stopped promoting it in favour of Tumbleweed.  8/10.

Connection Games

Gonnect A fine game that results from a very simple idea: what if we kept most of the rules of Go (except passing) and just changed the goal to a connective one?  The result is an interesting experience, and a nice example of how connection games can incorporate capture successfully.  Some players dislike how close games enter a ‘cold war’ phase where the game essentially becomes No-Pass Go, but I guess as a Go fan this doesn’t bother me too much.  Trying this is a no-brainer if you have a Go set lying around (and you should, you can play about a billion different games using a Go set).  8/10.

slither19-10s-1

Slither — Conceptually this game has great appeal; stones are placed and then slide around each other as players attempt to connect opposite sides of the board.  In practice however, I find it hard to get a grip on this game.  I made a bit of an effort to understand it with the help of David Ploog’s excellent guide, but still it didn’t quite click.  Ultimately I gave up, because there are many connection games out there that I can comprehend much better than this one.  There is a nice community of players on Little Golem, which is a big point in its favour.  I suspect I’d do better with this game if I could stare at it over a Go board with a real human opponent, somehow.  6/10.

Symple Hex — Combining Symple and Hex gives us this game, which applies Symple’s remarkable move protocol to the connection genre.  The result is enjoyable, but somehow not as compelling as the other connection games I like.  I think it may be that the growth mechanic of Symple feels a bit strange in a connective context, as my brain wants to make big groups but that’s not necessarily the right thing to do to actually win the game!  In any case, I’m glad this game was made, and I hope another Symplistic connection game might iterate on this idea in the future.  7/10.

Unification Games

loa-10s-1

Lines of Action This bonafide modern classic birthed a genre, and for many remains the best example of it.  Here players try to unite their checkers into a single group, using a strange movement mechanic in which pieces may slide according to the number of pieces present in the direction they wish to move along.  The game is simple to learn but getting one’s head around the basics can be challenging initially.  I intend to spend more time with this game, having learned a lot about it from David Ploog’s guide.  As usual I’d love to see this expanded to a larger board with more pieces too; the original is easily playable with a Checkers set, so I want one playable with a Draughts set!  8/10.

Looping Games

coil1

I’ll save you some more time here too — honestly, just play Havannah or Coil instead!  Granted they have other win conditions besides loop-building, but they’re excellent games so who cares.  Coil (above) is such a cool game to me that I even programmed it for Ludii… only for the BGG abstracts forum to start exploding shortly afterward with endless loop-based game designs which explicitly aim to replace it.  That’s some bad timing.

Race Games

Ordo — I’m not generally a huge fan of race/traversal games, but Ordo is a good one.  Designed by Dieter Stein, creator of a number of interesting games, this one features movement of whole groups, which is always satisfying.  I recommend it, but again I’m no expert on this genre.  7/10.

Blockade Games

Stalemate games.

Monkey Trap A cute Amazons variant themed around monkeys flitting around the board dropping coconuts on the board behind them.  Christian presents this as a game for kids, but I think it’s fun enough for adults, too.  The reduction of the decision space relative to Amazons makes it more accessible, but there are still enough options on a typical turn to allow for surprising tactics to happen.  A good game, and maybe a commercially viable one — a jungle-themed board with cute plastic monkeys and big chunky coconut pieces would go down a treat amongst younger players.  6/10.

pilare-initpos-MS

Pilare Eventually tried this thanks to encouragement from David Ploog.  An ingenious 2D Mancala-like game designed by Jorge Gomez Arrausi, creator of the also-ingenious Unlur.  In Pilare, players pick up stacks topped with pieces of their colour, and sow their contents over the board, until someone is left without any stacks they can sow and thus loses.  Each move is potentially long and filled with possibilities, so the game ends up feeling tactically rich and loaded with mysteries.  Someday I hope to play more of this.  9/10.

Configuration Games

A hugely underrepresented category on MindSports, and in the abstracts community in general.  The n-in-a-row genre is ripe for some innovation, but the abstracts community seems to have largely abandoned it as a lost cause in recent years, which is a shame.

Hexade — Christian Freeling’s take on the n-in-a-row genre follows Havannah and grants the win under multiple conditions: victory comes after connecting six of one’s stones in a line, triangle or hexagon.  Capture occurs exactly as in Pente, but capture is not an alternate win condition as in that game.  The result is an appealing, varied game of interesting tactics.  Loses a couple points from me on the basis that Pente doesn’t feel much less rich despite the simpler win condition.  Must play more though to determine whether this is an accurate impression.  7/10.

pente1

Pente Once a popular game with a robust tournament community, Pente is a bit obscure nowadays but players still congregate and many games still take place at Pente.org.  Players compete to be the first to get five stones of their colour in a line, but in Pente players may also capture pairs of enemy stones if they place their stones at either end of that pair.  Captures also provide an alternate win condition for the game.  I like this game a lot, to the point that I programmed it for Ludii, alongside the excellent variant Keryo-Pente.  9/10.

Games With Various Other Goals

hexsymple-sz12-p10-sample-game1

HexSymple — Translating the Symple protocol to the hex grid works great, and produces a game with a strikingly different feel; the additional connectivity options present on the hexagonal grid shift the focus more toward strategy than tactics.  As a devoted fan of Symple I enjoy this game just as much, and sometimes I think it may even be better than the original, but that feeling fluctuates depending on my mood.  Like Symple, it’s deep, engaging, tense, and hugely flexible and scalable.  Just play it.  10/10. (read more here)

Multiplicity — Some of you will know of Omega, a clever game that uses multiplicative scoring, leading to interesting consequences when working out how to build groups that achieve the best score.  Multiplicity uses this same scoring mechanism, but unlike Omega, players place one stone per turn, may play stones only of their own colour, and the game opens using Christian’s one-bound, one-free opening protocol.  The resulting game is tense and fun, and shares with Omega the strange feeling of needing to avoid certain connections or one’s score can drop significantly.  One downside is that keeping accurate score is a bit annoying in OTB play, but on the other hand, just playing using basic concepts of trying to build groups of the optimum sizes can get you pretty far.  7/10.

Xodd/Yodd — This pair of games tasks players with building less groups of their colour on the board, but players may drop stones of either colour, and at the end of the turn the total number of groups on the board must always be odd.  The result is a very unique playing experience, with some highly unusual tactics and appealing whole-board strategies.  Xodd (on the square grid) is generally considered more tactical, and Yodd (on the hex grid) more strategic, but both are very worth playing.  For what it’s worth, I slightly prefer Yodd, not least because the use of the hex grid helps stop my brain from mistakenly applying Go concepts to this game!  Elsewhere I proposed Snodd, a variant played on the snub-square tiling which has five adjacencies on each point, precisely between Xodd’s four adjacencies and Yodd’s six.  Like most of my ideas it had no impact at all, but I still think it has potential.  9/10.

Draughts Games Not Appearing On MindSports

I thought Checkers, Russian Draughts, and some other Draughts variants used to be listed on MindSports, but they don’t seem to be available for play anymore (or maybe they never were?).  I decided to review some of these games anyway, since I play several of them regularly.

checkers-snip-1

Excerpt from the monumental Checkers opening guide by GM Richard Pask, Complete Checkers (2020).

Checkers — Also known as Draughts, English Draughts, or Straight Checkers, this 8×8 classic suffered unjustly from Jonathan Schaeffer and his engine Chinook weakly solving the game in 2007 (it’s a draw).  This game-theoretic result has no real bearing on actual play between humans, and alternative opening options like 11-Man Ballot ensure the game has plenty of life left in it.  GM Richard Pask has written some excellent books on the game in recent years (like Complete Checkers above), and great YouTubers like AZCheckers continue to play, analyse and promote this venerable game.  The upcoming World Championship has a $32,000 prize fund, so previous reports  that competitive Checkers is ‘as dead as the dodo’ were a bit exaggerated.  I urge players out there to download Pask’s Checkers for the Novice and give the game a chance; Checkers remains a playable and enjoyable game to this day, and strong opponents are easy to find.  8/10.

Italian DraughtsDama Italiana is a unique take on 8×8 English Draughts with one massive rules difference: kings cannot be captured by men.  This single change has a profound impact on endgame play especially, and for that reason alone is well worth checking out for fans of Draughts/Straight Checkers.  There are some additional wrinkles to the majority capturing rule, which take some getting used to.  The Italian Draughts Federation seems highly active, and supports OTB tournament play in both the Italian game and 10×10 International Draughts.  I’ve heard tales of 10×10 Dama Italiana being played in some parts of the country, which intrigues me, but I’ve yet to find confirmation.  8/10.

Unfortunately, Christian chose to describe this game in an oddly nasty way:

“It bears testimony to the idea that Italians either prefer ‘complicated’ to ‘simple’ or cannot distinguish between ‘complicated’ and ‘complex’, and in either case are obsessed with hierarchy.  Checkers is simple and complex. Italian Draughts is complicated and complex. There’s nothing gained except the loss of simplicity.” (here)

I don’t believe we can generalise about an entire nation on the basis of their Draughts preferences.  Besides, the Italian Draughts Federation runs more events for International Draughts than they do for Italian, so this claim doesn’t make any sense — clearly Italians can, and do, appreciate the ‘simpler’ side of the Draughts rules spectrum.  Also Dama Italiana does gain something unique from the powerful kings, and the more complex capturing rules work in service of that new dynamic.

Russian Checkers Known as Shashki in its native land, Russian Checkers has a distinguished history of high-level competition and sophisticated analysis.  Russian Draughts is nearly 8×8 International Draughts, but men can promote to king in mid-move (!), and players are not obligated to take the capture sequence of maximum length.  These two simple changes create a game with a distinct character, well worth playing.  Russian Checkers also has a large literature associated with it, but unsurprisingly nearly all of it is in the Russian language; a large archive of classic books on the game can be found here.  Tournament play occurs all over the world and is supported by the IDF64.  Online opponents are readily found on PlayOK.  9/10.

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American Pool Checkers — A game criminally underrated in its home country, American Pool Checkers is a close relative of Russian Checkers, where men no longer promote in mid-move.  The game found some popularity for a time, particularly among black men in the American South.  I hope this game can maintain a foothold, particularly because it’s so rare that we recognise and support the contribution of minority communities to the world of abstract games.  Captivating articles like this feature in The Bitter Southerner certainly can’t hurt; how could we not love a game featuring top players with nicknames like ‘Iron Claw’ and ‘Big Willie’?  In the meantime, give it a try on Ludoteka9/10.

Brazilian Draughts — This is a straightforward reduction of 10×10 Draughts to the 8×8 board, all rules are otherwise the same.  The result is a quick and action-packed game, great as an introduction to the world of 10×10 Draughts, a quick blitz between longer games, or as a deep and rewarding pursuit in its own right.  Like Russian Draughts, Brazilian Draughts is played all over the world and high-level tournament play exists both online and offline.  9/10.

Russian and Brazilian Draughts have one noteworthy difference from 10×10 Draughts, besides the obvious: in 10×10, four kings are required to ensure victory against one, but in these 8×8 games, three kings can trap a lone king so long as they can occupy the long diagonal.  The key formation is known as Petrov’s Triangle:


So there we go, a great big pile of reviews and impressions of many of the games on MindSports.  I hope someone out there finds this useful, at least fodder for discussion if nothing else; but if not, at least I’ve collected all these thoughts in one place for my own future reference.

As you can tell from this sizeable list, there are quite a lot of games on MindSports.  Ideally the Chess and Shogi sections would be more comprehensive — it’s a bit funny to me that MindSports has stuff like Armenian Draughts but not Shatranj, Makruk or Sittuyin — but there’s tremendous variety there nonetheless.  I highly recommend checking it out for yourself, and I’m happy to accept challenges on the site; just be aware I sometimes disappear for long periods due to being overworked.

I’ve resolved before to write future articles about certain things, and have often failed to follow through, partly due to a general lack of interest from others and partly from my own lack of time and energy.  About all I’m willing to promise anymore is that, assuming I survive the next pandemic wave(s), I’ll keep writing about games here and there, when I can.

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

UPDATE 6 Nov 2021 — Added info and screenshots on playing Courier Chess and Courier-Spiel in Ai Ai.


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.  In fact, the Elephants may only visit a quarter of the squares on the board!
  • 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.

Since I wrote the first version of this article, I began working with Stephen Tavener on his wonderful Ai Ai general game-playing software.  I work primarily on the Chess/Shogi side of things, and have added many dozens of variants in recent months.  We of course added implementations of Courier Chess and Courier-Spiel, so you may play both these games against AI or human opposition:

As you can see, the piece graphics are slightly different — the Queen and Fool have been replaced with the generic Ferz and Wazir, respectively, but the piece images are schematic and easy to remember.  Subsequently I have added a number of Courier-inspired modern variants to Ai Ai; more on these in a future article!

Alternatively, if you want to play against a tougher AI, 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 examine some modern extensions of the Courier Chess concept, all of which are available to play in Ai Ai.  I had previously planned to present some analysed games of Courier and Courier-Spiel, but due to a backup mishap I lost the substantial work I’d already done on these.  At some point I’ll do that work again, but for my own sanity I need some time before I dive back into that analysis a second time!

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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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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Symple: a game that matters

UPDATE 1 MAY 2020: Added ‘Playing Symple over the board’ section, and downloads for the Ai Ai .mgl files for large/oblong Symple boards and HexSymple.

Way back in Connection Games III: Havannah and Starweb, I praised designer Christian Freeling’s games but expressed a bit of skepticism regarding his list of six ‘games that matter’:

Christian has invented a tonne of well-regarded games over the years, and he has his own opinions on the most essential ones — namely Grand Chess, Dameo, Emergo, Sygo, Symple and Storisende.  Although I’m not sure I can agree with most of them, personally speaking — that list is mostly games I certainly admire, design-wise, but don’t particularly enjoy playing.

I still stand by most of that — I do admire all of those games, and still I’m not a super-fan of several of them.  But I’m here today to tell you that I was wrong, in fact very wrong, about two of them:  Symple and Sygo.  Today I’ll tell you about Symple, designed by Christian Freeling and Benedikt Rosenau, and in a future post I’ll introduce its descendant Sygo as well.

Full credit for this change of heart must go to David Ploog, who sent me a draft of an excellent article he’s writing for Abstract Games Magazine about games featuring many moves per player turn, with Symple being the star of the piece.  His explanation of the game massively piqued my interest, so I started exploring it via Stephen Tavener’s Ai Ai software — which I’ve recommended many times already, you really should download it!

What I discovered is that Symple is not just an ingenious piece of invention, it is that most elusive kind of ingenious invention — one that you see in action and think ‘how did no one think of this before?’  The core of it is easy to grasp, yet in play it surrounds you with staggering complexity while still remaining manageable.  Having been obsessed with it now for a little while, playing many games, and analysing many others with the AI, I’m convinced that this game is something truly special.  Had it been invented hundreds of years ago, I think today it’d be sat alongside Chess, Go and Shogi as one of the great traditional games.

Enough gushing — from here I’ll explain the game, show off a few example games, and maybe gush a bit more here and there.  In deference to David’s article, which will explain strategic concepts to you far more clearly and expertly than I could, I’ll shy away from detailed playing tips and simply direct you to play it on Mindsports or via Ai Ai and explore it until David’s article is out.

How to play Symple

Symple is best played on a Go board, using standard black and white Go stones.  I’d recommend the full 19×19 Go board (or even larger — more on that later), although for the first few games a 13×13 board or even 9×9 would be a good idea, to get used to the core concepts.  Here are the rules:

  1. Each player chooses a colour, Black or White — White always goes first.  Before starting, players should agree on an integer value P, which will affect the scoring at the end of the game.
  2. Key definition: a group is a set of horizontally and/or vertically adjacent stones (orthogonally adjacent, in other words) of the same colour.  A single stone is also a group.
  3. Making moves: on their turn, a player must do one of the following (players may not pass their turn):
    1. Plant: place one stone anywhere on the board that is not adjacent to any stones of the same colour, which creates a new group
    2. Grow: add one stone to every possible group of their colour on the board, by placing a stone on a vacant point horizontally or vertically adjacent to that group.  If a group has no vacant horizontally or vertically adjacent points, then that group may not be grown.
  4. Balancing mechanism: once per game, if neither player has yet made a growth move, Black may grow all of their groups and then plant one new group in the same turn.
  5. Move restrictions: if a group grows and the added stone touches another group, then both groups are considered to have grown (meaning the group the new stone touched now can’t grow this turn).  However, two groups may grow in such a way that only the two new stones are now adjacent.
  6. Scoring: the game ends once the board is completely full.  At that point, both players count up the total number of their stones on the board, and the number of separate groups they have.  Their final score is the total number of their stones, minus points for every group they have on the board.

To summarise, in Symple players seek to claim territory on the board for their groups of stones to grow in by first playing planting moves, then growing those groups all at once with subsequent growth moves.  Creating groups early in the game is important in order to claim territory and secure space for future growth, but creating a new group takes an entire turn for just one stone placement; conversely, during a growth turn, a player may place a huge number of stones in one turn, sometimes 10 stones or more during a 19×19 game.  The scoring system gives players a penalty of P points for each group of their stones at the end of the game, meaning that connecting one’s groups is paramount.

Growth turns give players an enormous array of choices.  A typical early-game growth turn might look something like this:

symple19-growth-example2

Here White is taking a growth turn, as depicted in the Ai Ai software.  In Ai Ai, groups that have a growth move already chosen are faded out, as in the top left of the image, and new stones are indicated with a ‘+’.  In this instance White has taken advantage of the two-stone separation between the two groups on the upper left to grow both groups in such a way that they are now connected.  Around the other groups, the green asterisks indicate where legal growth moves can be played.  At the end of this turn, White will have played up to a total of eight stones, one for each group.  Note that White could end up only playing seven, if they elect to grow one of the two top-right groups into connection with the other; that would then block the second group from growing that turn, and from then on they would be a single group.

Playing a fistful of stones in one turn is initially intimidating, but these massive multi-moves naturally keep one’s mind focussed on strategy over tactics.  You will find yourself considering the optimal directions of growth to restrict your opponent, facilitate your expansion, and develop opportunities for later connections between groups.  The growth mechanism makes the game feel organic and flowing; more than single stones, you’re manipulating amorphous, amoebic groups that ooze and coalesce across the board.  The feel of this game in play is unlike any other abstract strategy game I’ve played before.

Examples of play

Let’s look at some examples of completed games, to get a better idea of how the scoring system works.  A finished game of Symple looks something like this:

symple19-p10-10s-sample1

A finished game of Symple on a 19×19 board (P = 10).  Black wins, 128 points to 83.

In this game, the players agreed to play with P set to 10 points.  Black finished with 5 groups totalling 178 stones, for a final score of 178 – (5 * 10) = 128; White finished with 10 groups totalling 183 stones, for a final score of 183 – (10 * 10) = 83.  Black solidly outmanoeuvred White here, connecting more groups together to significantly reduce their point penalty and take the win.  Note White’s unfortunate 1- and 2-stone groups on the bottom right — these alone took 20 points from White’s score!

This GIF shows off the whole game:

symple19-p10-10s-sample-game1

The endgame in Symple can be quite challenging and subtle, as in this close game:

symple19-15s-sample1

A finished game of Symple on a 19×19 board (with P = 10).  White wins, 79 points to 62.

Here both players finished with 10 groups, but White managed a win.  By restricting Black’s ability to grow certain groups earlier in the game, White eventually forced Black to play stones into isolated squares in the late stages of the game, causing significant extra scoring penalties that secured the game for White.  Here’s the complete game in GIF form:

symple19-15s-sample-game1

In Symple, managing your growth carefully and strategically is very important, as the final score difference may end up coming down to ensuring that one’s final stone placements aren’t forced to be new, point-draining groups.

The balancing mechanism provides some great tension in the early game, as well.  Black has one opportunity to grow and plant in the same turn, but White knows this, of course, and can short-circuit that chance by playing a growth move earlier than expected.  But growing too early can be too committal, losing an important opportunity to plant a new group in key territory.  This dynamic provokes a pleasing little game of chicken, as both players try to suss out their opponent’s rhythms and strike at the right time — “should I do my double move now, or will White wait another turn to do their first growth turn?”

On the whole, Symple has a great flow to it, and every phase of the game feels consequential.  In the opening, players plant all over the board, attempting to claim space for future growth while impeding the opponent’s opportunities for later connection.  All the while the will-they-won’t-they tension of the balancing mechanism lurks in the background.  In the middlegame, players switch over to growth moves and their groups extend their tendrils across the board, competing with opposing groups for territory.   In the endgame, Symple turns ‘cold’, as players turn from aggressive expansion to cautious growth to avoid getting hemmed in, while trying to force their opponent into positions where they’re forced to plant a stone somewhere unfortunate.  The final result is shaped by key moments in each of those phases, making the whole experience feel cohesive and dynamic.

Playing Symple over the board

Playing Symple is very easy when using a computer program or web-based implementation, since the software will track group sizes and scores for you.  When playing on a real board, however, a bit more effort is required to keep track of things.

A single turn in Symple can require a lot of individual moves for each player, and one can easily get confused as to which group has already been grown.  Most players recommend using a second, easily distinguishable type of token or stone to mark your intended growth moves, and replacing them with normal stones once you’ve decided on all your moves for that turn.  That allows you to think about each growth move without getting confused about which group can still grow.  If you’re using a Go set and want to maintain the austere aesthetic of black and white stones, then consider using Chinese-style Go stones with one flat side as your markers, and Japanese-style double-convex stones for regular plays.

The other aspect is scoring, which in Symple involves a lot of counting.  However, the game continues until the board is completely full, so as David Ploog pointed out in a BGG discussion, scoring can be done quite efficiently: simply count the number of groups for each player, then remove all stones of one of the colours from the board, and count the stones for the other colour.  Since you’ve recorded the numbers of groups, you can freely rearrange the remaining stones into an easily-countable shape, too.  That’s all the info you need to then calculate the scores for both players.  Using this method, scoring a game of Symple shouldn’t take any longer than scoring a Go game.

An eminently flexible game

Alongside the straightforward rules, unique gameplay and immense strategic depth, Symple has some practical advantages that add even more interest.  An important element of the design is that the value of the group penalty is not fixed, and players can experiment with different values.  Smaller values reduce the emphasis on connecting groups, while larger values make it even more essential.  David Ploog recommends P = 10 for 19×19 games, and in my experiments so far I agree; I’ve also played some 19×19 games at 12, 14 and 16 and have enjoyed those too.  When experimenting with different values, bear in mind that on boards with odd numbers of squares, you should use an even value for P to ensure that draws are not possible.

The enormous multi-move turns of Symple also mean that the game is incredibly scalable.  Symple plays remarkably quickly even on 19×19, since each turn can easily provide 10 or more stone placements — and these mechanics tend to emphasise strategic concerns over tactical ones, which helps to keep the game from bogging down with excessive calculation for every stone placement.  As a consequence of these unique properties the game plays well even on ludicrously large boards.  Here’s a game I played against the AI on a 37×37 board:

symple37-p18-2s-close1

A game played against the AI on a 37×37 board (P = 18).  I won as Black by only 3 points, with a final score of 434 to White’s 431.

This game was huge, but still surprisingly playable; in the middlegame we were often placing well over 20 stones per turn, so even with 1,369 squares to fill the game moved at a good pace.  The result came right down to the wire — I won by only 3 points.  If you’re bored you can watch the whole game in animated GIF form here.

I’ve definitely never played an abstract game before Symple that could take place on a board that large and remain playable and fun.  Go is one of my all-time favourite games, but play on the standard 19×19 is already very challenging; I’d never go near 37×37 Go.  Symple’s mechanics mean that the board fills quickly, and strategy reigns supreme over tactics, and so even on boards this large one doesn’t feel too hopelessly confused.

I’ve also found that Symple presents some interesting challenges on rectangular boards.  Here’s a game played on a 19×29 board:

symple-rect-19x29-p12-2s-close1

A game of Symple on a 19×29 board (P = 12).  Black wins, 117 points to 110.

This was a test game between two AIs, played when I first modified the Symple file in Ai Ai to permit rectangular boards.  Note that both players took advantage of the strange board geometry, growing huge groups horizontally across the board.  You can view the whole game in GIF form here.

Note that Ai Ai by default only supports square boards up to 19×19; I have modified the Symple.mgl file in Ai Ai to permit rectangular boards with sizes up to 37 in either dimension.  You can download the .mgl file needed in this Google Drive folder; simply add it to the ‘mgl’ subfolder within your Ai Ai folder, and it will appear in your games list.  The file you need is called Symple-rect.mgl.

All my tests of weird board dimensions have confirmed that the core mechanics of Symple are not just clever and elegant, they’re also extremely robust.  The game remains interesting even with bizarre values of P, or when played on extremely large boards or weirdly-shaped boards.

HexSymple

Speaking of weird boards, it turns out that Symple is also incredibly good on hexagonal boards, too.  Christian Freeling calls it HexSymple, and in this variant the game is played on a hexhex board (a hexagon-shaped board composed of hexagonal spaces).  The rules are identical to regular Symple.  Here’s a game played on a hexhex board with 12 hexes to a side (that’s 397 hexes in total):

hexsymple-sz12-p10-sample1

A completed game of HexSymple on a hexhex-12 board (=10).  White wins with 153 points to Black’s 124.

In this game White managed to constrain Black’s growth along the left edge and take the win.  HexSymple has a very interesting character — the board geometry means that cutting off groups is more difficult than on the square board, since all hexes have six neighbours instead of four and there are no diagonal cuts possible.  The game feels very expansive as a result, with ambitious connections snaking across the board in every direction.  Here’s the full game in GIF form:

hexsymple-sz12-p10-sample-game1

Just as in regular Symple, HexSymple is incredibly scalable, and I’ve played a few games on very large boards because I am a bit crazy for large boards.  Here’s one on a hexhex-25 board (that’s 1,801 hexes):

hexsymple-sz25-p30-2s-sample1

A completed game of HexSymple on hexhex-25 (P = 30).  White wins, 643 points to 588.

You can see here how the expanded connectivity of hexes makes truly enormous groups possible; check out White’s gigantic group stretching from the top right all the way around the board to the top left!  You can see the whole game in GIF form by clicking here.

On the whole I highly recommend HexSymple.  The board topology creates some interesting wrinkles in play, but the overall strategy remains broadly similar to regular Symple.  The result is a fascinating variant that works as a great change of pace, and stands up as a great game in its own right, too.  I haven’t yet seen a consensus on what good values of might be for different sizes of boards, but in my experience you can safely use significantly larger values than on similarly-sized rectangular boards and get a similar experience, due to the increased connectivity between hexes.

Note that HexSymple is not implemented in Ai Ai by default, but a simple modification of the regular Symple.mgl file makes it possible to play.  You can download the file you need, helpfully titled HexSymple.mgl, from this Google Drive folder.  HexSymple of course has its own dedicated page on Mindsports, and you can play the game online there too.

 

A modern classic

In the very crowded field of modern abstract strategy games, Symple (and HexSymple) are rare specimens that feel like classics.  In some alternate universe, I imagine Symple having frequent high-level tournaments, with a professional player scene, ample literature on high-level play, and an online community with millions of players.  Perhaps in the not-too-distant future this may come to pass in this reality, too.  In the end I agree with Christian — this is certainly a ‘game that matters’.

Sometime in the (relatively) near future, I’ll post a follow-up to this and introduce Sygo, a combination of Symple and Go and Othello-style piece-flipping captures that seems like it shouldn’t work, but totally does.  Like most fans of Go I’m not very keen on most Go variants, because they normally just disturb the elegant balance of simplicity and depth that makes Go so seminal.  But Sygo feels different enough to have its own character, and HexSygo even more so.

Before that, I owe you all a couple of Shogi posts which are still in the works.  I’m pleased to say that the Japanese Chu Shogi Players Association — Chu Shogi Renmei — has sent me a treasure trove of historical information on the game.  It’s all in Japanese, of course, so it will take me some time to read, but with any luck I’ll have some interesting information to report further down the line.

In the meantime, please do yourself a favour and whip out your Go set, get yourself on Mindsports, download Ai Ai, or preferably all of the above, and give Symple a try.

 

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Connection Games II: Y, Poly-Y, Star and *Star

Welcome to part II of my series of posts about games, part of my mission to keep my brain busy while I’m on strike!

Moving on from the last post about Hex, this time we’re going to explore a whole series of connection games, each by the same designer and each a clear progression from the last.  By the time we get to the final game in the series, we’ll see one of the more complicated and sophisticated connection games out there.

The Game of Y

First though, let’s start with something simple.  In fact, this game is even simpler than Hex, which scarcely seems possible!  Recall that in Hex, each player has a slightly different goal — both seek to connect across the board, but each player is connecting different sides.

In the Game of Y, created by Craige Schensted (who later renamed himself Ea Ea) and Charles Titus in 1953, players have the same goal — to connect all three sides of a triangular board made of hexagons.  To sum it up:

  1. Players take turns placing one stone of their colour in any empty hexagon on the triangular board.  Once placed, stones do not move and are never removed.
  2. The first player to connect all three sides of the board wins.  Corner hexes count as part of both sides to which they are adjacent.

And that’s it!  Winning connections spanning the three sides look kind of like the letter Y, hence the name.  Just like Hex, Y cannot have draws, one player will always win eventually.  The first player has a winning advantage here, as well, so using the swap/pie rule is recommended to alleviate this.

Y is sometimes thought to be even more elemental than Hex, given the greater purity of the win condition.  In fact, Hex can be shown to be a special case of Y, but in practice the games are pretty distinct in terms of the tactics required.

Here’s a sample game I played against a simple AI on a triangular board 21 hexes on a side; I used Stephen Taverner’s excellent Ai Ai software that comes with a plethora of great connection games:

 

y-win-1

Y benefits from playing on a larger board, given the shorter distances between sides when compared to a Hex board.

One issue with Y is that, even more so than Hex, the centre hexes are very powerful.  Whichever player controls the centre is very likely to win.  Schensted and Titus developed a number of ideas for new boards that would reduce emphasis on the centre, and eventually the ‘official’ Y board became this interesting geodesic hemisphere:

y-17-curvedThis board reduces the connectivity of the central points, giving the sides and edges greater influence on play.  Some theorise however that on this board basically every first move should be swapped by the second player, although I don’t believe there’s any hard evidence that this is true.  Kadon Enterprises sells a lovely wooden version of this board, albeit smaller than the one above, with 91 points available for stone placement. 

UPDATE:  Phil Bordelon reports in the comments below that the Kadon Y board is so small that the game feels like a trivial first-player win!  So perhaps if you want to try this board shape, play the larger one on the Gorrion server, or print the larger pattern on a mat for face-to-face play.  David Bush also wrote to say that he believes the geodesic Y board can’t be balanced with just the pie rule, and given his serious pedigree in the connection games world I think I will take his word for it!  He also says that three-move equalisation can be a solution.  In this method, one player creates a position with two Black stones and one White, with White to move, and the other then decides whether to play White or Black.

Another alternative option to the geodesic Y board is known as Obtuse-Y.  In this version of the game we play on a hexagonal board tessellated with hexagons (a ‘hexhex’ board), with three pairs of sides marked — first player to connect all three of those marked sides is the winner.  I like this version of Y since a large board in this format is more compact than a gigantic triangle of hexes, and it’s easier to have a balanced game than on the geodesic board.  I made two boards for this version, which you can find on BoardGameGeek — a hexhex-10 (10 hexes on a side) and hexhex-12.

hexhex-10_Obtuse-Y-01

My hexhex-10 board for Obtuse-Y — connect all three colours to win!  There are 271 playable hexes on this board.

In any case, Y is another simple-yet-deep experience and highly recommended.  You can play against the AI using the Ai Ai software linked above, or against humans in real time via igGameCenter, or by correspondence on Richard’s PBEM Server.  The geodesic version is only playable on Gorrion — definitely give it a try.

Finally, I want to note that Y has a ‘Misère’ version, much like Hex, where you try to force the opponent to connect all three sides before you do.  This variant of Y is called ‘Y-Not’.  I just love that.

 

Mudcrack Y and Poly-Y

The next step in Y’s evolution came when Schensted and Titus published a gorgeous little book called Mudcrack Y and Poly-Y (you can still buy it from Kadon), which contained hundreds of strange hand-drawn boards for Y players.  They intended for players to use these boards by marking spaces with their chosen colour using coloured pencils.  These weird little boards seem totally different from the normal Y triangle or geodesic hemisphere, and yet turn out to be topologically equivalent.  Here’s a sample page:

mudcrack y1

A sample page of Mudcrack Y boards.  Print them out, grab a couple of coloured pencils and give them a go!

As part of their continued quest to improve on the Game of Y, this book also reveals Poly-Y, a follow-up game intended to be a further generalisation of Y:

  1. Players take turns placing a stone of their colour on any empty space on the board.  Once placed stones cannot move and are never removed.
  2. If a player’s stones connect two adjacent sides and a third non-adjacent side, that player controls the corner between the two adjacent sides.
  3. If a player controls a majority of the corners on the board, that player wins.

As you might have guessed, once again this game permits no draws (as long as you play on a board with an odd number of corners), so one player will always win.   The pie rule is used to mitigate the first-player advantage.

Wikipedia and BoardGameGeek claim there is no ‘official’ Poly-Y board, but this isn’t correct.  On the archived version of Craige/Ea Ea’s website you can find his summary of the history of Y/Poly-Y/Star/*Star, where he says this:

“Craige tried boards with more and more corners, 5, 7, 9, 15 … . At first it seemed that the more corners the better — there were more points to contest and a beautiful global strategic picture emerged. But as the number of corners increased, of necessity the length of the edges decreased. When the edges became too short it was found that it was too easy to make a Y touching 3 consecutive edges, thus “capturing” the middle edge and the two corners bounding it. This “edge capture” tended to make the game more tactical and local, focused on quick gains along the edge, thus losing the elegant global strategic flavor . So the strategic depth increased at first as the number of corners increased, but then decreased. Finally a board with 9 corners and 7 cells along each edge was chosen as the ideal balance….  Craige chose the 208 cell board with the 7-sided regions halfway to the center as the standard Poly-Y board.”

The same document has a picture of the standard board compared to two other candidates:

poly-y-board-official

The ‘standard’ Poly-Y board is in the centre.  The highlighted spaces on each board are the heptagons, required to allow the board to have 9 corners and still consist mostly of hexagons.

Here’s an example Poly-Y game won by Black on a board with 106 spaces and five corners — note here that the other player is Grey, and the yellow spaces are unoccupied:

poly-y-sample-game2

Black controls the corners on the left side, and has blocked Grey from catching up.

While Craige/Ea Ea endorses the 208-cell nonagon as the best Poly-Y board, in Mudcrack Y and Poly-Y they also state the game plays well on any board with the following characteristics:

  • Equal numbers of spaces along each side
  • Mostly six-sided board spaces
  • An odd number of sides (they prefer 5- and 9-sided boards)

Here’s sample 5-, 7- and 9-sided boards to print and play on:

poly-y-5-sided

5-sided Poly-Y board

poly-y-7-sided

7-sided Poly-Y board

poly-y-board9

9-sided Poly-Y board

 

Poly-Y is a clever game, and very deep; the win condition pushes players to extend their groups of stones all over the board, linking corners together through the centre to block the other player from securing their corners.  The oddly-shaped boards are also fun to play on, and give the game a certain quirky aesthetic appeal.  However, perhaps due to the rapid-fire iterations on Y produced by Schensted, Poly-Y never got the same level of recognition as Y itself.

 

Star

Schensted wasn’t quite done yet — far from it.  His next invention was Star, which ramped up the complexity of the scoring system from Poly-Y and created a game that pushes players to connect all over the board.  Star is another very deep game, and even on a small board presents a considerable challenge.

Star is played on a board of tessellated hexagons with uneven sides — in the sample small board below, you can see that three sides are five hexes long, and the other three are six hexes long; this ensures that there’s an uneven number of edge cells so that draws are impossible:

Star

A small board for Star with 75 hexes and 33 border cells.

Here’s how to play Star:

  1. Players take turns placing one stone of their colour on any empty hex.  Once placed, stones do not move and are never removed.
  2. A connected group of stones touching at least three of the dark partial hexes around the edge of the board is called a ‘star’.  Each star is worth two points less than the number of dark border hexes it touches.
  3. When both players pass or when the board is full, the player with the most points wins.
  4. As per usual, the pie rule is used to mitigate the first player advantage.

This may sound a bit opaque, but the basic gist is: form as many stars as you can, but connect them together to maximise your points.  The end result of a game of Star is an intricate web of connections snaking across the board for each player, attempting to connect and block simultaneously wherever possible.  Since the entire edge of the board is available for scoring, the whole board interior tends to come into play as well, and unlike most connection games the board tends to be nearly full when the game finishes.

Unfortunately, despite pretty much universal praise for this game it’s very difficult to find sample games of Star, so here’s the only one I could find from Cameron Browne’s book Connection Games — I can’t emphasise enough that this is a great book that you should definitely buy!

star-sample1

In this example, the edge scoring cells are marked by X’s rather than a border of partial hexagons.  Note that the completed game takes up nearly the entire board, and the pattern of connections formed is quite intricate even on this small playing area.

As with other connection games, playing on larger boards amps up the strategy.  I found these boards lurking around the Wayback Machine, do give them a try:

Star2

This board has 192 interior cells and 51 border cells.

Star3

This board has 243 interior cells and 57 border cells.

I liked these boards so much that I made a range of Star boards — sizes 8, 9, 10 and 12 (the number being the number of hexes on the longer sides).  I hope a few folks might print them out and give Star a try sometime.

Star-8_PURPLE-01

My size 8 Star board in purple

Unfortunately, despite the coolness of this game it’s been thoroughly overshadowed by its successor; Star does appear to be playable at Richard’s PBEM Server, albeit only with an ASCII interface.

 

*Star

Finally we come to the last in the line of games spawned from our old friend the Game of Y.  *Star takes yet another leap up in complexity, and to be completely honest, I don’t fully understand how this game works.  This is partly because the instructions are written in what feels like an alien language — scoring refers to things called ‘peries’ and ‘quarks’ and it’s all a bit strange.  However the abstract strategy game community praises this game nearly universally, so I remain keen to try and figure it out.

My understanding, questionable though it may be, is that the game essentially takes the core concept of Star — connect groups of edge-adjacent pieces together to maximise your points — to the next level by adding a scoring bonus for controlling corner spaces, and a significant scoring penalty (equal to twice the difference in the number of groups between the two players) for the player with the larger number of groups.  This heavily incentivises the players to connect their groups, and the end result of this is some beautiful patterns of stones snaking across the board, as in these two sample games from the manual (one tiny one and one normal-sized one):

Here’s a closeup of that awesome board:

starstar-board1

The *Star board.  The centre star can be used by either player as a connection between groups — neither player may place their stones on it.

Note that the board has thicker lines to define smaller board sub-regions, which allows players to ease themselves into the full game.  The game is popular enough to be produced in physical form by Kadon Enterprises, who make a wooden board set for *Star that I absolutely must buy at some point:

star-wood-board2starwood

How cool is that!  Someday I shall own this game, and I shall figure out exactly how to play it.

Luckily there’s a simpler game also playable on this board — Star-Ywhere the players compete to be the first to complete a connection between two adjacent sides and one side not adjacent to either of those two.  For *Star veterans there’s also Double-Star, where players place two stones per turn and the other rules remain the same; this seems like a small change but it significantly alters the play.  New tactics and strategies are necessary to cope with the new threats that are possible with two stone placements.

So there we have it — a hectic journey from the elemental Game of Y through to the complex but highly-regarded *Star, courtesy of the brilliant minds of Craige Schensted/Ea Ea and Charles Titus.  Craige/Ea Ea has stated that *Star is ‘what the other games were trying to be’, so from his perspective each game was improving on the last, and *Star is the best of the lot.

While researching and playing/trying to play these games, I’ve found that Star and *Star are frequently compared to Go, despite having connective goals rather than territorial ones.  Given the much more flexible nature of the connective goals in these two games, I can see why — instead of connecting specific sides, players define for themselves the key parts of the board as they play.  This is much more ‘Go-like’ in that the board is more of a blank slate, and does not inherently define the direction of play as much as in other connection games.  So, if you’re a Go fan and skeptical of connection games, maybe try these two.

If you’re new to connection games in general, I’d start with Hex, then Y, then Poly-Y.  You might enjoy Star and *Star more after trying some other games with more freeform connective goals, but with easier-to-grasp rules.  I’d recommend maybe trying Havannah and Starweb for that purpose — and lucky you, they’ll be in my next post 🙂

 

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Connection Games I: Hex

As you all have probably figured out by now, I really enjoy complicated board games — dense modern board games with tons of special components, 500-year-old Shogi variants with hundreds of pieces, all that stuff.  But I also have a great fondness for games on the other end of the scale: elegant abstract games with minimal rules and maximal depth.

Now an oft-cited example of this category might be Go — it’s certainly an elegant game, with rules that are easy to summarise yet a level of depth nearly unrivalled in board games.  But Go is also hard to understand, in that the goal is clear — secure more territory than your opponent — but working out how to get there is hard.  Most beginning players, myself included, are completely flummoxed by the empty board at the start of the game, and have no idea where to start.  And at the end of the game, it’s very difficult for newbies to figure out when the game is actually over!  There’s a reason a common proverb for beginning Go players is ‘lose a hundred games as fast as possible’ — building familiarity with the basics takes time and repetition.  It’s worth it, though.

But what I’m going to talk about here are games that are so simple as to be almost elemental, as in, it’s hard to imagine games with rules simpler than these.  For my money the best examples of these types of games are in the category of connection games.  In a connection game, players vie to be the first to connect key points on the board with their pieces — a simple goal, easy to see and easy to understand.  But underneath that these games offer surprising depths of strategy and tactics.

Now, the current bible for connection games is the book by Cameron Browne called — wait for it — Connection Games, which summarises the genre beautifully and includes rules and examples of play for numerous games.  It’s a great book that I certainly can’t compete with, so in this brief series of posts I’m just going to give you some details of my picks for the best games of this type, along with some useful resources and links to where you can play.

Hex

Any discussion of connection games has to start with Hex, the originator of the whole genre.  Strangely, despite the simplicity of these games, they weren’t around until quite recently.  Hex has a tangled history — now unravelled in the recent, and excellent, book Hex, Inside and Out: The Full Storyso I won’t attempt to summarise it all here.  The game was invented by Danish mathematician Piet Hein in 1942, and was initially called Polygon.  Hein sought to create a game that reflected his interests in topological properties of the plane and the four-colour theorem, and was stuck on this idea for some time, as any attempts to build his imagined game on a square grid didn’t work, as the players could easily become deadlocked.  Eventually he realised that a hexagonal grid would prevent this issue, and thus Polygon was born:

polygon-board-1

The Polygon board, an 11×11 rhombus composed of hexagons.

The rules of Polygon are incredibly simple:

  • Players turns placing a single symbol of their chosen type — star or circle — in any empty hexagon on the board.  Once placed, symbols don’t move and can never be removed.
  • The first player to connect the sides of the board marked with their symbol with an unbroken line of their symbols is the winner.

Easy, right?  But once he started playing, Hein realised the game was far more complicated than the rules suggested.  Soon after he launched the game in the Danish magazine Politiken with the board, rules and a call for challenging Polygon puzzles from readers.  It wasn’t long before pen-and-paper Polygon pads were selling like hotcakes all over Denmark, and the game became a bonafide hit.

polygon-puzzle-1

The famous first-ever Polygon puzzle.  The circle player has the move.  How can they win?

Eventually Hein sold a 12×12 version of Polygon with a very nice wooden board called Con-Tac-Tix, which enjoyed some small success as well — and in fact you can still buy a version of this today from Hein’s grandson.  But the game didn’t really take off around the world until later, when famous mathematician John Nash (of A Beautiful Mind fame) rediscovered the game in 1948.

When Nash started sharing his discovery with colleagues at Princeton, the game rapidly gained adherents.  They often called it Nash, for obvious reasons, but legend has it some called it John instead — not because of Nash’s name, but as a nod to the fact they played it on the hexagonal tiles of the bathroom in the department!  Nash became Hex when Parker Brothers tried to market the 11×11 game with that name.  Around the same time Nash was attempting to market the game and was quite upset to discover he’d been scooped.  He wasn’t aware at that time that Piet Hein had in fact scooped him several years earlier anyway.

In any case, the game became an object of enthusiastic study by Nash and his colleagues, and they made numerous interesting discoveries about its properties.  Hex was largely just an object of interest for academics for the most part, as Parker Brothers’ attempt to sell the game didn’t amount to much.  A few years later the mathematician Martin Gardner played a pivotal role in the eventual worldwide popularisation of the game — his 1957 Scientific American column on Hex brought the game to a whole new audience.

Hex remains highly popular with mathematicians and computer scientists today, as well as with gamers, as it has some fascinating properties.  For example, draws are completely impossible in Hex — no matter how inept or random the players’ moves, eventually one of the players will always make a winning connection across the board.  This result is actually a consequence of something called the Brouwer fixed-point theorem, which I won’t get into here.  We also know that a winning strategy for the first player exists, but we have no idea what it is (well, we’ve found it by brute-force computer calculation for 9×9 boards and smaller, but not on the boards we actually play on).  A quick browse of the literature on Hex will reveal some fascinating contributions from big names in maths and computer science.

The current state of play

In the years since Piet Hein’s invention of Polygon, Hex has evolved somewhat.  The classic 11×11 board is still popular, since it has a nice balance of speed of play and intricacy.  Games on the 11×11 board are over relatively quickly, yet these 121 hexagons allow for a staggering 1056 possible board positions, 10 billion times more than the number of possible Chess positions (1046)!

However many Hex players nowadays are using larger boards, with 13×13 and 19×19 being particularly popular. 14×14 is fairly common as well, particularly as that was John Nash’s preferred board size. In any case, larger boards push the game further into the realm of strategy rather than tactics, allowing for deeper moves with greater subtlety. Here’s how a 13×13 Hex board looks today:

hex13-sample

A 13×13 Hex board.

And here is a 19×19 Hex board that I designed and just had printed on a 19×19 neoprene mat.  The mat is 93cm x 56cm, and the hexes are large enough for use with Go stones.

Hex19-1

My 19×19 Hex board.

In general we’ve abandoned the circles and stars of Polygon’s heyday and opted for the two players using black and white stones to mark their hexes, with the board edges marked accordingly.  Often you’ll see blue and red stones used instead.

More importantly, now that we know that Hex gives the first player a winning advantage, we play Hex using the swap rule, an ingenious way to even things out.  When the first player places their stone, the second player may choose to play one of their colour in response, after which the game proceeds normally, or they may choose to swap colours and take that move for their own first move!

This clever rule change means that the first player must intentionally play a weaker opening move to avoid a swap, thereby mitigating their first-player advantage instantly.  In practice the strongest opening moves are in the centre of the board, as these allow for connecting stones to extend in every direction, so generally the first player will play around the edges at the start to avoid a swap.  As you might expect, the first-player advantage is somewhat diminished on larger boards, given that the impact of individual moves is smaller in general.

Side note — the swap rule is often called the pie rule as well, as it mirrors the fairest way to divide up a slice of pie between two people: one person cuts, the other chooses which slice they will eat.

 

Playing Hex

So, once we’ve grabbed a funky rhomboid board of our preferred size, a couple piles of stones and sat round a table to play, how does the game actually work?  Here’s a quick sample game, showing me defeating a basic computer opponent on the 11×11 board:

hex11-win1

I played this game using a fantastic bit of free Java-based software called Ai Ai, which has numerous awesome abstract strategy games available to play with a variety of AI opponents — find it here: http://mrraow.com/index.php/aiai-home/aiai/

 

The play in this game was reasonably simple, but if you jump onto the most popular site for playing Hex, Little Golem, and check out the larger boards you’ll soon see that the end result of a Hex game can look pretty complicated:

hex13-sample2

A game played earlier today on Little Golem (https://www.littlegolem.net/jsp/game/game.jsp?gid=2145661)

 

Black resigned after 70 moves, admitting defeat.  The reason why Black resigned may not be immediately obvious; after all, Black seems to have made good progress along the left side!  However, we can start to understand how games of Hex evolve once we understand some basic positions, particularly the bridge:

hex-bridge

An example of a bridge: White’s stones 2 and 4 can be connected no matter what Black does.

The bridge means that connection between the two relevant stones is unstoppable.  As you can see above, if Black plays at A to attempt to break apart White’s stones, White simply plays at B, and vice versa.  The bridge is a simple example of a template, a formation of stones and empty hexes that facilitates an unstoppable connection.

If you look again at the sample games above, you’ll see several examples of bridges being used to establish connections between stones.  Using this formation is far more efficient than placing stones methodically next to one another, but the connection they provide is just as solid!  Using bridges and similar templates allows you to build connections in fewer moves.  As you learn more of these templates in Hex, you’ll be able to spot a win or a loss coming long before the final stone is placed.

By the way, now that you know what a bridge is, you should be able to solve Piet Hein’s puzzle above!

Another key concept of Hex is that defence and offence are the same thing.  Remember that in Hex one player will always win — from this we can work out that if we prevent any possible win by the opponent, that means we have to win instead!  So when playing Hex, don’t be focussed just on your own bridge-building and forget your opponent — spending your moves on blocking them still gets you closer to a win.  Sometimes the best offence is a good defence.

To get started with Hex, I suggest you just jump right in and start playing some games.  You can play Hex  on Little Golem, Richard’s PBEM Server, Amecy Games, Gorrion, Hexy.games and igGameCenter among others.  You’ll soon find that Hex is an intricate and precise game with enormous amounts of depth.  If you work on building bridges, blocking your opponent, and getting a general feel for the flow of the game, you’ll soon start to get the hang of the basics.

After losing a few times and hopefully stumbling across a win or two, go and visit Matthew Seymour’s incredibly detailed guide on Hex strategy.  His site is details key concepts like ladders and edge templates, walks you through some sample games, and provides lots of useful resources, plus everything is demonstrated through interactive diagrams!  It’s an incredible guide.  The bridge example above is a screenshot from this site, which I hope will encourage you to visit.  On the real site you can experiment and play moves on all the diagrams, which really helps cement the concepts explained in the guide.

 

Hex Variants

As you might expect with a game this elemental, numerous Hex variants have been devised over the years to spice things up.  There’s a tonne of these so I’ll just briefly highlight a few interesting ones:

Misère HexThink of this as Opposite Hex — the first player to connect their sides of the board loses!  It’s an odd style of play to get your head around, where you need to force the opponent to connect while avoiding making progress yourself.  Interestingly, it’s been proven that the losing player has a strategy that guarantees every hex on the board will be filled before the game finishes.

Pex:  The rules here are the same as Hex, but the game is played on an unusual board — instead of hexagons, the board is tiled with irregular pentagons.  This changes the tactics significantly, given that the board spaces now have different connectivity, and makes for an interesting change of pace.   You can play Pex online at igGameCenter.

pex-iggc

An 8×8 Pex board.

Nex:  This intriguing variant uses the standard Hex board, but alongside your White and Black stones you add neutral Grey stones.  Grey stones can’t be part of either player’s winning connection, so they are obstacles to both players.  But what makes this game brilliant is the new options available — a player’s turn now gives them two possible moves:

  1. The player to move may add one stone of their colour AND one neutral stone to any empty hexes on the board, OR
  2. They may swap out two neutral stones for stones of their colour, and then replace one stone of their colour with a neutral one.

This means that moves are not permanent in Nex — your stones can be recycled when the board situation changes, and seemingly innocuous neutral stones can suddenly become new threats for either side when they transform.

Just like in Hex, there are no ties and one player must win.  You can play Nex on igGameCenter.

nex-sample-game1

A sample Nex game from the book Mathematical Games, Abstract Games — Black resigned.

Chameleon: Another intriguing variant that significantly changes up the play, Chameleon decouples players from colours.  In Chameleon, one player is Vertical and must make a connection of either colour from top to bottom, and the other is Horizontal and must make a connection of either colour from side to side.  On each turn a player may place a Black stone OR a White stone on the board on any empty hex.

The consequence of this is that players have to be aware of threats in the opponent’s direction from stones of either colour, making each move feel incredibly consequential!  It’s a bit of a mind-bender.  Chameleon benefits from playing on larger boards, as connections can happen too quickly on smaller ones given that players use both colours.  You can play it online using Richard’s PBEM Server.

 

What next?

Now that you’ve had an intro to the original connection game, you’ll be well-equipped to try your hand at Hex’s many fascinating cousins.  The basic concepts of Hex are helpful in a lot of other connection games too, although each of them adds their own unique wrinkles.

Over the next few posts, I’ll highlight some more connection games with interesting properties that are fun to play, including the Game of Y, TwixT, Havannah, ConHex, Unlur, and more.

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