Tag Archives: Christian Freeling

Oct 04 2020
7 Comments
Game Development, Games, News

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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Apr 28 2020
9 Comments
Games

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 P 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 P 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 (P =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 P 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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Mar 03 2020
9 Comments
Games

Connection Games III: Havannah and Starweb

In keeping with Part II, today I’m going to introduce two games by one designer — Christian Freeling, who maintains an invaluable website full of his creations including versions playable in your browser.   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.

However, there are two of his games that I find completely, indisputably brilliant:  Havannah and Starweb.  Both are fantastic additions to the connection game family.

Havannah

Havannah is a connection game that offers a completely unique take on the genre.  Connection games are typically characterised by a sense of absolute clarity — the goal is simple, singular, and direct.  Connect a thing to other things, and there you go.  But in Havannah, players can win in three different ways — and to play well, you need to threaten to do all of them and defend against all of them simultaneously.  The consequence is a game of intense depth and richness, and substantial challenge.

Here’s the basics:

  1. Two players, one with black stones and one with white, play Havannah on a hexagonal board tessellated with hexagons (known as a ‘hexhex’ board).  The commercial Havannah release used a hexhex board with 8 hexes on a side (169 playable hexes), but Freeling considers a hexhex-10 board to be ideal (271 playable hexes).
  2. The game starts with the swap/pie rule.
  3. Each turn, a player places one stone of their colour on any empty space on the board.  Once placed, stones do not move and are never removed.
  4. A player wins when they achieve one of the following configurations (these examples are from real games on Little Golem) —

A ring — a chain of pieces that completely surrounds at least one hex, which can be empty or occupied (by opposing stones or your own):

havannah-bigring1

Rings can get quite elaborate — can you see how White’s convoluted ring formation here?

havannah-ring1

Rings can also be tiny and enclose just one hex!  These are easier to spot so it can hurt when you lose this way….

A fork — a chain of stones connecting three non-corner hexes on three different sides of the board:

havannah-fork1

Black completes a fork here.  Note that it includes a corner hex, at the bottom, but also includes a non-corner one there too, so it still works!

havannah-elaboratefork

A rather impressively labyrinthine fork here from Black.  A clever win from what looks like a hard-fought game.

A bridge — a chain of stones connecting two corner hexagons:

havannah-bridgeproper1

White constructs a fairly convoluted bridge here from the top-right corner to the bottom corner

As you can see already, Havannah puts a lot on your plate as a player.  The rules are hardly any more complicated than any other connection game, but the objectives are many and varied.  The consequence of this is that at every turn you must be aware of the many possible implications of your opponent’s stones, and you have to learn to catch the signs of key strategic and tactical threats.

In fact the game is so strategically rich that in 2002 Christian Freeling instituted an AI challenge, betting €1000 that no computer could beat him even one game out of 10 on a hexhex-10 board within a decade.  Predictably, he lost that challenge in 2012 and lost 3 games of his ten-game match against the machines.

Now one might feel disappointed somehow when computer players surpass humans in games, but honestly having superhuman AI for a newer game is a good thing — it accelerates the decades- or centuries-long process we normally need to really probe how our games hold up at a high level of play.  That aside, to be fair to Christian Freeling, his game lasted nearly the full decade; these days, if anyone with some decent computing power is paying attention, any game would be lucky to last a few months.  Especially now that AI doesn’t even need to know the rules first to master a game!

Basic Havannah Tips

Havannah, even more than other connection games, really comes alive once you’re armed with a few key strategic and tactical concepts.  I’m by no means an expert here — at the end of this section I’ll link you to some people that are — but there’s a few tips I can offer to get you started:

  1. The game plays kind of like a combo of Go and Hex — a certain Go feel is apparent in how important whole-board strategic vision is, and that groups of stones can be ‘alive’ or ‘dead’ depending on their capability to form part of an attacking threat.  The Hex side manifests in the moment-to-moment tactics and the importance virtual connections (bridges, in Hex terms) between stones.
  2. Perhaps the most important strategic concept to learn is the frame — a set of stones forming the backbone of an unbreakable winning formation, regardless of the opponent’s response.  Check the guides I link below for some examples, and keep an eye out for your opponent threatening to make a frame!
  3. The one-hex ring enclosure — the mill — is a really important tool in Havannah.  Rarely will you beat an experienced opponent that way, but building a mill can force a response from your opponent, gaining you initiative — and can interfere with their plans for their own stones, as well.  Conversely, it’s important to learn how to defend against mill threats so you don’t fall prey to the same outcomes.
  4. Board size matters!  On smaller boards, bridges and forks are powerful.  On larger boards (hexhex-10 and up), bridges and forks are harder to build and rings become somewhat more prominent.
  5. Draws are possible in Havannah — but just barely.  Out of tens of thousands of online games, there are single-digit numbers of draws that have ever happened!  Therefore, don’t think an attempt at a drawing strategy will save you when things go bad — it’s extremely unlikely to work!

 

Havannah frames

An example of a ring frame (Black) and a fork frame (White)

To really dig into the complexities of Havannah, I strongly recommend the brief but comprehensive guide by David Ploog, available in PDF format here (and please see his other amazing guides for other games in the BGG thread here), which covers all the key concepts and includes numerous examples and some problems to test your comprehension.

For a bit of discussion and strategic and tactical guidance for Havannah from the creator himself, do check Christian Freeling’s Havannah website, and his articles in issues 14, 15 and 16 of Abstract Games Magazine (that link takes you to their back-issue archives).

Finally, when you feel up to the challenge, you can play Havannah via Stephen Tavener’s Ai Ai program, the Mindsports website, on Little Golem, Richard’s PBEM Server, igGameCenter, and probably other places too!  There’s a physical version of Havannah published by Ravensburger in 1981 that goes for very little on Ebay, but that only has a hexhex-8 board — for larger ones you’ll need to print something up yourself or repurpose another set, like Omega from Nestor Games.

While I’ve been on strike, my wife has helped me to learn Adobe Illustrator so I could make some nice hexhex-10 and hexhex-12 boards usable for Havannah and numerous other games.  The final results are available in three colour schemes from the BoardGameGeek Havannah files section.  These are sized for printing on 25 inch by 25 inch neoprene playmats, which are a popular way to get sturdy game boards made these days.  If you printed them on mats of that size you can use standard 22mm Go stones on these boards.

I also made hexhex boards of size 7, 8, 10, 11, and 12 in the style of the board used on Little Golem, which is probably the most popular place to play Havannah.  I like the random splash of colours across the hex grid, so I decided to create a range of print-and-play boards in that style.  You can find these boards at my BGG filepage for Havannah along with the other versions.

hexhex-10_RED-01

Hexhex-10 board, with highlighted borders to allow players to use this one board as a hexhex-9, 8, 7, etc. as well.  Two other colour schemes are available on BGG, too.

hexhex-12_LG style-01

Hexhex-12 board in Little Golem style.  I really am proud of this one, as it took some doing to replicate that colour pattern. 

Laika-hexhex10

Showing off how the game works on my neoprene-printed hexhex-10 Havannah board.  My dog Laika is fascinated.

However you go about playing it, Havannah is an absolute gem among the connection games.  It’s tactical and strategic, mind-bending, and always enticing to play.  If there were any justice in the world it’d be getting played by millions of people like Chess and Go, but alas, we’ve got to dig up players the old-fashioned way.  But Havannah’s worth the trouble.

 

Starweb

One thing you’ll notice about Christian Freeling if you start following developments in the abstract strategy games community is that he has claimed he was retiring from game design about 100 times, yet he always comes back.  Starweb appeared during one of these ephemeral retirements — he says the game came to his mind suddenly, basically fully-formed almost out of nowhere.  Lucky for us that it did, as in my opinion it’s another masterpiece.

Starweb is a clear descendant of Star/*Star, being a connection game that incentivises connecting certain key points on the board with as few groups of stones as possible.  What makes Starweb stand out is both the shape of the board, which creates 18 key corner hexes that drive the gameplay, and the triangular scoring mechanism.

Starweb’s simple and elegant rules lead to board-spanning strategic play, in some ways reminiscent of Havannah.  Here’s what the standard board looks like:

starweb-regular-01

Starweb standard board (dubbed size 10 in Ai Ai).  It’s a hexhex-7 board with six added chunks of 15 hexes on each side, giving us 217 playable hexes in total, and 18 corner hexes (highlighted in brown).  And yes, that is the font from Star Trek — bonus nerd points if you know what language that is underneath the Trek-style logo!

Play is appealingly simple, although the scoring mechanism takes a moment to sink in:

  1. Two players, Black and White, play on the standard Starweb board or one of its smaller variants.  The board starts empty.
  2. Play starts with the swap/pie rule.
  3. Each turn, a player places one stone of their colour on any empty hex on the board.  Once placed, stones never move and are never removed.  Players may also pass their turn and not place a stone.
  4. The game ends when both players pass in succession.
  5. Once the game ends, players calculate their score as follows:
    1. Players identify each group of their stones that contains at least one corner cell (a ‘group’ is a connected bunch of like-coloured stones)
    2. The score for a group containing n corners is the sum of n and all positive integers less than n.  In other words, a group containing 1 corner is worth 1 point; 2 corners = 2 + 1 = 3 points; 3 corners = 3 + 2 + 1 = 6 points; 4 corners = 4 + 3 + 2 + 1 = 10 points; and so on.
    3. The player with the highest score wins.  In the event of a tied score, the player who placed the second stone wins.

So, to win Starweb, you have to occupy corner cells and connect those corners together into united groups of stones to score more points — the more corners in your group, the more points you score.  At the start of the game the players will normally go back and forth occupying corner cells, and from there proceed to wind their way across the board trying to connect them together.  This leads to dense, complicated webs of connected stones — hence the name Starweb!

I have to admit I’m not a huge fan of the second-player-wins-draws rule, since there’s already a swap rule in place at the start — that reminds me of Armageddon Chess, where Black wins in the case of a draw, which is pretty widely disliked.  But the abstract games community generally seems very adamantly against draws, and designers tend to go to significant lengths to avoid them.  That seems somewhat strange to me, since that means the game is by definition unbalanced as one of the players will have a winning strategy with perfect play; I personally slightly prefer Havannah/Shogi scenarios where draws are possible but just quite rare.  In any case equal scores in Starweb are going to be pretty uncommon, so it’s not a big issue particularly, but the rule may influence your decision whether or not to swap your opponent’s opening move when going second.

Playing Starweb

The richness of Starweb becomes apparent once you discover that preventing your opponent’s connections between corners can be just as vital as connecting your own.  Early on Christian Freeling realised that a minority strategy — in which one player declines to take all the corners they could and instead works to invade the opponent’s territory and deny them connections — is quite viable.

Here’s an example game against AI on a small board that he posted on BoardGameGeek:

starweb-8-corners-small

You can see here that White (the AI) holds more corners (10 vs 8), but Black (Freeling) managed to cut several of them off, denying his opponent the ability to make big-scoring groups.  Meanwhile he was able to slice through the centre of the board, leading to a winning score despite holding less corners.

This game also shows off other nice properties of Starweb: the games tend to be intricate and long; and the game plays well even on much smaller boards.  The Starweb implementation in Ai Ai allows for boards even smaller than the above, and the game still holds up.  It’s definitely more fun on the normal-sized board though.

The minority strategy still works on the large board, too:

starweb-minority-strategy-large

After connecting stones 86 and 6 in the bottom right, Black will extend his lead by 5 more points. White is completely lost.

Freeling (Black) again takes less corners here, but manages to sprawl all the way across the board for a big-scoring connection.  White has no hope of catching up, as the AI’s largest groups are split down the middle by Black’s connection across the centre of the board, and the extra White corners elsewhere are completely walled off.

Through these sample games we can see that Starweb admits a variety of strategic approaches; when first learning the game we might think grabbing every corner is essential, but as we see above, denying your opponent scoring opportunities can compensate.  And by declining corners you can gain the initiative, exchanging turns you’d have spent on building a group for turns you can spend on attacking your opponent’s strategic goals.

At first the game might seem overly mathematical, in that counting corners and calculating scores seems so critical.  But in actual play that doesn’t really interfere; once corners are occupied, you don’t need to track them anymore, and that normally happens very early in the game.  Subsequently you just need to be aware of how many corners you need to connect to keep your opponent at bay.  So the numbers come into play when planning your approach to a particular early-game board situation, but after that you can focus mainly on tactics and trying to connect your groups and execute your plan.

For detailed and enlightening discussion on Starweb’s strategic complexities, you can check out the discussion from Freeling and others on BoardGameGeek.  That thread goes into more detail on the sample games I posted, and numerous others as well.  There’s also some useful discussion on the Arimaa Forums in this thread, starting at post #104, although sadly the image links are all broken now.  Starweb is still a young game, so as more people discover it perhaps we will see start to see guides on strategy and tactics on the level of those we can find for Havannah.

I highly recommend Starweb — you can play on Freeling’s MindSports site, or you can play against AI and human opponents on various board sizes via Stephen Tavener’s AiAi software of course.   In my opinion it’s an underrated gem, right up there with Havannah as one of the most strategically satisfying connection games.  It’s still early days for Starweb, as it was only developed in 2017, so hopefully as the years go by the game will develop the following it deserves.

Where next?

So, we’ve taken a look at the connection game titan Hex, the quirky and influential family of games by Craig Schensted/Ea Ea; and now two strategic masterpieces by Christian Freeling.  Already you could easily spend a lifetime exploring these games and never unlock all their secrets.

Of course that’s far from everything the genre has to offer!  Next time I’ll cover one more excellent connect-the-key-hexes game, Side Stitch, and then I’ll spend a fair bit of time talking about Unlur, an ingenious asymmetric connection game where the two players have different winning conditions.

 

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