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thoughts about and reviews of particular games

Abalone

Abalone is a two-player abstract strategy board game designed by Michel Lalet and Laurent Lévi in 1987. To win a player must push 6 of their opponent’s marbles off of the board.

My Abalone set arrived in the mail yesterday, and the first thing I noticed were the amazing aesthetics of the game. Lalet and Lévi created a game that engages multiple senses. Visually, the board and the marbles are beautiful, even more so when the opposing marbles are pushing into one another in a strategic battle. The game is incredibly tactile as well. The marbles are large and made out of glass rather than plastic so they have a nice weight to them. And the experience of pushing a row of marbles and feeling them click back into place is just fantastic. And the sounds of the game, the clicks of the marbles against each other and the sound of a marble being knocked into the gutter that surrounds the board, are wonderful too.

Beyond the aesthetics of the board and pieces though, the game itself is clearly a strategic triumph. The simple rules of the game naturally produce strategic principles such as control the center and make sure not to let your opponent split your marbles. Furthermore, there are certain shapes that are very strong or efficient and other shapes that are weak or inefficient. For example, since a maximum of three of your marbles can be pushed at one time, lines that are greater than 3 are bad shapes, since to use three of those marbles in a push would require disconnecting one’s own group. A rhombus with three marbles per side, by contrast, is an efficient, strong shape. It is safe from pushes along two out of the three board axes and can push in many directions itself. There is also a nice balance between material and positional advantages in this game. Although having pushed out more of your opponent’s marbles is certainly a significant advantage, a player could have a 4-2 or even 4-1 lead but nevertheless be losing because of positional factors.

The general feel of Abalone is much less tactical and dynamic than something like chess, although the ability to calculate/visualize possible position transformations is often still important.

The central pushing mechanism is also incredibly versatile. Not only can you get a different experience by trying a different starting position (though some starting positions are susceptible to deadlocks in which neither player can make any progress), but there are also more substantive variants as well, and I’m sure there are more as of now unimagined variants that would be possible.

Here are some ideas that Abalone players have come up with:

PLANETOID ABALONE

Planetoids are simply immovable objects placed on the Abalone game board. To create Planetoids, neutral-colored marbles are useful. There are several methods of Planetoid placement.

A. Place Planetoids in an agreed-upon pattern on the board before the start of play.

B. Place Planetoids at the start of play. Each player gets the same number of Planetoids and places them as desired on the board.

C. Each player gets the same number if Planetoids They are placed on the board during play as that player’s turn.

Special rule: Pieces completely blocked in by Planetoids are considered pushed off the board. It is possible by this rule to obtain a draw.

BLACK HOLE ABALONE

One or two marbles of a neutral color are placed on the board at the start of the game, either on the center space or on the two middle corner spaces. These marbles are “Black Holes.”

A marble that is pushed into a Black Hole does not move the Black Hole. Instead, that marble is removed from the board, but does not count toward victory for the opposing player.

Marbles moving or being pushed onto spaces next to a Black Hole are paralyzed. They may not push or move on their own, but they may be pushed by either side. Paralyzed Marbles count toward the maximum that can participate in a column of a single color (three total). In practice, only a single marble may participate in a column of three. This is because it takes two others to move it; two marbles would require three others to move them, bringing the total to five. Opposite-colored marbles are unaffected by their opponent’s plight; they are dealt with normally.

Note: moving a paralyzed piece immediately results in the moving piece becoming stuck.

See this page for further variants, as well as starting positions for 3, 4, 5, and 6 players:

If you’re interested in learning more about this game, I recommend watching the high level matches that are available on YouTube. For instance:

The Abalone World Championship is going to be held online on August 30th, so make sure to tune in or toss your hat in the ring yourself! I hope this wonderful game continues to attract followers!

I will also say that I am intrigued by what play would be like on a larger board with more marbles. Would this expansion allow for a deeper strategies, or would the game behave essentially the same?

Categories
my game designs

Turning Conway’s “Life” into a Game (Part 1)

This post takes up the project described in the previous one, so it makes sense to start there if you haven’t already seen it.

I take it that the essence of Conway’s Game of Life is that cells can die for two reasons.

  1. Isolation
  2. Overcrowding

And that conditions must be in between these two extremes for new cells to be born.

This essence must be preserved in whatever multiplayer game is to be derived from this cellular automaton. And the players must have input into the position, i.e., they must be able to make moves.

Other than these constants, there are many parameters that could be varied

  • Board geometry/number of ‘neighbors’
    • The number of neighbors on a 2D board could be 3, 4, 6, or 8 (as in the original) – the numbers for overcrowding and isolation would be changed accordingly
  • The move mechanism
    • Are moves made by placing tokens down on the board (making that cell alive) or by moving tokens already on the board (turning the starting cell dead and the ending cell alive)
  • Who has control over which tokens?
    • The most obvious idea is that there are tokens of two colors, with the goal being to eliminate the tokens of the opponent’s color, but there are other possibilities, e.g., a neutral kind of token that could be moved by either (or neither) player.
  • Goal
    • Again, perhaps the most natural goal is to eliminate the opponents colony of pieces, but there are others to consider:
      • Making a certain ‘goal cell’ alive. Or destroying a certain stable formation.
      • Territorial goals
      • Last to be able to move
  • Initial position
  • And I’m sure there are other variables that I’m not thinking of…

That’s it for today–just laying out what I take to be the essence of Conway’s Game of Life and some factors that could be varied while keeping that essence constant. Considering just the five variables above there is already the potential to construct many different games on the basis of “Life.” The next step is to try some of these out, and note what tends to work well and produce interesting games, and what doesn’t.

Categories
my game designs

Turning Cellular Automata into Multiplayer Games

A cellular automaton consists of a regular grid of cells, each in one of a finite number of states such as on and off. The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously.

A “glider gun” in Conway’s Game of Life

It is characteristic of many cellular automata, e.g., Conway’s Game of Life pictured above, that relatively simple rules for the evolution of one state to another generate a high degree of emergent complexity. For instance, the rules for the Game of Life are as follows. A live cell is “on” and a dead cell “off,” and the “neighbors” each cell interacts with are the eight adjacent cells.

  1. Any live cell with fewer than two live neighbours dies, as if by underpopulation.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by overpopulation.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

Notably, emergent complexity is also a highly praised feature of many games; a game like Go, for instance, has deep emergent strategy from a simply set of rules. Conway’s Game of Life as it stands is not really a game, or if it is, it is what is sometimes called a 0-player game. In other words, there are no players making moves, that is, changing the game state in the course of its evolution. But it already possesses a quality we care about in games. So this raises the following question for me: Can an emergently complex automata like the Game of Life be transformed into an emergently complex multiplayer game?

I plan to pursue this question in following posts, where I will document my attempt to turn Conway’s automaton into a game, but likely this is not the sort of task that can only be accomplished in one particular way, and I challenge the reader to make a stab at it too!

As we know from The Turk, a mechanical automaton can contain hidden life!

The Turk, an elaborate hoax exhibited as a chess automaton in the late 18th and early 19th centuries.
Categories
other essays and articles about games the philosophy of games

Organicity in Abstract Strategy Games

I first encountered Christian Freeling’s concept of organicity via a blog post by Nick Bentley, another accomplished abstract strategy game designer and mentee of Freeling. The concept of organicity has deeply shaped the way I think about games, so I’ve copied both Freeling’s article explaining the concept and Bentley’s introduction here. As both a chess player and a go player, I found the comparison of those two games with respect to organicity especially fascinating.

The introduction by Nick Bentley:

Note: This post wasn’t written by me (Nick Bentley), but rather by one of my game design mentors, Christian Freeling:

freeling-1
…who is probably insane

Christian is an éminence grise in the world of abstract strategy games and I wouldn’t be the designer I am without him. He shares my impossible love for these games and he’s designed some of the best in the world. But such games are rarely published, so his accomplishments aren’t widely known. This situation is, if not tragic, at least deeply silly.

In any case, it’s an honor to present the essay below. It’s about a quality Christian prizes in games (as do I), which he calls organicity. It’s a quality he speaks of often, but it’s not an easy concept to understand and discussions of the subject can spiral into confusion. This essay can be seen as an attempt to remedy that. 

You can read more by Christian at his website, Mindsports. If you want to try his games, I recommend starting with Dameo, which is not only one of his more accessible games, but also my personal favorite. As with any deep combinatorial game, you’ll likely need to play a bunch to really feel it in your bones, but when you do there’s a good chance it’ll stick with you forever. If games are like texts, great abstract games are poetry: you don’t understand everything about them at first, but they live and grow inside you. Christian’s games certainly qualify.

The original article by Christian Freeling:

Chess and Go
Organicity in abstract strategy games may be defined as “the degree to which a game’s behaviour may be perceived as organic, or ‘life like’”. There’s an objective side to it because Go is felt to be more organic than Chess, almost by consensus. There’s also a subjective side because organic behaviour is a way of perceiving rather than a provable property. And it’s not a quality issue either: Chess and Go are both great games.

If we look at both games in fast-forward, the behaviour of Chess looks mechanical. There are a lot of different kinds of moves and it looks somewhat like a complex sliding puzzle. Go on the other hand has no movement, yet looks like a living, growing organism. An enduring notion that came to my mind after I had just learned enough of the game to suddenly perceive its unity, was that of two conflicting sets of bacteria in a Petri dish. Something alive.

its-alive

Go actually is about growth and life and death so seeing it as something alive isn’t totally weird, but in my case it was the first time it came to me and it instantly made me understand the game on a different level. Not that I ever became a good Go player, but then, I never became very good at any game.

The games’ emergence in human consciousness
If we look at the history of both games, not in terms of periods and dates but in terms of their emergence in human consciousness, then we see a rather fundamental difference.

  • Chess – Chess evolved around its goal of checkmating the king. You can’t ‘think Chess’ without this a priori goal in mind so mechanics evolved around it.
  • Go – Go evolved around the mechanism of capturing stones or groups by depriving them from their liberties and this ‘elimination’ aspect is still crucial for the game. Go’s design started from this ‘core behaviour’.

Cycles and suicide

ko-freeling

One of the first things the progenitors of Go must have noticed is the Ko situation: Black can capture at A but White can recapture at B. This was good news and bad news.

The good news was that suicide, making a placement that leaves the placed stone or the group to which it belongs without liberties, obviously came in two forms. One is plain suicide which, at least with a regular goal in mind, seems to go against the spirit of a game. The other is ‘suicide including ressurection’ in which a stone is placed where it or its group has no liberties but where it gets at least one new liberty as the result of a simultaneous capture. This would seem a fair procedure and a just outcome in a ‘game to be’.

The bad news is that it is a cycle and thus needs regulation.

The change to a territorial goal
This wasn’t the only early discovery. The progenitors probably agreed that plain suicide would go against a game’s spirit. But making it illegal would mean that groups could emerge that were safe from capture! That in turn would be somewhat at odds with compulsory placement. Rather does it suggest that players should get the option to pass.

eye


The two black groups above share two liberties. Under a protocol of single placement, with suicide being illegal, they cannot be captured. These considerations regarding the game’s ‘core behaviour’ suggested building territory rather than capturing groups as its main goal. A very early change at the very cradle of its rules, but one that ultimately led to the game as it is played today.

Inside out, outside in
Go evolved ‘inside out’, that is, starting from its core behaviour of placement and capture by enclosure. Careful consideration of this behaviour led to a territorial goal, and while many implications still required regulation, Go in the process ‘became itself’.
Chess evolved ‘outside in’. It didn’t start from core behaviour but from a core concept: capturing the king. Pieces were assembled and mechanics were adapted to best serve the concept. Where they were felt to fall short they were modified to improve the game’s behaviour, but choosing pieces and rules always breathes a certain arbitrariness, even if the result is satisfactory.

A correlation of sorts
Chess evolved outside in and has a low degree of organicity. Go evolved inside out and has a high one. Is there a correlation between organicity and the way a game evolves? Generally speaking, yes. But Reversi, which later became popular as Othello, was invented inside out, starting from core behaviour that emphatically suggests a territorial goal. Havannah on the other hand was invented outside in, starting from a ‘connection’ goal and finding a working assembly of three types of connection by sheer luck. Yet Reversi behaves as an organism trapped in a poorly fitting exoskeleton, while Havannah displays a fair amount of organicity. So the correlation isn’t cast in concrete. Yet it is there, and it begs the question what makes a game display organicity.

The Game of Life


A striking example of organic behaviour of ‘pieces’ is John Conway’s Game of Life (above). The very name illustrates that the game is very suggestive of it and that this is generally recognised as such. If we look at how it actually works we see that …

  • it is uniform: there is only one kind of ‘piece’
  • it features growth
  • it features reduction
  • it features movement based on them
  • it has a simple protocol to create these features

If these are not actual conditions for organic behaviour, then they obviously have at least some affinity with it. Conway’s game is great to watch and its protocol isn’t hard to understand. In fact it isn’t unlike Go’s protocol: the fate of a piece depends on its neighbours. But the Game of Life, although it isn’t actually a game, has an immediacy about it that’s appealing. Watching a game of Go in fast forward has a similar appeal, but learning Go from the ground up takes a lifetime. There’s little immediacy about that.

Diversification
The core concept of Chess presumably emerged some 1500 years ago in India, in a game called Chaturanga:


It represented a battle between two armies, each led by a ‘Raja’ who commanded different ‘army divisions’. Note that the Rajas do not face each other. This concept diversified by travel and trade and war till it eventually survived in three main branches, ChessShogi and XiangQi, and a couple of thousands of variants.

Chess has been an international sport for some one and a half century now, while Shogi became big in Japan and XiangQi was big in China. This growth and diversification resulted from Chess being a concept rather than a specific game. It mimicked human warfare with a commander and a range of divisions, so it is no miracle that cultural influences helped shape its actual form at any given place and time. Pieces were interesting to look at and invited to be made with different designs. Rules were arbitrary and thus subject to modifications and adaptions. Because it was so much a representation of human conflict it soon overtook Go in terms of geographical spread.
Is it fair to assume Chess stimulated human imagination because of its exuberance? You had kings, generals or commanders, surrounded by knights, chariots, cannons, lances, elephants, rooks, bishops, infantry and the like, engaged in epic battle. And it offered abundant leeway to adapt it to different cultures.

The elite and the masses
Chess’ a priori goal of representing human warfare makes it very different from Go. The emergence of Go as a concept was preceded by its mechanics, not followed by it as in Chess. These mechanics were based on a square grid and plain black and white stones and they showed the way to Go, pun intended. The game to which they led looked nothing like any human battle. Far more an abstract battle than Chess and not at all fit to be adapted to different cultures in a different way. In the higher echelons of ancient China knowledge of the game was considered a requirement and learning it a privilege. But that was a rather elite player base and XiangQi, with its theatrical mimic of human conflict, became the game of the masses.

This restriction to the social and intellectual elite may have hampered Go’s spread. Its popularity in the West only increased from the mid-twentieth century onwards and comparisons with Chess were inevitable. Go could not be dismissed as less of an intellectual challenge, so it was often presented by its cognoscenti as more of an intellectual challenge. Since both games proved to be too much of an intellectual challenge for me, at least in terms of playing at any commendable level, I can’t really comment on the issue.

Chess versus Checkers
There were similar and ongoing comparisons between Chess on the one hand and Checkers and Draughts on the other. In these comparisons the roles of ‘elite versus working class’ had been reversed, with Chess being the game of the social and intellectual elite and Checkers as a kind of republican chess, in which hereditary kings had been replaced by common men who had reached a deserved promotion. A simple game for a working class that often couldn’t afford a Chess set in the first place.

From the very beginning there were some influential voices in support of the qualities of Checkers, like Edgar Allan Poe who wrote a famous paragraph about it in “The Murders in the Rue Morgue“:

I will, therefore, take occasion to assert that the higher powers of the reflective intellect are more decidedly and more usefully tasked by the unostentatious game of draughts than by all the elaborate frivolity of chess. In this latter, where the pieces have different and bizarre motions, with various and variable values, what is only complex is mistaken (a not unusual error) for what is profound. The attention is here called powerfully into play. If it flag for an instant, an oversight is committed, resulting in injury or defeat. The possible moves being not only manifold but involute, the chances of such oversights are multiplied; and in nine cases out of ten it is the more concentrative rather than the more acute player who conquers. In draughts, on the contrary, where the moves are unique and have but little variation, the probabilities of inadvertence are diminished, and the mere attention being left comparatively unemployed, what advantages are obtained by either party are obtained by superior acumen.

I feel this is not entirely fair to Chess but at the same time the writer draws attention to Checkers’ organicity as opposed to Chess’ supposed ‘frivolity’.

Checkers’ organicity
The organicity of Checkers is lower than that of Go. Checkers has an initial position, lacks growth and isn’t quite that uniform due to promotion, all of which is not very organic. It is fairly uniform nonetheless and has movement and capture in its favour. Most importantly, Poe emphasises the unity of Checkers’ modus operandi, as a single organism rather than a multifunctional mechanism. But an ‘organism’ would rather feature growth and lack reduction than vice versa. Another thing an organism would strive for is more freedom. Checkers gave rise to International Draughts which is more free in its capture options and king moves, and capable of magnificent combinations that are reminiscent of a physical sport like judo. It therefore feels more organic than its ancestor.

Is Go the only truly organic game?
Definitely not, but if we look at the status of abstract strategy games other than Go in terms of organicity, the landscape is bleak. We already mentioned Othello as a questionable outcome of inside out design and Checkers doesn’t quite live up to organic behaviour either.

Then there’s Hex. A delight to some, a desert to others, but in a popular vote the ‘deserts’ would win by a landslide. You can’t even tell if the ‘design process’ was inside out or outside in or indeed at all, because the goal and the mechanism are so inseparably connected that ‘seeing’ it operate means you invented the game.

Hex is a simple uniform ‘growth only’ connection game, a pencil and paper game in fact, but its strategy is very complex and rather monomaniacal. It’s hard to see anything as a ‘local issue’ or to distinguish between local and general priorities. The few people that mastered the game to a high degree often play moves that seem incomprehensible to beginners. That’s a big difference with Go, where local issues are abundant and where a beginner can more or less understand the general flow of a game between masters. Territory is everywhere, but where is that connection? Somewhere?

So Hex is brilliant, but it suffers from its inherent goal. Elimination and conquering territory are part of human behaviour and worth fighting for. So far as ‘making connections’ is inherently human, it is a more of a social activity and not so much a source of conflict. Great games have always been existential or territorial. It suggests that core behaviour is most promising if it points to either goal or indeed, as I found out recently, to both.

Is there any future for highly organic games?
Most designers work for a market. Their designs are almost inherently ‘outside in’ because the games have to look good and they must be fast and tricky. Any object will do, there’s hardly any hierarchy. Games also must be ‘assembled’ to create market demand because uniformity is felt to be boring. It’s hard to assemble uniformity so things must be added.

I’m not going to comment on any recent abstracts but I do understand their designers. You can decide to make a game for the market, especially if backed by a manufacturer. It’s a rational process based on market research and you make sure that the outcome has visual appeal. You can not decide to find promising core behaviour, and if you do there’s always a chance that it will unfold into a game that behaves beautifully, but looks dull. Like if you can play it on a chess board with checkers. Some choice.

The first wave
As a kid I had Draughts players among my heroes, can you imagine? Around thirty my interest in abstract games became more general, not to mention more obsessive. Then, in the eighties, I invented a lot of games without bothering about inside out or outside in. Two of them are worth mentioning, Grand Chess and Emergo.

With Grand Chess I completed Chess and I did a good job, freeing the rooks and modifying promotion in the process. Grand Chess, I’m sure, will ultimately prove to be a better sport weapon than Chess. But ‘organicity’ had no part in it.

That cannot be said of Emergo because Emergo is all organicity. But I didn’t think in those terms yet, I simply extracted the ‘core behaviour’ of column checkers from a game in which it seemed trapped, and followed it through to its inherent conclusion. And that turned out to be an organism that is spiralling upwards in an inticate dance, with fewer and fewer pieces growing higher and higher till inevitably one color is on top of all pieces. It is poetry in motion and turned out to be an unparalelled source of truly deep combinations that require powers of visualisation similar to the ones that good Draughts players must have. And it is more decisive than Dameo.

The curious thing is that this beautifully simple and utterly decisive behaviour isn’t at all recognised by the abstract game community at large. Here is the only ‘checkers’ game that features growth, but no reduction. The only existential game that is totally organic. Almost the only one that behaves omni-directional, in a pit rather than on a track. Almost the only totally uniform one. And certainly the only column checkers game that didn’t emerge as the ‘columnification’ of an existing checkers variant. But you can’t sell it, metaphorically speaking, to the BGG abstract games community.

An intermediate game
Then came the year 2000 and with it Dameo. Dameo is ‘checkers’ so it looks dull. You can’t sell it because everyone already has it. And not being able to buy it is seen as a major handicap at BGG. Thus it took my esteemed fellow designer Nick Bentley [editor’s note: that’s me!] one and a half decade to discover the game. If I may quote him from a mail regarding this very article:

I love this sentence: “Yet Reversi behaves as an organism trapped in a poorly fitting exoskeleton”. Incidentally, “poorly fitting exoskeleton” is how I feel about most draughts variants, and one reason I’ve come to cherish Dameo so much. It’s structured to showcase the thing that makes draughts good, and it does uniquely well in that regard.

And that’s how most people feel about checkers variants. Nick has an antenna for organic behaviour so he eventually discovered that Dameo has a high degree of it … for a draughts game. But it doesn’t pervade the game like it does Emergo.

The second wave
Circumstances made that it wasn’t till 2008 that I became involved again by translating the rules of games at iGGC to dutch. It was hard not to think about games. It brought me back to the games world and thus the second wave started.

In Moving Forward Looking Back I mention five games that matter to me and that I feel should matter to the abstract games community at large. Two of them are Symple and Sygo. Both use a move protocol that is organic in itself. The difference is that Symple is a territory/connection hybrid and Sygo is a Go variant. They look very much alike and both look very much like Go and are played on a Go board. Some irony. But all three behave very differently.

These games weren’t invented with any a priori intention regarding their behaviour. I found the move protocol in the magical moments again, in the dark, looking for behaviour. It is a generic protocol with an affinity for placement games and it turned out to harbour a high resolution balancing mechanism that is totally fair. It seamlessly adapted to the slightly different demands of both games. Where Symple requires compulsory placement, Sygo is a Go variant and requires the option to pass wholly or partly. Both have natural behaviour with a very high organicity, but neither has the progressive refinement of tactics that Go has. On the bright side, their tactics are more than adequate to serve strategy and strategy itself may be no less difficult than Go strategy.

Not seeing the game for the rules
I’m fascinated by organic behaviour and by the games it may render. The main characteristic of starting from ‘core behaviour’ is that you’ll have to find it in the first place, but after that the process is largely self-explanatory. There may be inherent issues in want of regulation, such as cycles in Go for instance, but these are usually easy to solve. Play testing such a game is seldom needed to evaluate the rules, because they follow an inherent logic. But its behaviour needs to be evaluated as it may reveal some surprises, because core behaviour provides only a few clues about actual behaviour.

There’s also a drawback in communicating such a game. I can visualise behaviour before even thinking about rules. I’ve been made aware that only a few people can do the reverse, to ‘see through the rules’ all the way to the organism that gave rise them. Most people can’t and this constitutes an almost inherent hurdle. Organic behaviour is fascinating once you understand it, and if the rules don’t immediately speak to someone, that is unlikely to happen.

To be or not to be
I never did all that much to promote my games. I invented. More in particular, I never did much to introduce Grand Chess to the Chess world or Dameo to the Draughts world. But they persisted and will continue to do so because they are better than Chess and Draughts.

I’m not sure about Emergo but I can’t imagine players will let the most organic elimination game ever, the most dramatic one and one of the the richest ones in terms of combinations, slip into oblivion.

I’m also certain that they will have less reservations to do exactly that with Symple and Sygo. These games weren’t meant to top Go and they indeed don’t. They primarily resulted from finding the Symple move protocol and discovering its properties. To bid them farewell I’ll summarise their properties one last time.

Symple merges a territorial goal and a connection goal in a most intricate and simple way. A group is worth the number of its stones minus a ‘group penalty’ that every separate group carries as an original sin. Thus connecting two groups gets rid of one penalty. The penalty is variable and must be agreed on before a game. The higher the penalty, the more the emphasis leans towards connection in the territory/connection balance. The game displays a great elasticity in this respect that cannot be found in any other game. Symple has compulsory placement and no capture, and in a balanced game the final stages may pan out very dramatically. A slight misperception or miscalculation may deprive a player of growing options and force him to an involontary invasion, gaining a point or maybe two or three, but losing the number of points of the penalty.

Sygo is a Go variant based on ‘othelloanian capture‘. The redeeming quality of this way of capture, also known as ‘flip capture’, is that it is cycle free. Not so redeeming is the fact that it is very difficult to create eyes and get life. Several inventors, tempted by the prospect of being rid of cycles, made that very discovery. Most of them felt that the problem only could be solved by an additional safety criterion. Thus they got things to ‘work’ but at the price of somewhat betraying the very mechanics that gave rise to Go.

Sygo does not need any additional safety criterion. The simultaneous growth of groups makes creating eyes and getting life possible. It’s not always easy, and you can’t always save every group, but it’s effective enough to shape the very behaviour of the game. A player may pass, wholly or in part, without losing the right to move in a subsequent turn and suicide is illegal. Sounds familiar doesn’t it?

Sygo is a cycle free Go variant that needs no Komi. It is a flip capture variant that needs no artificial additives. These hard to get qualities were much sought after by the abstract games community, and still are for that matter, because inventing games is as human as playing them. I didn’t seek them, but I found them anyway.

The story of Storisende


The last loose end
In December 2016 I invented Io, the organic version of Othello, and announced once again it would be my last game. But in July 2017 Starweb appeared out of the blue, an accidental invention because the drive to invent had gone.

That is, almost. There was one nagging concept that had emerged about half way, and it wouldn’t let go. It was a hex grid with separate territories consisting of cells, that would grow cell by cell, until growing by a particular cell would mean a merger with one or more adjacent territories. Since separate territories would never merge, that was the basic idea, a cell of ‘the Wall’ would appear on the offending cell. The process eventually would result in territories that were tightly squeezed together and separated by a web-like Wall. A very organic ‘core behaviour’ taken from Mu.

In Mu’s case all complexity derives from the explosion mechanism, not from the manner the Wall arises, so I was focusing on the latter. If this manner could be fuelled, I thought, by a simple single step move-and-grow mechanism it might lead to an intriguing game.

The invention process
When finally decided to give in, the process turned out to be rather obvious. I saw the board covered with hex tiles, as in Mu, and a tile would either disappear or be flipped over to become a cell of the Wall, the first time any piece would vacate it. So there I had the basis: the organic emergence of the Wall as a result of both players’ actions. But ‘pieces’ were obviously inherent, so what about them?

Again I reverted to Mu’s organicity. Pieces in Mu are uniform and able to form columns that move according to their height, in a straight line in any of the six main directions. They capture by simple replacement, regardless of their size. It means that columns always consist of one player’s men and that they may split or merge. Nice and simple, but how to get them in the first place?

For me it immediately implied ‘growth’. You don’t start an organic game with an initial position, not if you can avoid it. So I needed a start, for instance an entering protocol, and a growing mechanism.

Only couples can breed
Growing a new man every time a tile would be vacated would fill the territories as well as the Wall indiscriminately and unconditionally. That seemed dull, boring and overdone. Then came the magical thought: “only couples can breed”. I call it ‘magical’ because it was one of those thoughts that will come out of the blue without any logical connection, although this one had a definite connection with humans and some of the other organic life forms on Earth. It of course translated to ‘only doubles can breed’ or, more specifically, as mentioned in the rules:

If and only if a tile is vacated by a ‘double’ – a column of two men – it will sprout one new man on the cell underneath, regardless of whether this cell becomes part of the territory or part of the Wall. This is actually the only way to get a man on the Wall.

The first thing I noticed about it, admittedly, was arbitrariness: why not singles or triples? But then the Medusa grid appeared:

A ‘double’ must move two spaces. So a ‘single double’ is bound to the pattern of the grey cells of the grid, a sub-grid it can’t leave. It can never reach an adjacent cell or even a diagonally adjacent cell. There are four such distinct sub-grids. It meant that in order to ‘cover the grid’ in terms of growing options, players would have to switch to those and would have to move singles and triples to get doubles on them. It meant limited and conditional growth and I could see the start of game behaviour.

Emerging game behaviour
Two distinct examples of core behaviour had merged into one and the goal was inherently territorial, so let me summarise what I saw as logical and self explanatory, and how much leeway I saw in its implementation.

  • I saw player interaction leading to an ‘organic’ division of the board into territories and ‘the Wall’, the latter as a coherent playing area, however divided.
  • Pieces on the Wall would be free to move to other cells of the Wall, but they of course could also move off the Wall. So they could move anywhere, provided as always that they would follow the move protocol.
  • Pieces off the Wall could never get back on – that would undermine the whole division that I saw as crucial – but I saw a bit of leeway if pieces were allowed to jump over the Wall if those wall-cell(s) were occupied by pieces of the same colour. This is very conditional. For one, it excludes singles from making such jumps because of the move protocol. And it would provide a modest measure of interconnectivity and freedom that serves the unity of the organism.
  • I saw limited and conditional growth and an initial race to maximise it, including the necessary switches to other sub-grids. Growth would not be limited to the opening though, but also extend well into the middle game.
  • Starting the game would be simple: decide on a board, place one double and give the opponent the option to swap. If he declines he must place his own double, and if he swaps you place another double and the game is on.
  • It would work on any board but the obvious choice I had, or rather the bit of ‘inventor’s leeway’ I got, was between ‘hex hex’ and ‘modular’. I chose modular because I didn’t want another ‘sport weapon’. I wanted the last one for fun, mine and yours. A modular board allows for ‘lakes’ inside and ‘inlets’ at the periphery, that seemed a fun option. Moreover, it would prevent any opening theory from emerging. It required regulation of course: pieces may move over them but not land in them.
  • I saw all the way through it up to, but not including, the endgame.

In short, I saw core behaviour mold itself into a game, and I was following the behaviour’s requirements and its intended direction so far as I could see it, using any leeway that might be available. I’m good at that, but core behaviour isn’t quite as explicit as actual behaviour, so visualising it all, beginning to end, is usually not possible. And it proved particularly impossible in Storisende. I could see the game would be finite but I couldn’t quite see how an endgame might pan out. So I walked for weeks in the game’s empty rooms and corridors and hallways, seeing that it all fitted nicely and that it all made sense, but I was still unable to visualise how it would end.

On the bright side, this blindness helped me to formulate the explicit goal because what I did see was that the endgame would be a battle of attrition that would take a heavy toll on material. It made me doubt if in an endgame there would be enough men left to claim all territories. So claiming a territory should be possible with a minimum of men. Thus the explicit way to claim a territory became ‘to be the only colour present within it’ and one man is enough for that.

There was another inherent issue to solve. At the end of a game there might still be tiles present on the board. The least problematic solution was to remove them before counting, leaving any men on them behind, and count them as territory. It implies that a player may choose not to vacate a tile during play because it would cost him territory that he could have at the end.

What are we fighting for?
All great games are either existential, like Chess and Draughts, or territorial like Go. You can fight over anything, but not everything is worth fighting over. Goals for abstract strategy games are plentiful. You can have fight over who will get the last move or indeed the reverse, who will be the first to be unable to move, or be the first to get five men in a row, or be the first to get to an arbitrary number of points, or a combination of those, or to connect side A to side B, or to get to the other side, or whatever. These games may not lack ‘depth’ but they lack the deep-rooted connection to the primordial depths of human consciousness, that great games indeed have. Quarrelling over small issues is a popular modern pastime, and for casual players those fights shouldn’t take too long either, because yet other fights over similar issues require attention. And they should come in a box.

I posted Storisende’s concept under the provisional name Stiles at the BGG abstract games forum the very day it came to me. It got the interest of a few posters who were aware of the difference between ‘inside out’ and ‘outside in’ inventing. They eventually were helpful in improving the wording of the rules and I thank them for that. But the unity of behaviour that the game displays and that is characteristic for ‘inside out’ inventing, was lost on the majority of the community – they couldn’t see the game for the rules. And it didn’t come in a box. So I inserted this little paragraph to warn casual players who feel that ‘anything goes’ in terms of goals as long as the game is ‘fast and tricky’, that Storisende is long and tricky. Come to think of it, I should have put that at the top of the article.

The game of everything
It was unusually difficult for me to visualise an endgame in Storisende. I inherently imagine balanced positions because unbalanced positions don’t talk. One way is to imagine a draw. Draws are possible in Storisende, it wasn’t very difficult to see that, but what would it take? First and foremost, an equilibrium in the territories: same number of cells in the ones that players own, stalemate in the ones they share. But whether such a division is final would depend on the situation on the Wall. If it is empty, then the situation in the territories is final, but what if it is not?

A situation with many men in the territories and on the Wall, however evenly divided, doesn’t look very ‘final’ in any way. Men on the Wall can go anywhere and they provide options for territory men to invade adjacent territories. So to get anything ‘final’ that would include an equilibrium on the Wall, the number of men on it would have to be low. That means that an endgame that is proceeding in a continuous state of balance will eventually become a battle of attrition and if any men remain on the Wall, maybe still providing options to invade, then the manoeuvring will eventually become slow and tricky rather than fast and tricky.

Storisende is a territory game but it is as much ‘territorial’ as it is ‘existential’. In actual play these goals compete. If you want to be strong on the Wall you will have to grow men there early on, so you go for small territories and quickly try to erect wall cells between them. In that strategy you don’t care too much about territories because you can claim them later – if it works out. However, if the opponent follows similar considerations, it may not quite work out and the battle will first and foremost be existential. As I write, I am still uncertain how a balanced battle of attrition would eventually pan out because in the games I played against Stephen Tavener’s excellent AiAi game engine, it never came close enough. Regardless of who won, games were always decided before that.

For me the most surprising thing about Storisende is first and foremost how it manages to merge the two most important goals of abstract gaming in a uniform organism with unified behaviour. I’m not sure if any abstract game does the same in such an intricate way. It shows once more that in an ‘inside out’ process you never quite know what you will be arriving at. And it’s not only that. Several goals that are well known as main goals in abstract games, such as connection, breakthrough, race and blockade, pervade different stages of the game as sub-goals. ‘Connection’ is already provided by the Wall itself: it arises where separate territories threathen to connect. Pieces may conditionally jump over the Wall, which provides options for breakthrough and invasion. The opening is a race for growth, the middle game is pervaded by blockades, the endgame may feature careful manoeuvring and long term planning of the kind that a ‘fast and tricky’ player might call tedious. It’s a game of everything and it unfolds in an increasing resolution and variety of tactics.

Enschede, the Netherlands,
May 31, 2018,

christian freeling

Categories
thoughts about and reviews of particular games

A Chess Player Learning Shogi

I have played chess for close to twenty years now, and along the way I’ve picked up quite a number of chess variants. One of the most exciting and popular chess variants is called bughouse. Bughouse is essentially 2 v. 2 team chess in which each player feeds the pieces they’ve captured to their teammate who can then place them on their board instead of making a move.

Bughouse Chess Variant - Chess Terms - Chess.com
A game of bughouse

Because pieces cycle back onto the board after being captured the games are often very double-edged with many more sacrificial attacking combinations than regular chess. These tactics plus the distinctive team dynamics (communicating with your partner about which piece trades are advantageous or disadvantageous and coordinating your time management) make bughouse a fascinating chess variant. It perfectly satisfies the two competing criteria for game variants:

  1. A variant should retain some of the soul of the original game.
  2. A variant should also be different in interesting ways from the original game; it should enable new experiences that aren’t possible in the original.

In other words, a game variant has to feel partly like the same game and partly like something new. The best variants produce this nice mix of familiarity and novelty, like bughouse.

After encountering bughouse at my local chess club, I learned that there was another chess variant with the same ‘cycling piece’ mechanic but without teams. This variant, called crazyhouse, requires two chess sets to play over the board, since when you capture, for example, a black knight from your opponent you have to switch it for a white knight to be able to put it on the board as your own. Crazyhouse produces a lot of the same sacrificial attacking play that bughouse does, but unlike bughouse there is a sense in which everything is under your control, just as it is in a ordinary chess game. If you lose, for instance, there is no one to blame except yourself since you had all the information you needed to do better. This aspect of crazyhouse makes it feel very different than bughouse, (better than bughouse for certain temperaments or moods, worse for others).

I really enjoy both variants but I have always found it clumsy that crazyhouse requires two sets of chess pieces. This sometimes bothers me a bit even when I play online where the computer automatically switch the color of the captured piece. There is something artificial about it in a way that there isn’t anything artificial about the piece cycling in bughouse. This artificiality is mostly covered up in online play, but regardless of the extent to which this cover-up is successful, there is something non-ideal about a chess variant that for the most part can only be enjoyably played online. (I searched for images of people playing crazyhouse over the board and could not find any, but I found plently of images of people playing online.)

Given that there is a lot that works well about crazyhouse as a chess variant you can imagine how excited I was when I realized the same piece cycling mechanic could be implemented without the two-piece-set clumsiness of over-the-board crazyhouse. Not only was this possible, but it had already been done, hundreds of years ago in fact!

Shogi, initial position

The above image shows the initial position in a game of shogi. Shogi and chess are similar in various respects. The different kinds of pieces move differently, and the goal is to checkmate the opponents king. The king moves the same way it does in chess, one square in any direction, and there are also rooks (orthogonal movement) and bishops (diagonal movement). You will even find shogi being called a “chess variant” although it is not a chess variant as I have been using that phase. Crazyhouse and bughouse were invented after chess by a process of intentional modification of its rules, but shogi is not related to chess in this way. The similarities they bear to one another are due to a common ancestor: an ancient Indian strategy game called Chaturanga.

Krishna and Radha playing chaturanga on an 8×8 ashtāpada

Chess and shogi evolved along very different paths, however. In shogi, the two different armies are not identified by color but by shape, (a five-sided arrow-like shape pointing toward the opponent,) which allows for the captured pieces to be cycled back onto the board without any swapping with a secondary set. In other words, shogi is a much better version of crazyhouse.

A shogi game in progress. The captured pieces wait on the piece stands before they are put back in the fray, now fighting for the other side. Apparently the practice of placing captured pieces was inspired by captured 15th century mercinaries who chose to fight for their captors instead of being killed.

However, besides allowing for the placement of captured pieces like crazyhouse, there are a number of features that make it a quite different (and arguably richer) game.

  1. The shogi board is 9×9; the chess board is 8×8.
  2. Shogi has five pieces with no counterpart in chess: the gold and silver generals, the lance, the promoted rook and the promoted bishop. Chess has one piece with no counterpart in shogi: the queen. The knight’s move in shogi is much more restricted than in chess (only 2 out of the 8 knight’s moves in chess are legal). Pieces in shogi generally have a much smaller range of movement than in chess.
  3. The initial position in shogi is different than that of chess. It takes up three ranks instead of two with the middle rank being mostly empty. Since there is no queen in shogi, the 1st rank of the initial position is entirely symmetrical with the king in the center.
  4. In shogi, all pieces except the gold general and the king can promote, but only to one kind of piece. Promotion is easier in shogi because the promotion zone is closer to the starting position of the pieces (especially pawns). In chess, only the pawn can promote, but it can promote to any other piece except the king. This more expansive promotion is really fun, and each piece that promotes has its promoted value inscribed on its reverse side. Flipping the piece over is really delightful!
  5. There is no special castling move in shogi. The term “castle” is used in shogi to denote a defensive formation consisting of (usually) three generals which protect the king. There are many such castles (about 40 or so have names) and they will be better or worse based on the overall strategic situation. This makes consideration of how to best defend your king more interesting in shogi than it is in chess or crazyhouse.
  6. In shogi, pawns capture the same way they move. There is no initial two-space pawn move and hence no en-passant captures. In chess, pawns capture only diagonally which means that opposing pawns can block each other. This difference is especially hard to internalize as a chess player.
The pawns are the smallest pieces. As in chess, they are the most common and least valuable pieces on the board. They all have the same inscription. Can you find the 13 pawns in this picture? (Hint: 2 are partially cut off).

The pawn in the center of the frame looks to the chess-playing shogi beginner as if it is defended by each of the two pawns diagonally behind it. It also may look like it cannot move forward because of the opponent’s pawn in its way. In fact, neither thing is true. It is not defended by any pawns (though it is defended by a knight) and it can capture the pawn in front of it (or vice versa, depending on who’s turn it is).

In general, the pawn structure in shogi is much less static (really, much less of a structure).

As challenging as the pawns have been for me, keeping track of the pieces while I’m still familiarizing myself with the characters has been even more difficult. It makes playing shogi feel a lot like playing blindfold chess for me at this stage. When I’m not able to immediately recognize a piece for what it is, I have to rely more on my memory of where that piece started and what moves its made.

But the challenge has been incredibly rewarding so far, and I’m looking forward to playing more games and learning more strategy!

Categories
about me and the blog

Welcome to GAME PRAXIS!

Hi! My name is Andrew Stone and I’m currently a philosophy PhD student at the University of Chicago. Not only do I have a philosophical interest in games, but I am also an avid game player and aspiring game designer. My favorite games tend to be abstract strategy games like chess and go. I’ve created this blog as a place to collect my thoughts about games, thoughts that might be about particular games, games in general, or something else that I see as somehow relating to games. I may also document some of my own attempts at game design.

The title of the blog is a play on “game theory,” a subject that also interests me philosophically, but doesn’t seem to have much to do with the activity that we refer to as “playing games” in particular. Game theory is about any situation in which an outcome depends jointly on the actions of multiple agents, where each agent may need to take the goals, beliefs, and reasoning of the other agents into account to best achieve their own goals. The games we play with each other are certainly meet this criterion, but so do many other kinds of interactions that we would not classify as games. Still, I suspect game theory and the actual activity of game playing are less far apart than they might seem. Maybe some of the assumptions of game theory implicitly rely on us having games rather than other kinds of interaction in mind, for instance. This is not primarily a blog about game theory, it is about game praxis, the actual activities of game playing and game designing. But as in other domains, there may be some unexpected feedback between theory and praxis here.