Seven that matter
Grand Chess

Like Johan Cruijff and David Bowie I was born in 1947 so it may be an appropriate moment to look back a bit and speculate on what is yet to come. I think it's fair to say that my generation has gone through some significant changes and that humanity is now in a transitional period the likes of which it has never seen before and the end of which isn't in sight. 'Interesting times' so to say.

The changes didn't fail to affect the small niche labelled "abstract strategy games" in a fundamental way. I happened to be there most of the time, from the frustration of early programmers when their brainchild failed to find a mate in a king+rook versus king endgame, to the point where AI has become vastly superior in Chess and Draughts, and will soon have the same status in Go and Shogi (*). Improving these programs is an ongoing challenge, but programming new games is somewhat less so nowadays. Commercial abstracts come with apps and an AI opponent to go with it, but that's more a routine than a challenge. And if new games do have leverage enough to actually challenge programmers, then the programs will need less time to become 'vastly superior' because humans learn slowly and will need time to catch up. This is the new reality. It means that insofar abstract games are played as sports, the champions will have new and superior tutors and championships will be played out between the best pupils.

My interest has always been in abstract games that can be played as sports, that is games that are

  • inexhaustible in human terms
  • 'strategic' by allowing advantageous and calculable sub-goals to be reached
  • varied in range and applicability of tactics
  • not prone to draws

In short, games that can live up to a century or so of analysis while becoming more interesting in the process.

Sport weapons of the mind
That's how I see those games and while Chess does not particularly excel at the fourth point and Draughts actually fails at it, Shogi and Go live up to all four of them. So does XiangQi, I'm told, but its archaic character doesn't seem to help its spread beyond China.
Hex on the other hand has spread throughout the western world, but very thinly. My personal feeling is that the goal of connecting opposite sides of a board may not appeal to players quite the same way as playing Chess or Draughts or Go does. These games play out existential or territorial goals that are deeply rooted in human history and human conciousness. Moreover, things happen in these games that appeal to a well informed audience. In Hex the only thing that happens is the next placement of a stone and well informed onlookers are scarce. With no apparent signs of drama and a certain 'shallowness' in its goal, Hex may actually be considered too deep and learning to understand it too difficult to even bother to attempt it.
The odd one out would be Othello. After its commercial release in the early seventies it has gathered a significant following and yearly worldchampionships have been held since 1977. Its popularity may partly have resulted from clever marketing but half a century of serious play has not brought it significantly nearer to being 'exhaustible'. That's not bad.
In terms of strategy Othello's primary sub-goals are obvious, maybe even too much so. An occupied corner is usually advantageous and always permanent. That makes that point three, tactics, mainly consists of memorising opening patterns and cataloguing them according to their success rate. There's hardly any other way because every move's intended effect inherently has unintended side effects.
Othello has never won me over because of its rigid character. A move must be a capture, and if no capture is possible, then the player must pass. That's not exactly the pinnacle of elegance. For those who like the game, or indeed dislike it, I seriously recommend trying out Io as an alternative, though I won't back it up with clever marketing.

How do my games fit in?
So far as marketing goes I'd say 'hardly'. And you're welcome to forget all about the games in the Pit and even about most in the ArenA, though they go a long way in satisfying the requirements for 'sport weapons'. But I'm sure that at least seven of them will prove to be able to live up to "a century or so of analysis while becoming more interesting in the process". I want to talk about those seven.

Grand Chess
In About Grand Chess I said, about a decade ago:

   We live in a time not unlike the renaissance. In those days the printed word accelerated events and led to almost aggressive innovation, now the internet does the same. At the current rate of development, Chess will show serious signs of fatigue within a decade. More study, better programs, more knowledge, less fun, less adventure, more grandmasters, more draws and no more heroes.
I'll allow for one more player to define an era like Fischer or Kasparov.

And sure enough there's Magnus Carlsen and his era was still extending in 2017. World Championship matches are mondial events that are in a constant state of transition. Live streaming, AI supported live analysis by renowned grandmasters, live chatrooms and accessibility through a multitude of media - in the near future we may all be able to attend and discuss the games in a virtual environment. But things other than coverage change too.
As I write, the last world championship was held in New York in November 2016. Carlsen's opponent was the equally young Russian Sergey Karjakin. After twelve regular games the score was equal with two decisions and 10 draws and a series of 4 tiebreaker games was needed to decide the match. Carlsen won.
I won't say that this result is predictive, but if one would consider Chess as a metropolis then it might be argued that AI can turn on the lights in uncharted alleys in ways that never before in its history have been possible. And that light is now used by all top players.

The 'best pupil' era
Exploring new alleys in well charted areas has always been the pride and joy of Chess progress. Till a few decades ago this herculian task was driven by the efforts of masters and grandmasters. That in a way is still the case, but computer programs have evolved into indispensable employees that search the branches departing from the chosen alleys with a hard artificial light and at an incredible speed. Flawed lines are detected fast even if the flaws become apparent farther down the line than humans might go in their analysis. These programs don't care about style, they don't lie and they are available to all.

It may be difficult to establish how much of a Chess player's success is due to talent and how much is sheer preparation. Talent is an evasive property to define and preparation goes as far as it goes. In the old days, when I was young, grandmasters had different styles, resulting from different temperaments and different ways of approaching the game. Computerprograms have neither temperament nor styles resulting from it. They may have different ways of approaching the game, but not all that different and in any case better than the player using them. At the preparation end things go much faster because of this, and nothing much can be kept a secret for very long. Beyond the preparation horizon talent is still a significant factor, but thorough and unrelenting preparation pushes that boundary ever further. That means that once a game takes to uncharted territory, differences in talent may often turn out not to be enough to force a decision.

The games in world championship matches or tournaments will increasingly be channeled into the narrow alleys carved out by stronger AI. It may not go so far as to reduce the players to a medium for contests between programs, but games will increasingly be 'flavoured' by it. Understanding what's actually going on on the board will increasingly be the prerogative of top players who are aware of the latest developments. The rest of us will see great games, with a constant eye on what the AI evaluation makes of it to guide our judgement.
With quantum computers on the horizon I deem nothing impossible in the future, but as yet Chess is lightyears away from being 'solved'. So there's no proof for or against the assumption that it is a determined draw. But you can bet your boots on it. It means that under AI driven preparation the number of draws will slowly but surely increase. Carlsen is the first exponent of a generation that grew up with AI and he became the one where talent and timing coincided to make him define an era. But he's bound to be the last. Chess world championship matches will increasingly be decided by preparation. Preparation to the point where the boundaries between it and 'talent' fade and all have the same equipment to make the best pupils rule.

What has Grand Chess to do with this?
Insofar Grand Chess represents 'Chess with a complete set of pieces', the same as it always has. Including the Queen as a composite piece naturally implies a question about the other two composite pieces. I've written about that in How I invented ... Grand Chess.
Grand Chess

Look at the diagram and you see that each side has one king, three composite pieces, six single pieces and ten pawns. That's the triangular series. It breathes balance (diagram source).
Grand Chess' particular arrangement is arbitrary but it emerged naturally and thirty years of play by a range of qualified players, grandmaster Larry Kaufman among them, have not revealed any opening unbalance. Kaufman applied 8 criteria to chess variants and rated Grand Chess second after Shogi and higher than Chess, Chu Shogi and XiangQi.
But there's more arbitrariness, especially with regard to promotion. And it's all Philidor's fault.

Philidor's issues
In the mid eighteen's century André Danican Philidor was both the world's strongest and its most famous Chess player. His Analyse du jeu des Échecs was considered a standard chess manual till well into the nineteenth century. It abided by the current rules, yet Philidor had some issues with these. He doubted the initial double pawn move and ridiculed en passant capture. That's no issue anymore and Grand Chess abides by consensus. He had some issue with castling too, but that's no issue anymore either and in Grand Chess it never was in the first place. But his thought regarding promotion are still topical. Here they are:

So far as I know Philidor was never concerned with Chess' lack of structural completeness, but promotion to any chosen piece, which was to all intents and purposes promotion to a queen, certainly violated his sense of material completeness. Concerning his fellow countrymen and Chess players he remarks:

   I presume they have been led away (like myself, formerly) by a bad custom established in all probability by the person who first brought Chess into France; I'm inclined to believe it must have been some player at Draughts, who knowing little more than the moves of the pieces, imagined one might make as many queens in the game of Chess, as at Draughts. I would only ask what a fine sight it is to see upon a Chess board, two pawns on the same square, to distinguish a second queen; and if by chance a third should be made (as I have often seen it at Paris) then it is still a finer sight while the bottom of one pawn is almost sufficient to cover a square on the board. Is not therefore this method most ridiculous, especially as it is practised in no country where the game of Chess is known?

Since he blames those darn Draughts players for deforming Chess, I don't think Philidor would have liked using topsy turvy rooks any better. Was he right? Obviously not, but he stuck a chord regarding Grand Chess. I'm used to looking at games not from a historical but from a more general point of view. I hold structural completeness in high regard, but like Philidor I also value material completeness. And where Chess would certainly become less of a 'sport weapon' if promotion were restricted to pieces captured by the opponent, in Grand Chess things are quite different. The price of material completeness isn't quite that high because there are three composite pieces. Of course you must have one available for promotion and even if that will usually be the case, it yet poses a restriction that sometimes may require the exchange of a composite piece before an intended promotion can be effectuated. To be on the safe side regarding the consequences, which would include the inherent emergence of some interesting purpose driven tactics, I gave pawns the option to promote upon reaching the eighth or nineth rank and the obligation to do so upon reaching the tenth. Compared to Chess it means that a pawn starts one rank closer to promotion.

Back to the future
Chess has no problems, but something has been lost forever. We will keep seeing players with different temperaments but no longer will they be able to afford having these affect their approach too much. A player like Mikhail Tali, who's attacking, combinatorial style was pervaded with improvisation and unpredictability, wouldn't stand much of a chance in the new reality. He would have to face walls of preparation and early deviation into 'uncharted territory' would reveal that this territory wasn't quite as uncharted as he imagined. His namesake and contemporary Mikhail Botvinnik on the other hand would probably have felt quite at home in it.
If we compare Grand Chess with a metropolis, it would relate to Chess like New York to Volendam. But an old Volendam with a well lit center and well lit suburbs, where top players know their way around, and where more sparsely lit alleys are only to be found beyond the limits of the city proper. Grand Chess on the other hand is a very young New York, where steetlights are sparse, even in the central areas. There's no 'preparation horizon' because none was needed yet. Main alleys radiating from the center still have to be carved out and computer programs to guide the process still have to materialise. It's an environment where players like Tal can again thrive and where talent and daring are ready to take on thorough preparation. It's bringing the past back to the future.

With the current knowledge of Chess programming, if programmers care to make one, a Grand Chess program that outplays 99,99% of human players would soon be a reality. It would be a tremendous tool to carve out main alleys of opening play. But even under constant improvement it would not allow a preparation horizon with a ply depth equal to what is currently the case in Chess. Grand Chess is simply too wide to allow humans to prepare that deep, ever. The ratio of more or less charted areas to the great uncharted ones will always be significantly lower than in Chess. Thus adventurous, daring and talent driven play will stand every chance against study and preparation. As I said before, preparation goes as far as it goes, and in Grand Chess that will only ever be so far. And yes, I love tautologies.

Marshall and Cardinal
Marshall and Cardinal the way I prefer them

There's no special insight required to see that Grand Chess is a well considered implementation of a structurally complete Chess, better than the one of Capablanca and a number of subsequent variants including Gothic Chess (among others), Embassy Chess and Janus Chess. All three employ 8x10 boards with the rooks once again tucked tight in the corner and a castling rule to 'solve the problem' - it's not a bug, it's a feature. Gothic Chess uses the same set as Grand Chess, Embassy Chess the same set in the same configuration and Janus Chess features two cardinals but no marshall - worth mentioning only because it's so weird.
Speaking of which, inventors being what they are, the emergence of Capablanca random Chess was of course all but inevitable. Bad examples tend to be followed.

The notion of a structurally complete Chess is firmly rooted in the Chess community's collective consciousness and in the past 30+ years Grand Chess has given it a focus that is beyond disappearing and clearly growing. I have neither the means nor the skills nor indeed the inclination to influence this growth. I'm quite happy to know that players will enjoy the game for much longer than I'll be able to watch it.

In 1972, after a training match against fellow grandmaster Andreas Kuijken, Ton Sijbrands commented in a national daily newspaper: "Dat is dammen zoals God het wil!" (that is Draughts the way God wants it). This didn't go down very well in the Netherlands where God at the time was considered a protestant Who's main interest was in his subjects' sins, which excluded Draughts. The comment and the reactions to it went viral in the then available media. I'm not inclined to consider religious matters, but looking at the world I can't imagine God loves draws that much.

Holy bluntness or Draughts the way God wants it
Many top Draughts players have an almost religious connection to the game and joining the congregation is both easy and rewarding. Draughts is beautiful and exciting as a game and on a club level it lives up to its purpose. But not on a professional level. Draughts as a sport weapon has become far to blunt to captivate anyone outside the congregation.

If we look at world championship matches, the first one to end in 20 draws was Andreiko-Koeperman in 1971, but Dybman and Gantwarg repeated the performance in 1987. Next best were the matches Wiersma-van der Wal 1983 with 19 draws, and Sijbrands-Andreiko 1973, Wiersma-Gantwarg 1981, Wiersma-Virni 1984, Tsjizjov-Sijbrands 1989 and Tsjizjov-Wiersma 1993, all with 18 draws.
To remedy the problem, the matches from 1995 onwards were organized in sets. In 2004 the 'tie break' was introduced. The 2009 match between Schwartzman and Georgiev started of with 12 regular games, ending in 12 regular draws, then proceeded with blitzgames, so called 'micro matches' in which Schwartzman finally reached the required three wins.
In 2013 the rules changed. If a regular game ended in a draw, then the session would proceed with a rapid game, then a blitz and then a tie break (!). The 7 regular games rendered 5 draws and 2 decisions. Georgiev won one rapid, Schwartzman none. In 2015 the 7 regular games between Georgiev and Jean-Marc Ndjofang all ended in a draw, but Georgiev won a rapid and a blitz.
In 2016 Georgiev withdrew because, after ten world titles and countless draws he had lost the ambition. Then a curious thing happened in the match between the runner up of the 2015 tournament, Jan Groenendijk, and the number three, Roel Boomstra. Both are young Dutch players and Boomstra won 4 of the 12 games. There were news items, live streaming, interviews and an appearance in a popular talkshow where they were allowed to demonstrate how much fun Draughts can be. A true advertising campaign showing that Draughts is young and vibrant and pretty decisive! In the background the monumental figure of Harm Wiersma commented favourably on the new developments. Remarkable developments indeed!

But Draughts hasn't suddenly and mysteriously changed. Where Checkers is a proven draw, Draughts is merely a not yet proven draw, but with quantum computers on the horizon that's a just matter of time. More scrutiny therefore will inherently open more alleys to draws. The current Draughts programs are already invincible as it is. Pitted against itself on an equal basis such a program will draw. Which is also the most that top players will get from it.
In terms of assistance in preparation, Groenendijk and Boomstra were better equipped than any players before them. Yet Groenendijk obviously made some serious mistakes. That's very remarkable and very sad for Groenendijk. But it is considered good for overhauling Draughts' image, at least by those in denial of the fact that Draughts has grown old under the weight of its accumulated theory and has become disfunctional as a sport weapon. Like Wiersma.

A river in Egypt
Remedying a problem while in denial of its existence can become quite spasmodic. That's the case when you try to promote a game as if no such problem exists, while listing 25 suggestions to solve it. The fact that some are better or less weird than others doesn't make any of them good. They're all band aids. I have only one solution, here it is:


Note the extent of my commecial interest: every Draughts player already has the game in his or her possession. I see Dameo as the next step in the evolution of Draughts (which is played not 'the way God wants it' but rather the way man made it). I have argued this point extensively in issue 2 of the Game & Puzzle Design Journal but also throughout the Dameo sections in this site. So I'll only give a brief summary of the similarities and the differeces between the games.

  • Dameo has the same general structure as Draughts and the same rules regarding capture and its priorities.
  • All capture is orthogonal instead of diagonal. This is a difference in orientation rather than in topology. It means captures have more elbow-room because they align with the board edges.
  • Men move one square straight or diagonally forwards. A straight line of men may as a whole move one square straight or diagonally forwards. Kings move any distance straight or diagonally.

The game's combinatorial implications are at least as wide and deep as those of Draughts. Its pace is at least as fast, but usually faster due to linear movement. There's no one-on-one opposition as in Draughts, so it is hard to keep a game closed and it is far more decisive.

What does Dameo need that it doesn't already have?
In my opinion nothing more than a couple of young seasoned Draughts players who are slightly bothered by the prospect of seeing their progress eventually leading them into a quagmire of draws. I hope I live to see it happen. They can trust the game to live up to the highest expectations.

Emergo emerged one day at Ed van Zon's place. He insisted that "some very beautiful things" were happening in Stapeldammen and he explained them. So I ended up seeing wrestling columns each of which had a life cycle. A piece would always start at its strongest, but weaken by interaction and by the burden of the prisoners it made in the process, a growing load under a shrinking cap, eventually making it a liability in want of protection. That of course wouldn't always succeed, and then the freshly liberated column would dramatically change the landscape, starting at its strongest, but weakening ... even writing it down turns into a cycle. But it wouldn't go on ad infinitum.

A revelation
"See", Ed pointed out, "every time a single is captured, there's one piece less. But if a single is freed, it doesn't affect the number of pieces. So the whole game is 'spiraling up' at a decreasing rate, into ever less and ever higher pieces".

That not only made sense, it was so bafflingly beautiful that I was overwhelmed by it. To see this organism interact with itself in this rolling wrestling fashion and see it terminate of its own without any Draughts jacket was a true revelation.

Back to Earth. It was a good thing that Ed's explanation bypassed any Checkers framework. I therefore saw the game behaving in a pit rather than on a track. I even ridiculed the fact that in Stapeldammen pieces would get stuck on the back rank. This youthful hubris and excess of self-confidence fortunately prevented me from looking better. What I ridiculed is not a bug but a feature, and I say this without any of the usually implied sarcasm. Stapeldammen is a truly great game. If I had realised that at the time, then Emergo might never have seen the light of day.
As it was, we rejected an initial position in favour of an entering procedure. A hard separation between entering and moving could be prevented by making capture obligatory in both phases. Then we started entering and capturing and it went haywire. Clearly regulating the entering stage was required and after an hour or so a simple rule hit me that tied it all neatly together, as if it had been waiting to reveal itself. It made inducing a capture in the entering stage conditional. It works great, but it also turned out to be a rule that would be very prone to misinterpretation. Be warned.

If you cover a column and a row of a Chess board you can play on the diagonal sub-grid with 8 men each

Emergo is a pure column checkers game and the only one not to emerge as the 'columnification' of an existing checkers variant. If you're using the dark squares of a checkered board, then its size must be odd. That makes both sub grids symmetric, which serves the pit-like character of the game. The pieces may each go through a life cycle, the moves do not, at least not often. There is a curious instance of 3-fold known on a hex grid, that runs on automatic. On the square one this particular type is not possible, but there are instances of cycles that can be maintained by one player against any attempt by the opponent to break it. They are rare though.

Would Emergo make an efficient sport weapon?
Not without an unlikely large player base so I tend to see it as more of an ad hoc recreational weapon. Here are some points that might speak against it:

  • Games are on average longer than Draughts.
  • Under time pressure some significant manual dexterity would be required, even with the smoothest of material, to perform multiple captures fast and accurately.
  • Barring the entering stage, theory would be quite exhaustible because strategy is basically simple and tactics are quite uniform.

There are applets and apps to deal with any physical disadvantages, and before long we'll probably be able to play abstracts in virtual reality. Given a basically simple strategy and a relatively small branching factor, making an AI with superhuman strength will hardly be a problem. So here are some points speaking for it:

  • Despite its limited material the number of positions in Emergo's game tree largely surpasses the ones of the other four games listed here.
  • Advantageous and calculable sub-goals are permanently and clearly present and their pursuit offers room for dramatic reversals throughout a game.
  • The game is absolutely inexhaustible in human terms and very decisive.

Strategy in the entering stage is more complex than in the movement stage and may differ for Black and White because being the first to move after it is an advantage. That in principle gives White an edge, but Black may upset events to have them topple either way: get the first move or get a solid shadow piece. Growth of a shadow piece gives negative feedback on keeping the first move. In the worst case scenario your opponent has the first move while your shadow piece is a single man.

Poetry in motion
Seeing the game rolling and moving following its simple rules, and working itself upward to its inevitable conclusion, is poetry in motion. There are zillions of possible positions, but in each and every one judging the state of affairs and identifying advantageous sub-goals (whether or not they would appear immediately achievable) is easy, even for a moderately trained eye. Liberating pieces is an inherent sub-goal the impact of which can range from inconsequential to dramatic. It may start with say a 2-on-3 that you can tuck away by exchange as a 1-on-4. A nice efficient catch if you can hold on to it. But if, by the slightest oversight, it can be drawn into a combination, then it will usually be liberated as at least a piece of 5 and possibly higher if it is forced to make additional captures before it falls. For critical pieces with small caps and big loads, the difference between having prisoners safely tucked away or facing an even higher opponent's piece instead, provides a form of drama that pervades strategy in virtually every stage.

Big tree, narrow branches
Emergo's branching factor is low. Not only is capture compulsory, maximal capture is too. That implicitly narrows a branch. It also gives rise to the sticker as a tactical means. A sticker is a piece that is exposed, but cannot be jumped because a majority capture elsewhere takes precedence. It's role in Emergo is even more prominent than it is in Draughts. Captures by both sides are often subsequent, narrowing a branch to a single line over an extended ply depth. Computers can do it sleeping. Humans to a degree can learn it too, but sometimes combinations take twists and turns that make it hard or even impossible to keep track. That's the beauty. Rules are simple and barring the entering stage strategy is too. Tactics are fairly uniform and calculable to a significant extent, but combinations can be unfathomably deep. The two main sources of drama are the liberation of large pieces and combinations going astray by miscalculation.

What about draws?
A position in which a player cannot legally enter is impossible. A position in which a player cannot move is possible and counts as a draw. It's easy to demonstrate a combination leading to such a position, but in actual play its occurrence is rare. Cycles can occur but are even rarer. In endgames with equal caps, the player 'having the move' has an advantage. Having the move means being able to take opposition.

When I'm dead
Then the above board will be engraved in my gravestone. Bring cushions to sit and pieces to play and come together over me!

I have sufficiently documented Symple's emergence in About Symple and in How I invented ... Symple. It shows that it's hard to recognise tunnel vision when you're inside one. That's how I made 'Superstar' and coinvented 'YvY' with David Bush, games you won't find here anymore because Symple has made them redundant.

Symple is a placement game, without movement or capture. It is territorial with a twist called 'group penalty': every stone is a point, but every distinct group is penalised with an even number of points. Thus a group must grow up to the penalty value to even get even. Now consider the following:

  • The penalty makes you want the number of your groups to be as low as possible.
  • Simultaneous growth at every possible group makes you want the number of your
    groups to be as high as possible.

That's the core dilemma, but not the only dilemma. What about the choice, at each turn, between growing every posiible group or placing an isolated stone. Growing all groups is great but every group starts as an isolated stone. It's a choice between immediate growth and investing in future growth.

Compulsory placement
That's what lends drama to every balanced game. Symple is drawless so the final placement may be deciding. If it's yours and you're forced to invade because none of your groups can grow, which is often the case under these circumstances, then the penalty on the new group may cost you the game.

The penalty is even because that, in combination with an odd-sized board, eliminates draws. Symple's penalty is variable which can alter the game's strategy without altering its tactics. A higher penalty lowers the incentive to start new groups and heightens the importance of connectivity between them. The timing of invading an area by starting a new group changes under different group penalties, because the conditions for a group to have enough 'breathing space' are different. This feature of a shifting parameter that induces a change of strategy in what essentially remains the same game is rather uncommon in the realm of abstract strategy games, if not indeed unique.

A game in progress, white to move

Balance included
The Symple balancing mechanism is embedded in the move protocol and completely fair. You can find the details under the link, but both players face a dilemma in which the relative value of a couple of extra stones and their future 'influence' must be measured against the relative value of having 'the move', that is having the turn when the number of groups is equal. And so long as no growth has take place, either player can decide to accept or refrain at any moment. When it's done it's done, it's a one time occurrence. These 'relative values' are a human estimate and thus implicitly opaque. It's completely fair because there's no rational way to complain about the outcome. It also has a very high resolution. Much higher than the pie rule actually, but it is limited to the protocol in which it is embedded.
Symple is an excellent sport weapon: fast, inexhaustible and decisive. Its tactics are not nearly as intricate as those of Go but considerations regarding strategy can measure up to it, not to mention that they will change with the height of the penalty.

The holy grail
For inventors of abstract games who dislike draws, or even abhor draws in rare cases, finding a simple drawless game that is 'perfectly balanced' is like the holy grail. So Symple is the holy grail, you can stop looking for it. And mind, I don't even dislike draws if they keep a low profile.

Sygo is a Go variant that uses the Symple move protocol. I remember inventing it a couple of days after the latter's emergence. I had given no thought at all to a flip capture variant without the need for additional rules to ensure ways to get life. It just so happened that afterwards, when the game was ready, it turned out that there wasn't any need for them.

Get life
In Go variants flip capture gets rid of cycles, but at a price: it's hard to get life. Read all about it in Othelloanian capture in Go variants. All games, but one, therefore have some additional means to ensure it.These means may be more or less elegant, but each is 'wearing its intent on its sleeve'. In Sygo simultaneous growth allows cooperation between groups and this inherently provides sufficient options to get life. No additives and no need for additives.

A game in progress, white to move

Where Symple derives its drama from compulsory placement and forced invasions, Sygo abides by Go rules and makes placement optional, to which the move protocol seamlessly adapts. Sygo derives its drama from capture. The tactics of both games are not nearly as inticate as those found in Go, but in either case the depth of strategy justifies the qualification 'sport weapon'. Measured by the number of turns, both games are fast: Sygo usually ends within between twenty and thirty moves, while Symple needs maybe between forty and fifty. Sygo is touched ever so lightly by indecisiveness: it can end in a draw. Mind, it needs at least one seki to do so.

Getting on with life
There's no alternative for moving forward but I suppose there must be alternatives for being an inventor of abstract strategy games. In any case I'm bound to find that out now. I don't remember how life began and I won't remember how it ended, and in between things weren't all that clear either, but here at least is a legacy of seven games that I consider worthy sport weapons, able to serve human players for another century or more. As it happens, they all turned out generic: if someone wants to try a game, getting the board and pieces isn't much of a hurdle. In the future there should be ample alternative ways to play them and the games' future may actually depend on those.

It was a curious run over some forty years, in which I saw many fellow inventors pay lip service to simplicity and depth while producing ultra lights with a short shelf life, the shelf usually being the prime purpose in the first place. It's art for art's sake but money for God's sake. Let me mention Luis Bolaños Mures as a notable exception who's vision is not blurred by commercialism. With me out of the game, there aren't many left.

Enschede, March 2017

christian freeling

That was March 2017. In July Starweb came out of the blue. Two seconds and purely accidental, I swear it, I didn't even get the time to not invent it. Starweb turned out to be as 'ArenA worthy' as Havannah with which it shares a certain behaviour.
Less accidental was the invention of Storisende half a year later, a last loose end that refused to let go. As the name suggests, it is my intended last game, but accidents like Starweb cannot be fully excluded. The way in which it emerged is described in the essay Organicity in Abstract Strategy Games.

As my final contribution to the field I decided to make it a fun game, hence the board that is made up of 7-cell modules that more or less prevent a simple use of coordinates. The image shows a 7-modules compact display in Stephen Tavener's AiAi in which checkers-like pieces have been replaced by nice figurines, with 'couples' indeed holding hands to indicate that only they may breed. The AI plays an excellent game by the way.

I didn't really expect Storisende to be a 'sport weapon' and don't actually know if it would qualify if played on a say base-5 or base-6 hex hex board, but it very well might. The reason that it is a game that matters is that it has uniform material and a unified behaviour and with these it manages to inticately merge the two most prominent goals in the realm of abstract strategy games: elimination and territory, the former up on the Wall, the latter down in the territories. This property emerged during play and it was not at all intended, but it is there and it makes Storisende an inherently significant game.

Enschede, March 2018

christian freeling

I have documented Shakala's emergence in About Shakala and in How I invented ... Shakala. It is noteworthy that I considered Storisende as my final invention, back in 2018. It didn't quite work out that way because I invented 22 games since then, but only the last of these mattered enough to add it to the few games that I consider to be the core of my work. In this case I would like to leave it at the mere duplication of "About Shakala".

Far far away, all the way back in the seventies, I invented a mancala game called The Glass Bead Game. It introduces beads of different values that can be captured with beads of zero-value. They are called 'gems' and 'stones' and only gems can be captured while only stones can capture. Compared to existing mancala games the material has been drastically reduced, with only two rows of five pits that initially hold two beads per pit, a stone and a gem. The game introduces a fundamentally different approach to mancalas.

Most regular mancalas have one track with a north- and a south side, in which pits are chosen on a player's own side and the content, the beads, are distrubited in one direction over the whole track. The Glass Bead Game is no exception.

I did actually consider changing this topology several times in the past, but it was only after Mike Zapawa tried to rekindle interest in the mancala family of games at the BGG Abstract Games Forum that I gave it some serious thought.
Mike admires the Glass Bead Game and had come up with his own coloured beads mancala Rainbow Chase a few weeks before.

So I returned to an old idea of different intersecting tracks and at a certain point it occured to me that I could give players an actual choice of which track to take. That was the clue and instead of two rows of five pits I suddenly saw four rows of four pits, that is: a regular 4x4 board of pits.

Shakala is a kind of Glass Bead Game 2.0. It introduces another generic change that in principle can be applied to most mancalas: a double track at both the North and the South side with two 'fork pits' where players may choose which track to follow.

To sow a 'house', a pit with enough beads to go all the way around for a multiple capture, a player can in principle choose between four tracks: inner-inner, inner-outer, outer-inner and outer-outer.

If you follow the little black arrows between the pits in the above initial position, you see that the general direction is anti-clockwise, left to right for each player on their own side. Fourteen pits have one incoming and one outgoing arrow, while the H- and h-pit, have two incoming arrows and the E- and e-pit, have two outgoing arrows. The latter are the 'fork-pits' where the app gives the choice to proceed on either the inner- or the outer track. The complete outer track is four pits longer than the inner one.

The consequences
These are far from cosmetic. As in the Glass Bead Game, Shakala strategy revolves around building a 'house', a pit that has enough beads to sow a full round and end up sowing into pits of the opponent's side for the second time, to harvest the gems that were sowed during the first time or, indirectly, an amount of gems from the opponent's pits, at the moving player's choice.

The most obvious pit by far for a house is the last one before entering the opponent's side. That way there's maximum room behind it for tempo manoeuvring. Which track to choose may depend on the number of beads in the house: the inner-inner track needs from 8 to 11, the outer-outer from 12 to 17 and the intermediate tracks both start at 10 and go belly up after 13 or 15, depending on which of the two is taken. Since these numbers overlap, a single house can be aimed at more than one pit. That is a difference with single-track mancalas, including the Glass Bead Game, the importance of which cannot be overestimated. It turns a deep but rather one-dimensional strategy into a layered one that lifts Shakala into the realm of truly great strategy games.

A two storey house
In Shakala the obvious 'house-pits' are H and h. From there the inner track has eight pits, including the house-pits themselves, but when going all around, which is the case when sowing a house, the pit that is being sowed must be skipped in the process, so the eight's bead falls into the same pit as the first. That means that for harvesting an inner track house it must contain eight to eleven beads. The twelfth bead would end up in the moving player's pits again, making the house useless. That is, in a one-track mancala.
In Shakala things are quite different. If the house gets a twelfth bead, it goes belly up so far as the inner track is concerned. But not for the outer track, which has twelve pits, meaning that the twelfth bead falls into the same pit as the first. Nor for intermediate tracks that combine an outer and an inner track. An outer track house may harvest if it contains twelve to seventeen beads. So when the inner track house goes belly up at twelve beads, it may switch to an intermediate or an outer track and in the latter case grow up to seventeen beads.

Simultaneous atacks on two pits
As I already pointed out, simultaneous atacks on two pits are an inherent feature. Pits with stones that, if sowed, end up with two, three or four beads landing in the opponent's pits, always attack two of them, one in the inner track and one in the outer one. Of course it's harder to defend against both of them, whether it's against a house or against a shorter attack from one of a player's pits immediately to the other side. If these attacks require an immediate answer, they have a habit of upsetting tempo conditions.

Trapping pits
If you've ever played mancalas you have probably encountered the phenomenon of trapped pits. In the Glass bead Game you may have a leftmost pit filled with valuables and, due to tempo conditions and forced movement, you will have to sow it at one of your next turns. Say that the first three pits that receive a bead from it are empty. That's still at the players own side, so they each get one bead. Your opponent has a pit aimed at precisely the last one of these, so you'll have to put your head on the chopping block and take your losses. At best you may be able to avoid a multiple capture.
On the other side of the picture, the attacker also faces tempo conditions and he ties to avoid adding a bead to the attacking pit because then it will overshoot its target. Shakala harbours a basically new way to do this, by using the other track and thus avoiding the attacking pit to go belly up.

Extended tempo play
Tempo play in the Glass Bead Game can be excruciating. "How many moves can I make within my own side, without spilling over to my opponent's side and provide him with additional tempo moves"? "Do I speed up and spill over or slow down by playing the rightmost pits first, thus possibly leaving pits that can be trapped"? "If I move, do I leave singles exposed that can be captured"? "How do I keep a pit defended that is attacked by a house"? Those are the questions that come up time and again. Shakala is pervaded by the very same dilemmas but its double track topology provides new answers to them by offering two alternative routes to provide more flexibility and breathing space for both defense and attack.

Shakala provides significantly more strategic depth and flexibility to the concept of its ancestor, and a much wider array of tactical tools, lifting it into the realm of truly great games.

Christian Freeling, Enschede, May 2022

Shakala © MindSports


* AlphaZero has become superior in Go, Chess and Shogi:
In 2017 the AlphaGo Zero algorithm achieved superhuman performance in the game of Go, by representing Go knowledge using deep convolutional neural networks, trained solely by reinforcement learning from games of self-play. In this paper, we apply a similar but fully generic algorithm, which we call AlphaZero, to the games of chess and shogi as well as Go, without any additional domain knowledge except the rules of the game, demonstrating that a general-purpose reinforcement learning algorithm can achieve, tabula rasa, superhuman performance across many challenging domains.