AlphaZero/Kramnik: Exploring new chess variants

9/10/2020 – Modifying the existing rules for chess, attempting to make it more dynamic or decisive, is a non-trivial task: You need years of experience and large numbers of people playing new versions in order to assess the quality and appeal of any new variant. Former World Champion Vladimir Kramnik has proposed nine new variants, and DeepMind has used their AI technology to evaluate them in a much shorter period of time. Here are their findings.

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Assessing Game Balance with AlphaZero

The following is excerpts from a 97-page scientific treaties submitted by Nenad Tomašev (DeepMind), Ulrich Paquet (DeepMind), Demis Hassabis (DeepMind) and Vladimir Kramnik (World Chess Champion 2000–2007). We will excerpt this paper in multiple parts, providing you with example games for your own evaluation. 

AlphaZero is a reinforcement learning system that can learn near-optimal strategies for any rule set from scratch without any human supervision, and provides an in silico alternative for game balance assessment. In their paper the team demonstrate the potential of AlphaZero to be used as a tool for creative exploration and design of new chess variants. Given the increasing depth of known chess opening theory, the high percentage of draws in professional play, and the non-negligible number of games that end while both players are still in their home preparation, there has recently been an increasing interest in chess variants, such as Fischer Random Chess.

In their study, the team has used AlphaZero to explore nine chess variants that involve atomic changes to the rules of chess, keeping the game close to the original, while allowing for novel strategic and tactical patterns. By effectively simulating decades of human play in a matter of hours, they are able to answer what the games between strong human players would potentially look like, if these variants were to be adopted. In this process, they identified several variants of chess that appear to be very dynamic and interesting. The findings demonstrate the rich possibilities that lie beyond the modern chess rules. They state:

Rule design is a critical part of game development, and small alterations of game rules can have a large effect on the overall playability and game dynamics. Fine-tuning and balancing rule sets in games is often a time-consuming, laborious process and automating the balancing process is an open area of research, where machine learning and evolutionary methods have recently been used to help game designers balance the games more efficiently. Here we examine the potential of AlphaZero to be used as an exploration tool for investigating game balance and game dynamics under different rule sets in board games, taking chess as an example use case.

Popular games often evolve over time, and modern-day chess is no exception. The original game of chess is thought to have been conceived in India in the sixth century, from where it initially spread to Persia, then the Muslim world and later to Europe and globally. In medieval times, European chess was still largely based on Shatranj, an early variant originating from the Sasanian Empire that was based on the Indian Chaturanga. Notably, the queen and the bishop (alfin) moves were much more restricted, and the pieces were not as powerful as those in modern chess. Castling did not exist, but the king’s leap and the queen’s leap existed instead as special first king and queen moves. Apart from checkmate, it was also possible to win by baring the opposite king, leaving the piece isolated with the entirety of its army having been captured. In Shatranj, stalemate was considered a win, whereas these days it is considered a draw.

The evolution of chess variants over the centuries can be viewed through the lens of changes in search space complexity and the expected final outcome uncertainty throughout the game, the latter being emphasized by modern rules and seen as important for the overall entertainment value. Modern chess was introduced in the fifteenth century, and is one of the most popular games to date, captivating the imagination of players around the world.

The interest in further development of chess has not subsided, especially considering a decreasing number of decisive games in professional chess and an increasing reliance on theory and home preparation with chess engines. This trend, coupled with curiosity and desire to tinker with such an inspiring game, has given rise to many variants of chess that have been proposed over the years. These variants involve alterations to the board, the piece placement, or the rules, to offer players “something subtle, sparkling, or amusing which cannot be done in ordinary chess” (Beasly, 1998). Probably the most well-known and popular chess variant is the so-called Chess960 or Fischer Random Chess, where pieces on the first rank are placed in one of 960 random permutations, making theoretical preparation infeasible.

AlphaZero had demonstrated state-of-the-art results in playing go, chess, and shogi – learning from self-play without any human supervision. In doing so, AlphaZero demonstrated a unique playing style at the time, later analysed in Game Changer (Sadler & Regan, 2019). This in turn gave rise to new projects like Leela Chess Zero and improvements in existing chess engines. CrazyAra employs a related approach for playing the Crazyhouse chess variant, though it involved pre-training from existing human games. A model-based extension of the original system was shown to generalise to domains like Atari, while maintaining its performance on chess even without an exact environment simulator. AlphaZero has also shown promise beyond game environments, as a recent application of the model to global optimisation of quantum dynamics suggests.

This is how the AlphaZero team describe the project:

Rule Alterations

There are many ways in which the rules of chess could be altered and in this work we limit ourselves to considering atomic changes that keep the game as close as possible to classical chess. In some cases, secondary changes needed to be made to the 50-move rule to avoid potentially infinite games. The idea was to try to preserve the symmetry and the aesthetic appeal of the original game, while hoping to uncover dynamic variants with new open-ing, middlegame or endgame patterns and a novel body of opening theory. With that in mind, we did not consider any alterations involving changes to the board itself, the number of pieces, or their arrangement. Such changes were outside of the scope of this initial exploration. Rule alterations that we examine are listed in Table 1. The variants in Table 1 are by no means new to this paper, and many are guised under other names: Self-capture is sometimes referred to as “Reform Chess” or “Free Capture Chess”, while Pawn-back is called “Wren’s Game” by Pritchard (1994). None have yet come under intense scrutiny, and the impact of counting stalemate as a win is a lingering open question in the chess community.

Each of the hypothetical rule alterations listed in Table 1 could potentially affect the game either in desired or undesired ways. As an example, consider No-castling chess. One possible outcome of disallowing castling is that it would result in an aggressive playing style and attacking games, given that the kings are more exposed during the game and it takes time to get them to safety. Yet, the inability to easily safeguard one’s own king might make attacking itself a poor choice, due to the counterattacking opportunities that open up for the defending side. In Classical chess, players usually castle prior to launching an attack. Therefore, such a change could alternatively be seen as leading to unenterprising play and a much more restrained approach to the game.

Historically, the only way to assess such ideas would have been for a large number of human players to play the game over a long period of time, until enough experience and understanding has been accumulated. Not only is this a long process, but it also requires the support of a large number of players to begin with. With AlphaZero, we can automate this process and simulate the equivalent of decades of human play within a day, allowing us to test these hypotheses in silico and observe the emerging patterns and theory for each of the considered variations of the game.

Variant Primary rule change Secondary rule change
No-castling Castling is disallowed throughout the game
No-castling (10) Castling is disallowed for the first 10 moves (20 plies)
Pawn one square Pawns can only move by one square
Stalemate=win Forcing stalemate is a win rather than a draw
Torpedo Pawns can move by 1 or 2 squares
anywhere on the board. En passant can happen anywhere on the board.
Semi-torpedo Pawns can move by two square both from the 2nd and the 3rd rank
Pawn-back Pawns can move backwards by one square, but only back to the 2nd/7th rank for White/Black Pawn moves do not count towards the 50 move rule
Pawn-sideways Pawns can also move laterally by one square. Captures are unchanged, diagonally upwards Sideway pawn moves do not count towards the 50 move rule
Self-capture It is possible to capture one’s own pieces

Table 1. A list of considered alterations to the rules of chess.

Qualitative assessment

To evaluate the differences in play between the set of chess variations considered in this study, we couple the quantitative assessment of the variations with expert analysis based on a large set of representative games. While the overall decisiveness and opening diversity add to the appeal of any chess variation, the subjective questions of aesthetic value and the types of positions, moves and patterns that arise are not possible to fully capture quantitatively. For providing a deep qualitative assessment of the appeal of these chess variations, we rely on the experience of chess grandmaster Vladimir Kramnik, an ex-world chess champion and an authority on the game. By characterising typical patterns, we hope to provide players with insights to help them judge for themselves if they would find some of these chess variants interesting enough to try out in practice. What we provide here are preliminary findings.

In the following weeks we will present you with the results and example games and positions from each of these variants. For today you can check out the first in the list, No Castling Chess, which we already described (Vladimir Kramnik proposes an exciting chess variant!).

In fact we organised a full tournament with OTB play, under the supervision of Vladimir Kramnik himself. The result: a dramatic reduction of the number of undecided games: First ever "no-castling" tournament results in 89% decisive games!


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Karsten Müller Karsten Müller 9/13/2020 05:30
Vladimir Kramnik wants to answer Arno Nickel's questions:
Dear Karsten,

Thanks for your feedback. I can answer Mr. Nickel's letter point by point.

First, we have checked those variations in the sense of purely chess aspects, I mean what are the characteristic patterns, statistics, aesthetic feeling of each variation. Lasker's proposal is about counting stalemate differently in competitive sense, and this makes certain sense definitely but does not correspond to the spirit of our work.

Second, AZ level in all those variations was the same as in standard chess. Tested in several ways.
Otherwise the whole work would become senseless :).

And, I mention there, talking about every variation, that statistics of computer games doesn’t mean that it will be similar in human games and furthermore, most definitely not but it gives some indication about the so called mathematical balance of a new variation.

Each variant is fine. Matter of taste and preferences. Including stalemate equals mate.

The idea is to check them all and offer many different variations that everyone makes his own choice. Since my idea was mainly trying to find variations which eliminate opening theory and make players think from the very beginning this stalemate variation is least suitable for this particular purpose but definitely interesting in its way, no doubt.

Best regards, Vladimir
Yasser Seirawan Yasser Seirawan 9/12/2020 12:42
S-Chess will make future generations of chess players very happy!

Agt the Walker Agt the Walker 9/12/2020 12:07
I am very happy to see the 14th undisputed world champion propose more chess variants (and checking them with AlphaZero!).

Combining no-castling with Chess 960 would unfortunately halve the number of starting positions, since RKQBBNNR would become identical to RNNBBQKR for instance. However we could make castling less attractive (i.e. nerf it) to make it occasional instead of frequent.

For example, a player castling first would forfeit the ability to move a pawn forward two squares (the first time it is moved), until his opponent castles. This combines both "No-castling" and "Pawn one square" ideas ;).
ICCF Grandmaster ICCF Grandmaster 9/11/2020 02:52
@wb_munchausen and @flachspieler:
This is what Kramnik says on p.38:
"In terms of the anticipated effect on human play,
I would still expect this rule change to lead to a
higher percentage of wins in endgames where one
side has a clear advantage, but probably not as
much as one would otherwise have been expecting.
This may be a nice variation of chess for chess
enthusiasts with an interest in endgame patterns."
Very interesting, as I am promoting the idea of "stalemate=3/4 - 1/4 point" since many years, esp. in computer-assisted correspondence chess.
Yet, two critical remarks to Kramnik and the AZ paper:
1) Why completely burying the stalemate idea as something special? A slight change like suggested above (and first suggested by Emanuel Lasker and Richard Réti) makes much more sense. It would still be a goal in a worse position to save oneself by stalemate instead of getting mated, while on the other side the better player still gets a reward for his achievement.
2) I doubt whether AZ's self-learning and training was already that good in order to evaluate long-term strategic endgame motifs for this kind of test. Given the "intructive" game AZ-8 on p. 39 (played with 1 minute per move) I doubt that any strong player would really prefer 11.0-0-0?! here (in respect of the rule change!), giving away the h2-pawn for almost nothing. And, of course, are things much different in human play (regarding more complex problems and differences in playing strength), so that we can not simply transpose the AZ statistical results to human chess, as also Kramnik knows very well.
Arno Nickel
flachspieler flachspieler 9/11/2020 12:47
@wb_munchausen: I think the stalemate = win variant has some merit. Many or even most of the drawn endgames would then be wins.

No. We analysed several 5-piece endgames for this variant (in particular K+R+B vs K+R). Almost nothing changed.
Ingo Althöfer.
wb_munchausen wb_munchausen 9/11/2020 12:32
I think the stalemate = win variant has some merit. Many or even most of the drawn endgames would then be wins.
fgkdjlkag fgkdjlkag 9/11/2020 08:12
Are these people crazy? Kramnik was heavily criticized, and rightfully so, for the ridiculous suggestion of no-castling chess, which does nothing more than push the current problem of opening theory back for a few decades or longer (considering the strong computers available today), while keeping chess's problem of requiring voluminous amounts of opening memorization. Is it really worth it to gain a few decades considering this is a 1500 year old game? It was accompanied by a ridiculous article on a low percentage of draws in a BLITZ tournament.

No castling for the first 10 moves?! Really? Now we have to keep track of each move number? What about casual players who are not keeping notation? I have a serious suggestion for a variant: No castling from moves 5-15 which is the most dynamic part of the game, then at move 15 the pawn can move sideways until move 20, and after move 20, each pawn can go backwards 2 squares once per game (a reverse 1st move for each pawn). This will create a golden age of chess.

And what kind of sense does it make for 1 player to make a qualitative assessment? Of course if a different player was selected, the qualitative assessment could be diametrically opposed to Kramnik's...
Daniel Quigley Daniel Quigley 9/11/2020 06:58
When did Kramnik go blind?
MrPickl3 MrPickl3 9/11/2020 06:14
Negi's variant is probably the only one that is AI-resistant, including against AlphaZero.

The variant is real chess but each side cannot see each other's pieces.
GrayRazorback GrayRazorback 9/10/2020 10:24
Start playing chess variants? Don't think so. I will stick with real chess.
dbergan dbergan 9/10/2020 03:42
This is an exciting project and I look forward to the results. In addition to the above, I wish they had included two variants from chess legends:

a) "Pre-chess" from David Bronstein:

b) "Stalemate = 0.8–0.2" from Emanuel Lasker:

Kind regards,
Thomas_A_Anderson Thomas_A_Anderson 9/10/2020 02:40
No refernece? Presumably
flachspieler flachspieler 9/10/2020 08:58
Interesting article. About 15 years ago I used (other) artificial intelligence software to evaluate new board games. That way, the game "EinStein wurfelt nicht" was created and tuned. In 2008, Cameron Browne completed his Ph.D. thesis on completely automatic board game design. One of the findings of his program was the very nice board game "Yavalath".
Ingo Althoefer.