AlphaZero/Kramnik: More variants

by Frederic Friedel
9/30/2020 – Modifying the existing rules for chess 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 new variants, and DeepMind has used their AI technology to evaluate them in a much shorter period of time. Here are their findings for No-castling, Pawn one square and Stalemate=win chess.

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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 be describing the contents in multiple parts, providing you with example games for your own evaluation. Here for your reference is the previous article.

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. 

Here are the nine variants that were evaluated:

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
--

Qualitative assessment

To evaluate the differences in play between the set of chess variations considered in this study, the AlphaZero team coupled 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, the team relied on the experience of chess grandmaster Vladimir Kramnik, a recognised authority on the game.

For this analysis, they used 1,000 one-minute per move games as well as 200 one-minute per move games from a diverse set of early opening positions that covered all of the major opening systems. By looking at the former, experts were able to assess AlphaZero’s preferred style of play in each chess variant, and by looking at the latter, they could assess how the treatment of different opening lines changes and which of those become more or less promising under each of the rule changes.

Here are two illustrative positions for the chess variants No-castling and No-castling (10):

No-castling chess: This is a typical position where both kings haven’t found immediate safety and remain exposed into the middlegame.

No-castling(10) chess: The play tends to be slower and more strategic, to allow for later castling. Here, on the 11th move, Black castles at the very first opportunity and White castles immediately after as well.

You can read more about No Castling Chess in the article 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!

Here is the qualitative analysis provided by GM Vladimir Kramnik.

No-castling chess is a potentially exciting variant, given that king safety is often compromised for both players, allowing for simultaneous attacking and counter-attacking and the equality, when reached, tends to be dynamic in nature rather than “dry”. The multitude of approaches to evacuate the king, and their timing, adds complexity to the opening play. No-castling (10), where castling is not permitted for the first 10 moves (20 plies) is a partial restriction, rather than an absolute one – which does not change the game to the same extent. Due to castling being such a powerful option, the lines preferred by AlphaZero all tend to involve castling, only delayed – resulting in a preference for slower, closed positions, and a less attractive style of play. Such partial castling restrictions can be considered if the desire is to sidestep opening theory and preparation, but this may not be of interest for the wider chess audience.

And here the assessment of two further variants:

Pawn one square may appeal to players who enjoy slower, strategic play – as well as a training tool for understanding pawn structures, due to the transpositional possibilities when setting up the pawns. The reduced pawn mobility makes it harder to launch fast attacks, making the game overall less decisive.

Stalemate=win has little effect on the opening and middlegame play, mostly affecting the evaluation of certain endgames. As such, it does not increase decisiveness of the game by much, as it seems to almost always be possible to defend without relying on stalemate as a drawing resource. Therefore, this chess variant is not likely to be useful for sidestepping known theory or for making the game substantially more decisive at the high level. The overall effect of the change seems to be minor.

The first position would have been a draw in classical chess is now a win instead. K+N+N vs K are now wins rather than draws! In the second position, with White to move, in classical chess the position would be a draw due to stalemate after Ke6. Yet, the same move wins in this variation of chess, so the defending side needs to steer away from these types of endgames.

Vladimir Kramnik's assessment of Stalemate=win

I was at first somewhat surprised that the decisive game percentage in this variation was roughly equal to that of classical chess, with similar levels of performance for White and Black. I was personally expecting the change to lead to more decisive games and a higher winning percentage for White. It seems that the openings and the middlegame remain very similar to regular chess, with very few exceptions, but that there is a significant difference in endgame play since some basic endgame like K+P vs K are already winning instead of being drawn depending on the position.

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.

Replay a sample of variant games here:

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1.d4 d5 2.c4 e6 3.Nc3 c5 4.cxd5 exd5 5.Nf3 Nf6 6.g3 Nc6 7.Bg2 h6 8.h4 Be6 9.Kf1 Rc8 10.Be3 Ng4 11.Qd2 b5 12.Nxb5 Qb6 13.a4 a6 14.dxc5 Nxe3+ 15.Qxe3 Bxc5 16.Nd6+ Ke7 17.Nxc8+ Rxc8 18.a5 Qa7 19.Qb3 Bxf2 20.Bh3 Rb8 21.Qa3+ Bc5 22.Qd3 Nb4 23.Qh7 Qd7 24.Bxe6 Qxe6 25.Rc1 Be3 26.Rc3 d4 27.Rc5 Kd6 28.Re5 Qg4 29.Qf5 Qxg3 30.Rh2 Qg6 31.Rg2 Qxf5 32.Rxf5 Ke6 33.Rc5 Kd6 34.Rf5 Ke6 35.Re5+ Kf6 36.h5 Rc8 37.Rg4 Rc1+ 38.Kg2 Nc6 39.Re8 Rc2 40.Kh3 Rc5 41.Kh4 Bf2+ 42.Kh3 Be3 43.Rh4 Rxa5 44.Kg3 Ra1 45.Rhe4 Kf5 46.Nh4+ Kf6 47.Rc8 Ne7 48.Re8 Nc6 49.Nf3 Kf5 50.b3 Rb1 51.Nh4+ Kf6 52.Ra8 Ra1 53.Kh3 Ne5 54.Re8 Rh1+ 55.Kg3 Nc6 56.Ra8 Ra1 57.b4 Nxb4 58.Rd8 Rg1+ 59.Kh3 Rh1+ 60.Kg2 Rg1+ 61.Kh3 Rh1+ 62.Kg3 Rg1+ 63.Ng2 Nc2 64.Kh2 Rf1 65.Rc8 Kf5 66.Nxe3+ Nxe3 67.Rxd4 Kg5 68.Rc5+ f5 69.Kg3 Kxh5 70.Re4 Ng4 71.Kg2 Rf2+ 72.Kg1 Nf6 73.Re7 Rf4 74.Rxg7 Ng4 75.Rc3 Kh4 76.Re7 Kg5 77.Ra3 h5 78.Rxa6 Rb4 79.Ra5 h4 80.Ra3 Nf6 81.Rg7+ Kh5 82.Rf7 Kg5 83.Rg7+ Kh5 84.Kh1 Rb2 85.Ra5 Kh6 86.Rg2 Rb1+ 87.Rg1 Rxg1+ 88.Kxg1 Kg5 89.Ra8 Ne4 90.Kg2 Kg4 91.Ra4 Kg5 F 92.Rb4 Kg4 93.Rd4 Kh5 94.Kh3 Ng5+ 95.Kh2 Ne4 96.Kg2 Kg4 97.Rb4 Kg5 98.Kf3 Nd2+ 99.Ke3 Ne4 100.Rb7 Kg4 101.Rg7+ Ng5 102.Rg8 h3 103.Kf2 f4 104.Kg1 Kh4 105.Rd8 Kg4 106.Rd4 Ne6 107.Re4 Ng5 108.Ra4 Kg3 109.Ra3+ Kg4 110.Kh2 Kf5 111.Ra1 Kg4 112.Ra4 Kf5 113.Rc4 Ke5 114.Rc5+ Kf6 115.Rd5 Kg6 116.Rb5 Kf6 117.Rb3 Kf5 118.e3 fxe3 119.Rxe3 Kg4 120.Rg3+ Kf5 121.Ra3 Kf4 122.Ra4+ Ke5 123.Kg3 Ne6 124.Ra1 Kd5 125.Kh2 Nd4 126.Ra5+ Kc6 127.Ra1 Kc5 128.Kxh3 Nb3 129.Ra8 Nd4 130.Kg2 Nc6 131.Kg1 Kb5 132.Ra1 Ne5 133.Ra7 Kb6 134.Ra8 Kc6 135.Ra5 Kd6 136.Ra1 Kc5 137.Ra7 Kb6 138.Re7 Nc6 139.Re1 Kc5 140.Rc1+ Kd5 141.Rd1+ Kc5 142.Re1 Kd5 143.Ra1 Ne5 144.Ra7 Kd6 145.Ra5 Nf3+ 146.Kh1 Ne5 147.Ra6+ Kc5 148.Kg1 Kb5 149.Ra3 Kc5 150.Ra5+ Kd6 151.Ra6+ Kc5 152.Ra8 Kc6 153.Kg2 Kd6 154.Kf1 Kc5 155.Ra6 Nc6 156.Ra1 Ne5 157.Ra8 Kd6 158.Kg2 Nc6 159.Kf2 Kc5 160.Rh8 Kd6 161.Rh1 Nd4 162.Ke3 Ke5 163.Kf2 Kd5 164.Ke3 Nf5+ 165.Kf4 Nd4 166.Rf1 Nb5 167.Ke3 Nd6 168.Kf4 Nb5 169.Ke3 Nd6 170.Ra1 Kc5 171.Kd3 Kd5 172.Ke3 Kc5 173.Rb1 Kc4 174.Kd2 Kd4 175.Kc2 Ke3 176.Kc3 Ne4+ 177.Kc2 Ke2 178.Rb2 ½–½
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WhiteEloWBlackEloBResYearECOEventRnd
NoCastling_1min-NoCastling_1min-½–½2020Computer Match, selfplay from move 0 ga
NoCastling_1min-NoCastling_1min-½–½2020Computer Match, selfplay from move 0 ga
NoCastling_1min-NoCastling_1min-½–½2020Computer Match, selfplay from move 0 ga
NoCastling10_1min-NoCastling10_1min-½–½2020A40Computer Match, selfplay from move 0 ga
NoCastling10_1min-NoCastling10_1min-½–½2020A28Computer Match, selfplay from move 0 ga
PawnOneSquare_1min-PawnOneSquare_1min-½–½2020A00London, UK
PawnOneSquare_1min-PawnOneSquare_1min-½–½2020A00Computer Match, selfplay from move 0 gam
Stalemate=win_1min-Stalemate=win_1min-1–02020Computer Match, selfplay from move 0 game_type=3 at 2020-01-17T03:25:38.871982538-08:00

If you find the results puzzling you should remember that most of the high-quality games of AlphaZero end up as draws – with a few decisive games in between. This is because the level of play is so high that it become seriously difficult for one side to defeat an opponent of equal strength. In games with faster time controls (1s/move) the play is usually more aggressive and decisive – but obviously less accurate as well.

You can read the entire 98-page paper here:

Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess
Submitted on 9 Sep 2020 (v1), last revised 15 Sep 2020 (this version, v2)
By Nenad Tomašev, Ulrich Paquet, Demis Hassabis, Vladimir Kramnik

Abstract: It is non-trivial to design engaging and balanced sets of game rules. Modern chess has evolved over centuries, but without a similar recourse to history, the consequences of rule changes to game dynamics are difficult to predict. AlphaZero provides an alternative in silico means of game balance assessment. It is a system that can learn near-optimal strategies for any rule set from scratch, without any human supervision, by continually learning from its own experience. In this study we use AlphaZero to creatively explore and design new chess variants. There is growing interest in chess variants like Fischer Random Chess, because of classical chess's voluminous 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. We compare nine other variants that involve atomic changes to the rules of chess. The changes allow for novel strategic and tactical patterns to emerge, while keeping the games close to the original. By learning near-optimal strategies for each variant with AlphaZero, we determine what games between strong human players might look like if these variants were adopted. Qualitatively, several variants are very dynamic. An analytic comparison show that pieces are valued differently between variants, and that some variants are more decisive than classical chess. Our findings demonstrate the rich possibilities that lie beyond the rules of modern chess.      


Editor-in-Chief emeritus of the ChessBase News page. Studied Philosophy and Linguistics at the University of Hamburg and Oxford, graduating with a thesis on speech act theory and moral language. He started a university career but switched to science journalism, producing documentaries for German TV. In 1986 he co-founded ChessBase.

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