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:

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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ICCF Grandmaster ICCF Grandmaster 10/2/2020 01:52
@genem. - Not only "some dead drawn endgames" would be affected by a "no repetition rule". All perpetuals would appear in a different light, and that would be quite tricky.
I show you one of my correspondence games with a line that later on got completely adopted by over-the-board players.

A. Nickel - Alois Lanc, ICCF WC21/final, 2005-2007
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O Be7 6. Re1 b5 7. Bb3 d6 8. c3
O-O 9. h3 Bb7 10. d4 Re8 11. Ng5 Rf8 12. Nf3 Re8 13. Nbd2 Bf8 14. a4 h6 15. Bc2
exd4 16. cxd4 Nb4 17. Bb1 c5 18. d5 Nd7 19. Ra3 c4 20. axb5 axb5 21. Nd4 Qb6
22. Nf5 Ne5 23. Rg3 g6 24. Nf3 Ned3 25. Qd2 Nxe1 26. Nxe1 Ra1 27. Nxh6+ Bxh6
28. Qxh6 Nxd5

29. Rxg6+ 1/2-1/2
The point is, Black would lose here, if not allowed to repeat his king move after 29...fxg6 30.Qxg6+ Kh8 31.Qg6+.
At first glance it looks like White is repeating a move by 31.Qxg6+, but in fact he doesn't, because 30.Qxg6+ captured a pawn and 31.Qg6+ is without capturing. (Of course there are similiar positions where the attacking player would be punished by the "no repetition rule". - Yet, I don't simply reject that idea, but I think, perpetual checks should be handled differently from other kind of move repetitions. Quite complicated stuff ...
I worked a lot on these questions, as I am looking for changes in order to lower the extremely high draw rate in correspondence chess. May be I will publish my latest paper here that I addressed to ICCF in June 2020 suggesting a set of decent changes for the tie-break rules.
genem genem 10/2/2020 05:05
@MeisterZinger is probably right in that It should be illegal to cause a repetition of a position. This would prevent the easy way for two players to overpower the Sofia rule that forbids offering or accepting a draw until after at least 40 move pairs have been completed. However, this no repetition rule would have a big effect on some dead draw endgames, and the details would need to be studied and documented. At best, the no repetition rule would work, thereby compelling the already tired players to play on from an early endgame because neither can resign. It would be too difficult to know whether the no repetition rule would prevent the usual draw if played to the last pawn.
ICCF Grandmaster ICCF Grandmaster 10/1/2020 03:36
@conillet, yes we need more testing and of course between human players. Note, that Kramnik makes a difference between AZ results and what he expects for human play. In my view, stalemate = win is not the perfect solution; stalemate counting 3/4 : 1/4 is more suitable. I remember a game Giri - Shankland in Wijk aan Zee 2019, where Sam resigned in a position, when he could have saved himself by stalemate. That was shocking. But if stalemate would be counted as win, we would no longer see such nice subtleties. Stalemate = 3/4 : 1/4 makes chess a bit more complex, as there would be three outcomes of a game: 1, 1/2, 3/4 (1/4).
Giri-Shankland (Black to move):
conillet conillet 10/1/2020 02:14
I wish somebody would organise a tournament with stalemate as win (preferably Rapid Fischer Random). I find it hard to believe that the impact on draw rates is as small as the article seems to suggest. This needs more testing, by human players.
philidorchess philidorchess 10/1/2020 05:06
Exploring new ideas.Like it.Fascinating like astronomy.
fgkdjlkag fgkdjlkag 9/30/2020 09:30
@rubinsteinak, this was already analyzed by the Sesse supercomputer 2 years ago. 2/3 of the starting fischer random positions have a smaller white opening advantage than the standard chess518 starting position:
https://docs.google.com/spreadsheets/d/1JVT6_ROOlCTtMmazzBe0lhcGv54rB6JCq67QOhaRp6U/edit#gid=0

I do not find anything novel here. The strategic changes that occurred in castling10 should have been obvious without any sophisticated AI computer analysis.
Tralala1 Tralala1 9/30/2020 08:47
Corrected now :)
rubinsteinak rubinsteinak 9/30/2020 07:10
I'd be interested to know how AlphaZero evaluates Fischerandom. Namely, of the 959 alternate starting positions, how many vastly favor white, and what are the attributes of these starting positions?
Tralala1 Tralala1 9/30/2020 06:43
Hmm. It seems the picture is wrong. Black king can move.
Interesting article.
MeisterZinger MeisterZinger 9/30/2020 05:36
Interesting stuff, and I'm looking forward to reading the whole paper (have just skimmed it). Two comments: First, it would be interesting to see whether there are other openings whose playability is grossly impacted by these rule changes, as appears to be the case for the QGD Chigorin Defense (1. d4 d5 2. c4 Nc6). I specifically wonder about things involving pawn sacrifices for long-term compensation like the Benko Gambit, Evans Gambit, Staunton Gambit in the Dutch, Marshall Attack in the Ruy -- or maybe these are already unplayable at the Alpha-Zero level! How do these fare in stalemate-win chess, since the possibility of escaping into a drawable pawn-down endgame would likely be reduced?

Second, I'm surprised that the simplest rule change of all, yet possibly the one with the largest balance effect, wasn't on this list: forbidding repetition of position, as is done in Go, Shogi and lots of other games. I suspect that the large draw probability in A0 vs. A0 games would all but go away, and who knows, it might turn out that White is in zugzwang on move 1! Has any work like this been done on such a rules change?

Great stuff, whatever the answers to my questions. Thanks for supporting it.
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