Nenad Tomašev, Ulrich Paquet, Demis Hassabis, Vladimir Kramnik
2020 · arXiv
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.
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DeepMind and Kramnik had an interesting paper a few months back exploring possible chess variants: https://arxiv.org/abs/2009.04374 The basic idea is to train AlphaZero on proposed variants, and look for ones that have fewer draws and a smaller advantage for white.
According to the paper (https://arxiv.org/pdf/2009.04374.pdf) removing the special handling of stalemates did not really change the draw ratio much. So the weaker party can still gun for the draw in most situations. (However, they had really good computers play, who do not get stressed out, albeit they do make worse moves on shorter time controls.)
AlphaZero has been used to more objectively study chess variants in this paper: https://arxiv.org/pdf/2009.04374.pdf I don't think they mention anything about speeding up training. The original training time for AlphaZero was only a few hours anyway so I don't think that was ever a major constraint. I would imagine that each neural network performed best on the variant on which it was trained.
Here is a link https://arxiv.org/abs/2009.04374 to the paper you are probably talking about. Coming from DeepMind (and with Former world champion Vladimir Kramnik as a coauthor), they studied a bunch of chess variants by training AlphaZero to play on them. In addition to no-castling, they also studied variants where pawns can always move two steps forward, and where it's possible to capture your own pieces.
The important thing to mention: in many respects, you can pretend that in chess the objective is to capture the opposing king. But for historical reasons, the game actually tops one move before, and the king is never captured. But they also have weird rules that both (A) forbid putting your king in check, and (B) hand you a draw when you are out of legal moves. A simpler version of chess would actually play until the king is captured, and allow people to move into check. https://arxiv.org/pdf/2009.04374.pdf reports on some experiments with variants like this. Another interesting thing to try out is to allow players to capture their own pieces. Or to abolish castling.
Yes, you are right that this is only an intellectual exercise. (Btw, it's quite popular in the Go world to reformulate the ancient clunky rules of Go into a more modern, mathematical version that might or might not have small differences in gameplay.) However, I don't actually think that removing check rules make chess worse. But that's subject to experiment. See https://arxiv.org/pdf/2009.04374.pdf for exactly such experiments.
When people complain about chess being uninteresting, they usually complain about too many draws. Adding more opportunities to turn draws into wins/losses might seem like a good thing? > Now the middle game is less interesting, because taking any kind of risk is never worth it. Chess is a zero sum game. Taking the right risk can also increase your chances of winning (instead of just stalemating). (I mention the zero sum game, because eg real life war is not a zero sum game. So it's perfectly possible for certain actions, like starting to shoot medics, to be bad for both parties. But in chess, what's bad for one party is automatically good for the other.) > [..] which…
means it's incredibly easy to trade into a winning endgame from the middle game. You know that the other guy gets to have a vote on this, too? You can also have a look at the Eastern chess variations (Shogi etc) that https://news.ycombinator.com/item?id=39141452 mentions that don't have check rules, and see whether for them every game is boring? Btw, see https://arxiv.org/pdf/2009.04374.pdf for an investigation of the impact of no-check-rules on western chess. It doesn't make everything boring.
Thanks for bringing up the Chinese chess example! Btw, see https://arxiv.org/pdf/2009.04374.pdf for an investigation. > Now stalemate by repeated back-and-forth is a different matter. I would favor some variant of Go's Ko rule, which is that you may not make a move if the result would be a board that looked exactly the same as it had in the past. I would favour that rule as well, but keep in mind that even in Go that is a very modern formulation / variation of this rule. Past formulations were about as clunky as chess's stalemate rules, and even left some situation (that were extremely rare in practice) without a satisfactory resolution. Btw, in Go the 'board' isn't the…
only state the game has: you also count prisoners. After a complicated ko exchange, the board might look the same, but the prisoner count has gone up for both players. I assume the rules probably only care about the difference in prisoner counts (and board state) to determine whether a state has been repeated; not the absolute prisoner count.
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