Almost three years since DeepMind’s AlphaZero shocked the chess world by taking just four hours to go from zero to the best chess-playing entity anywhere, the team is back with another party trick. This time AlphaZero used its self-learning ability to learn variants of chess, so we can see how such changes as banning castling, making stalemate a win or letting pawns move sideways or backwards would change the game after decades, or even centuries, of top-level play. 14th World Chess Champion Vladimir Kramnik was on hand to assess the results.
DeepMind today published the 98-page academic paper Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess (click to download), authored by Deep Mind’s Nenad Tomašev, Ulrich Paquet, Demis Hassabis and 14th World Chess Champion Vladimir Kramnik.
The paper features some mathematical formulas that the average reader will skim over, but the analysis, based on a large number of sample games, is much more accessible and packed with interesting detail. For instance, the piece values for regular chess (the authors caution this should not be taken as “a gold standard”) are Knight = 3.05 pawns, Bishop = 3.33 pawns, Rook = 5.63 pawns and Queen = 9.5 pawns.
The highlight for most chess fans, however, will be the over 70-page appendix with sample games, positions and commentary from Russia’s Vladimir Kramnik. It’s a treasure trove of fun positions and curiosities, but let’s first take a look at the chess motivation for the study.
3rd World Chess Champion José Raúl Capablanca feared the “draw death” of chess a century ago and came up with Capablanca Chess, played on a 10x8 board with two new pieces. It didn’t catch on, but 11th World Chess Champion Bobby Fischer’s Fischer Random Chess, or Chess960, has fared better. The variant he announced in 1996 sees the pieces on the back rank shuffled randomly before a game into one of 960 possible combinations – all but eliminating opening theory, since no-one is capable of analysing or memorising so many different positions in any depth (though come to think of it – it sounds like a job for AlphaZero!).
Rebranded as Chess9LX we’re going to see that game in action this weekend, as 13th World Champion Garry Kasparov will take part and face 9 players who include the 16th and current World Champion Magnus Carlsen – their first competitive meeting at the board in 16 years!
Both those solutions are radical, however, while 14th World Champion Vladimir Kramnik was drawn to something subtler. The scene is Kazan, Russia in 2011, where the Candidates Matches are taking place to decide Vishy Anand’s next challenger. Magnus Carlsen, already clearly the world no. 1, is missing after deciding not to participate for reasons that left his colleagues puzzled, but his replacement Alexander Grischuk is in top form at the press conferences:
I think, in general, we’re witnessing the burial of classical chess. Two decisive games in 21; that’s about the same as in checkers! On the one hand, that’s a great disappointment – to keep playing such boring games, but on the other hand – maybe we’re doing a good thing.
Grischuk, who welcomed the end of classical chess, was speaking after a third draw in his 4-game semi-final against Kramnik. He went on to draw again, win the tiebreak and, by the time of the 6th and final classical game in the final match, we’d seen 2 decisive classical games in 29, while Grischuk had drawn 13 in a row. It was unlucky 14, however, as Boris Gelfand won to make it 3 decisive games in 30 and earn a match against Anand.
It really was a low point for long, classical games, and after the first game of the Kramnik-Grischuk match, Vladimir also shared his thoughts on the situation:
It’s obvious that the outcome of almost any opening is going to be equality. The stronger computers get, the more lines are neutralised, the more drawing resources are found for Black, unfortunately. Therefore, I don’t know… by the way, yesterday we discussed that at dinner. My seconds and I discussed the idea that instead of, for example, Chess960, maybe we could change the form of chess by making some tiny changes to the rules which leave it almost untouched. For instance, I had the idea of banning castling before the tenth move. That’s an example. Essentially it doesn’t change the game at all, but it gets rid of all the theory i.e. you have to create new theory, but while that theory’s being created we can still play for another 50 years or so.
You can think up a lot of such little ideas. I’d be glad, overall. It strikes me that maybe it’ll come to that. Despite the inexhaustibility of chess it’s becoming harder and harder, and as the years go by the tendency’s becoming more and more pronounced, particularly at the top level where everyone’s well prepared. So perhaps it’d make sense to make such minor changes. That was just one thought… we had some other ideas, like only allowing pawns to advance one square at a time. But then it’d be hard for White to get an edge. It’d be completely even. Or stopping capturing en-passant. A minor detail, in principle. It doesn’t change much, but a lot of theoretical positions would be altered. We were a fountain of new ideas over dinner. (smiles)
9 years later, and now retired from classical chess, it turns out those thoughts never left Kramnik! But whereas before a statement such as, “it’d be completely even,” would be hard to prove or disprove without organising multiple tournaments and giving top players time to prepare and devise new strategies, we can now do it “in silico”, as the paper puts it. For AlphaZero it’s no harder to become a 3000+ rated player of normal chess than to do the same for a variant, and when it plays its only rival, itself, we get a glimpse of the balance of power and richness of each new game.
The variants investigated by AlphaZero all retain the normal board and pieces in their standard starting positions, with the authors explaining:
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 opening, middlegame or endgame patterns and a novel body of opening theory.
Let’s take a look at the variants and, just for fun, try to rank them in terms of their appeal. What follows is, of course, subjective, and you may well disagree! (please let us know in the comments section)
This was the first option Vladimir came up with 9 years ago in that post-game press conference, but it feels like an artificial trick to confuse professional chess players rather than an interesting new avenue for chess. You have to keep count in your head or on paper, and Vladimir notes something that could logically have been guessed at:
AlphaZero usually aims at playing slower lines where castling does indeed take place after the first 10 moves.
The variant led to far fewer decisive games not just compared to “no castling chess” but to normal chess, and is unlikely to catch on.
The dream of English Grandmaster Nigel Short, who brought it up, for instance, during the 2018 World Championship match:
Treating stalemate as a win was unlikely to affect early play in games, but Kramnik also thought it would make chess less drawish. That didn’t turn out to be the case, to any significant degree, at least when AlphaZero was given more time to think.
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.
He reasons that many of the endings that can be defended by stalemate can be defended by other methods if stalemate isn’t available. Also, while stalemate (=mate) rather than mate did account for an impressive 37.2% of AlphaZero’s wins, the authors explain this was largely based on the computer preferring stalemate to checkmate when both were options. All in all, not a convincing case to alter what many consider a beautiful motif of chess endings.
A torpedo pawn move is advancing two squares, which in these variants can be done not only on a pawn's first move. “Semi-torpedo”, however, only allows the extra option of such a move from the 3rd rank, so as Kramnik points out if you want to advance your pawn to h5 you could first play h3, keeping the position solid, and only then h5. A fianchetto with g3 or b3 can also suddenly become an attacking lunge with g5 or b5. Vladimir explains the variant as follows:
It is an interesting variation, to be potentially considered by those who like the general middlegame flavor of Torpedo chess, but are unwilling to abandon existing endgame theory.
Still, who wants to play “semi”-torpedo?
When Kramnik mentioned this option back in 2011 he noted, “But then it’d be hard for White to get an edge – it’d be completely even”. It turns out that’s not quite true, since White gets an edge in every variant tested, but here it is less than in classical chess and draws are more likely. The authors point out that the slower play gives players more plausible options – they looked at this while trying to assess the “richness” of the games quantitatively – but this feels more like an attempt to dodge existing opening theory than an exciting game to watch.
If there’s one thing we’re drilled about when it comes to pawns it’s that they can’t move backwards, but in this variant they can! Any pawn can move backwards one square, but not further back than the starting rank.
Vladimir Kramnik points out this has some curious opening implications:
It was interesting to see AlphaZero’s strong preference for playing the French defence under these rules, the point being that the light-squared bishop is no longer bad, as it can be developed via c8-b7 followed by a timely d5-d6 back-move.
Other openings change as well. After the standard 1. e4 e5 2. Nf3 Nc6, there comes a surprise: 3. c4!
It is followed by 3...Bc5 4. e3 (a back-move!) 4…Bb6 5. d4 d6
Who would have guessed that we are on move 5, after the game having started with e4 e5?
Another amusing finding is that this is the opening in which the Dutch Defence is soundest. As Artur Yusupov is reported to have said:
The problem with the Dutch is that Black very often in the middlegame finds that his best available move is f5-f7.
Here you’d have to play f7-f6 and only then f6-f5, but even that might be worth it! Overall, however, it’s unlikely pawn-back chess is the solution to the game’s perceived problems, since at least in AlphaZero’s games it helped the defending side and reduced the number of decisive games.
This is where things get wild, as in this variant pawns can do all they usually do, but also move one square sideways.
Such moves occurred in 99.6% of AlphaZero’s games and accounted for 11.4% of all moves. The ability to move sideways transforms the power of pawns, making the other pieces much less valuable in comparison:
“This is the most perplexing and “alien” of all variants of chess that we have considered,” said Kramnik, who pointed out how it changes endgames:
In classical chess, White would be completely lost. Here, White can play b7-a7 or b7-c7, changing files. The rook can follow, but the pawn can always step aside. In this particular position, after b7-c7, Rc3, c7-d7 – Black has no way of stopping the pawn from queening, and instead of losing – White actually wins!
Perhaps, however, it’s just too complicated and different to become a popular alternative to normal chess?
This variant has many virtues. It eliminates the only move in chess where two pieces are moved at the same time, and would therefore ease the task for beginners or spectators (and perhaps even for grandmasters when it comes to Chess960 - Vassily Ivanchuk recently noted in our Q&A session that castling there feels “unnatural” to him). It’s also a change that can be implemented anywhere simply by players agreeing not to castle and has already been trialled “in the wild”, during the London Chess Classic and a tournament in Chennai, India.
The complete ban on castling means kings are stranded in the centre of the board and, as might be expected, are more susceptible to attacks, leading to an increased number of decisive games. For Kramnik, however, the main factor is simply to skip existing opening theory, where castling early is key to most openings:
One of the main advantages of no-castling chess is that it eliminates the nowadays overwhelming importance of the opening preparation in professional chess, for years to come, and makes players think creatively from the very beginning of each game. This would inevitably lead to a considerably higher amount of decisive games in chess tournaments until the new theory develops, and more creativity would be required in order to win. These factors could also increase the following of professional chess tournaments among chess enthusiasts.
There’s an element of self-sacrifice here, since AlphaZero’s love affair with Kramnik’s Berlin Defence, which it considers by far the best defence against 1.e4, ends when castling is ruled out.
No half-measures! Full torpedo means that pawns can move one or two squares at any time, and not just on their first move or from the 2nd and 3rd ranks. That means that the dictum that Vladimir Kramnik’s passed pawns always queen is more likely to be true than ever, with 28.7% of the AlphaZero games featuring pawn promotion.
27.Qc2!! was AlphaZero's amazing move here, attacking the a4-rook and h7-bishop. If 27...Bxc2 then 28.h8=Q+! and there's a new queen on the board.
The 14th World Chess Champion comments:
All of the attacking opportunities increase and this strongly favours the side with the initiative, which makes taking initiative a crucial part of the game. Pawns are very fast, so less of a strategical asset and much more tactical instead. The game becomes more tactical and calculative compared to standard chess.
In fact Kramnik points out that the players are forced to play prophylactically to try and keep the pawns tied down, but nevertheless this is the variant with the most decisive games and biggest advantage for White, even if a draw still remains the most likely outcome. This would be a dramatically different form of chess despite the rule change arguably making the game more logical – no special case for the first move of a pawn.
This is the variant that gets the most glowing recommendation from Vladimir himself:
I like this variation a lot, I would even go as far as to say that to me this is simply an improved version of regular chess… To conclude, I would highly recommend this variation for chess lovers who value beauty in the game on top of everything else.
The idea really is powerful but elegant, since it’s even easier to explain to a beginner than the current rules – instead of only being able to capture your opponent’s pieces you can capture your own as well.
That unleashes numerous new options, with Kramnik pointing out this position in the Ruy Lopez:
Here the black queen can play Qxh7!, suddenly threatening mate after capturing on h2. The bigger changes occur in the middlegame and endgame, however, with many fortresses easily dismantled. For instance:
In normal chess the white pawn can never queen, but here simply Bc8 and bxc8=Q wins the game.
At the same time, the balance of power seems to remain very close to that of regular chess. Which brings us to…
If it ain’t broke, don’t fix it, and it’s far from obvious that even at the very highest level chess is any more broke now than Capablanca imagined it was back in the 1920s. The 10% of decisive results in 2011 didn’t prove to be the herald of things to come, and in fact computers such as AlphaZero or its accessible counterpart Leela Zero have been showing that all kinds of chess openings that were considered dubious are perfectly playable – think Daniil Dubov turning the Philidor Defence into a fearsome weapon.
We continue to see exciting games in super-tournaments and, for instance, the 2018 Candidates Tournament featured 36% decisive games, although admittedly Kramnik was involved in 7 of those 20 games! The best argument for classical chess being in trouble was perhaps the 12 draws in the 2018 World Championship match, but in normal circumstances Magnus would have converted his winning position in Game 1 and what followed might have looked very different. In any case, many of the draws, especially when Magnus played the Sveshnikov, were thrillers.
It’s unclear if current professionals would relish these variants, since rather than making preparation unfeasible, as Chess960 does, they simply mean you'd have to work harder than ever to develop a whole new theory - of course aided by computers. Even if the players were up for that challenge, does it make sense to force chess fans to learn new variants and the new tactics and strategy involved? If chess has a problem compared to other sports it’s that a certain amount of knowledge is all but essential to enjoy the action. Raising that barrier any higher is unlikely to be the best way forward.
Nevertheless, being able to answer such “what if?” questions about different chess variants is another fantastic application of DeepMind’s AI, and one that is no doubt more generally applicable. One suggestion appears in the paper.
We believe that a similar approach could be used for auto-balancing game mechanics in other types of games, including computer games, in cases when a sufficiently performant reinforcement learning system is available.
Computer games, especially new ones, aren’t tied to a long tradition that it makes sense to uphold. You suspect, however, that AlphaZero can do more than help out in software design.
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