AlphaZero Tackles Chess Variants

Break out the physical chess sets for this one.

In keeping with the tradition of (some of) his great predecessors, retired former World Chess Champion Vladimir Kramnik has spent some time the last few years devising and (lightly) promoting a number of chess variants. For Jose Raul Capablanca, the problem was the “draw death” of chess; for Bobby Fischer, it was the burden of opening theory and the resulting lack of creativity at the board. We can smile at their pessimism, though they may not have been so much wrong as premature, or (to my mind) a bit too sanguine about the powers of the human mind. (Let’s see how bad the “draw death” problem will prove to be in a match between Magnus Carlsen and Stockfish.)

Back to Kramnik and his variants. The times being what they are, there’s no sense in proposing something that fosters creativity and an escape from the ubiquity of the engine’s influence if you’re not going to immediately see what AlphaZero “thinks” about it. Have a look at this paper (direct link to the PDF here; HT: David McCarthy), written by three members of the Deep Mind team and Kramnik himself. It starts with a bit of history and a description of the new variants, gets into some statistics, and then fairly quickly - page 17 - gets into a qualitative discussion of the new variants. Some more math follows, and starting on page 25 all the way to the end on page 98, it’s what we all want most: chess and lots of it - the variants, anyway. There’s a lot of fun, beauty, and humor there, so you’ll want to have a look.

One remark, en passant, about the earlier material. On page 16 the authors give AlphaZero’s table of the pieces’ values, starting with normal chess and continuing with the different variants discussed in the paper. I can’t speak to the assessments it makes in the variants, but I’m (extremely) surprised by how highly it rates rooks in classical chess. With the pawn = 1, as usual, it gives 3.05 for the knight (no problem), 3.33 for the bishop (very plausible), 9.5 for the queen (also plausible), and 5.63 for the rook (wait, what?).

There is a bit of throat clearing there, and rightly so:

The piece values in Table 6 should not be taken as a gold standard, as the sample of AlphaZero games that they were estimated on does not fully capture the diversity of human play, and the game lengths do not correspond to that of human games, which tend to be shorter.

I think the last part in particular is crucial: computer vs. computer games often go 100 moves or more, and it’s in endgames where the rooks finally come into their own. As a guide for middlegame play, especially for humans, taking those figures at face value is a recipe for disaster. Experienced players know, for instance, that trading a bishop and a knight for a rook and a pawn (e.g. on f7) is generally terrible unless there’s some further payoff. And no GM would dream that two bishops are only .03 better than a rook and a pawn in any sort of normal position with multiple pawns on the board. So while those numbers may be right for AlphaZero vs. Stockfish or against itself, based in part on a data set with a significant number of 150-250 move games, I would not recommend that we carbon-based players weight the rook as heavily (in general).

This is a very minor point, and not what’s at the heart of the paper. So tolle lege, and enjoy.