What is Chess Strength?

You've probably got that one player, always rated 100 or so points higher than you, who you seem to do well against. If not, then you've definitely got players for whom you are that "good customer"; players with significantly lower ratings who are unduly hard for you to beat.

I don't think there is any profound problem here. A rating is just an estimation and a statistical guide. But there is a little ambiguity in the notion of strength. Chess (or any similar game) requires a handful of skills.

Consider this scenario: A 2000 rated player routinely outplays a 1900 rated opponent in the opening, wins material in the middlegame, and yet loses or concedes draws due to poor endgame technique. And yet the 2000 rated player might beat other players the 1900 is unable to beat? So who is stronger? That might be the wrong question. Or the question might be too ambiguous to be answered without the ultimate platitude--"it depends". 

One way to disambiguate the question might be to ask, "do you mean in a tournament or a match setting?" After Lasker lost his title to Capablanca (technically he resigned it and then failed to win it back, but this is whatever) Lasker (to my knowledge) never had any interest in a rematch, but still placed ahead of Capablanca in tournaments, while Capablanca was the World Champion. The prevailing view is that Capablanca played more safely or correctly, taking fewer risks, where Lasker took more risks. His moves were (perhaps) objectively worse, but from the perspective of his opponents, they were harder to deal with.

So who was stronger, Capablanca, or Lasker? Did it simply depend on the format of play? This seems like an odd and implausible answer. It seems better to say that Capablanca understood chess more deeply than not only Lasker, but anyone else, while he was champion. He ought to have understood it more deeply, since had the advantage of being later, giving him the chance to build on the knowledge of previous masters. (Prodigy or not, if he had been born in an earlier time he would not be playing 1.d4.)

There is also an important difference between knowing that something is the case, and knowing how something is the case. Many club players know that a lone King is forcibly checkmated by King, Knight, and Bishop, but cannot actually execute the checkmate. Alternatively, many players are flagged in positions they know exactly how to win, but don't have the speed of movement for. Should it count against your chess strength if you are slow with the mouse? Probably not. 

One practical corollary of all of this is that if there are three players, A, B, and C, and A beats B, and B beats C, it does not follow that A will beat C. The "stronger than" relation is not like the "taller than" relation. If person A is taller than person B, and B is taller than C, then A is going to be taller than C. Chess strength is not like tallness. So when playing someone who beats someone who does well against you, you can play without fear. Although if for some strange reason you are trying to be taller than someone, if that person is taller than another person who is taller than you, you will most likely not succeed and might as well give up there. How can this be? Tallness, is just one property. Chess strength is a collection of properties. Exactly what properties, I am not sure. Perhaps chess strength could be broken down into parts--opening knowledge, positional skill, tactical acumen, mating pattern recognition, defense, and endgame technique. But since chess is a game of complete information, then there is presumably some deeper explanation of the moves than the ones we currently give. Whether or not it consists purely of long variations or of concepts like King safety and pawn structure is perhaps an open question. I assume that the ideal player, who sees every possibility in chess as easily as we see tic-tac-toe variations, would know what the deepest explanation of the moves are. It would make short work of even the strongest engine currently on offer. 

Returning to the question of Capablanca and Lasker, it might be that the ideal player would prefer Capablanca's moves. Lasker's imaginative and double-edged play might, from the perspective of the ideal player, be considered foolish blunders which allow extremely long forced mate sequences.

And yet Lasker would have been unwise not to play as he did. Many articles about him talk about his chess psychology. I think it would have been better simply to talk about a theory of mind--taking into account what your opponent knows and can discover. How deeply can my opponent see, and what positions make it harder for my opponent to see deeply? I am a strong believer in "playing to your audience". It may be that in some inferior positions, all moves are losing, and so a key part of being a strong player is in creating practical chances. What I am saying sounds paradoxical but it isn't: stronger players know when to play weaker moves. 

Bughouse is even more strange with respect to strength, since it is a team game. In addition to taking account the knowledge and vision of one's opponents, one must also take into account the knowledge and vision of one's partner. This is to my mind, the only reason machines do not dominate the game, as they now dominate every other board game. 

Since time is fundamental to bughouse, it is hard to predict how powerful machines would play the game. What would a high level engine match in bughouse look like? My conjecture is that they would not play sharp sacrificial lines. Because for them, the time scramble is not the nerve-wracking mess that it is for humans and there would not be the same chance to make last second swindles. Humans make very poor moves in time scrambles, but machines don't. I would expect them to be extremely positional, fast, and safe. Human bughouse is very physical, since you always need to be up on time or if not, have a very good position to compensate for being down time--and so you need to be physically very fast. But hand or mouse speed is not an issue for a computer. 

How would an ideal player play bughouse? The question is possible in chess, but not in bughouse, unless a minimum time per move is specified. And we would also need to specify that both players on a team are ideal. An ideal player might be paired with a player of 2500 strength and after a few moves find the game resignable. The seeming paradox here is similar to the one above. An ideal player who sees all of the possibilities might be a very bad teammate if he or she plays without having some idea of what their partner knows. A 3000+ and 1500 partnership might lose in a situation where a 2500 and a 1500 partnership would win. Of course, human, non-ideal players have varying degrees of partner awareness. Bughouse requires players to look at more than just moves, and the element of strategy is part of the appeal. 

Playing to get stronger and playing to win more games are very distinct. Here I am talking about both chess and bughouse. Playing openings you are less comfortable with is a good way to get stronger, but a bad way to win games as reliably in the short term. The same can be said for trying to find mate with a few seconds on the clock. as opposed to blitzing out nonsensical moves to flag your opponent and win on time. The other problem I have with questions such as who is stronger?, is not just their ambiguity, but their lack of appreciation of time. (A bad mistake for a bughouse player!) Strength is not the same over time. I think the best way to think of strength is will some Ancient Greek philosophy. Heraclitus wrote obscure fragments, and it is not entirely clear how to interpret them. But he is known for the idea of flux. Everything is changing continuously and nothing really is as much as is becoming. One translation of one of Heraclitus' fragments is as follows. 

Into the same rivers we step and do not step, we are and are not. 

And so the question I prefer to ask about a player's strength is not their current knowledge, skill, or speed, but rather what those things will be in the future. This at least keeps me from going "full tilt" some of the time.