Epistemology of the Chess Advantage

Jun 25, 2011, 9:51 AM |

What does it mean when we speak of an "advantage" in the game of chess? Furthermore, what does it mean when a computer program evaluates a position at, for example, -0.38?

The chess analyst must always look upon computer analysis with suspicion because the computer evaluation of a position is most likely incorrect. The measure of "advantage" that you and I deal with regularly (i.e. centipawns) sits upon a questionable epistemological foundation. In any given position, there are only three “true” evaluations. These are:  1) 0.00 2) infinity 3) - infinity. Stated differently, assuming perfect play, a position must be a draw, a win for White, or a win for Black. Therefore, any evaluation which is not 0.00 or an announced mate in # is by definition wrong.

To illustrate this, take an endgame position with only a Black king, a White king and a White bishop. White cannot be said to have a 300 centipawn advantage. In such a situation, being “up a bishop” is meaningless. Since the computer recognizes such a position to be a draw, it will give us the correct evaluation of 0.00. In other less recognizable but perfectly drawn positions, the computer will insist that one side or another has an advantage of (insert number) of centipawns. The same is often true in positions where a forced win can, after more exhaustive analysis, be demonstrated.

If there was no move horizon beyond which the computer can not see then the computer would be able to see all possible forced results in any position (win, loss, or draw). If there was no move horizon then the only evaluations of any given position would be positive infinity, 0.00, negative infinity. Any evaluation which is not one of these three values is by definition incorrect. It is a product of the chess engine programming which is designed to compensate for imperfect information (i.e. move horizon).

Arithmetic evaluations of chess positions are useful but ultimately fictitious. 

This brings up the notion of ‘arithmeticism’ in chess. Especially with the appearance of chess-playing computers which update a numerical assessment of the position on every half-move, there are players who tend to think in terms of arithmetic advantages, e.g., ‘White is better by 0.33 pawns’. This has its uses, but can lead to a rather artificial view of the game. What happens when both sides make a few moves which are the best ones, and suddenly the 0.33 pawns is down to 0.00, or full equality? The defender of this point of view will say: ‘Well, I didn’t see far enough ahead. If I had, I would have accurately assessed the original position as 0.00. The only problem with this point of view is that chess is a draw, and all kinds of clear advantages (in the sense of having a good probability of winning a position in a practical game) are insufficient to force a win against perfect defense. So most positions would be assessed as 0.00, which is not very helpful. In the extreme, we have the same problem when we claim, for example, that 1.Nf3 is ‘better’ than 1.e4, or 1.d4 is better than 1.c4. These are rather meaningless statements, unless we put them in the context of ‘better against opponent X’ or ‘better from the standpoint of achieving good results with the least study’ or some such. As for the objective claim of superiority, what would be our criterion? I would suggest that only if a given first move consistently performs better than others against all levels of competition might we designate it as ‘better’ in a practical sense. Since all reasonable first moves lead to a draw with perfect play, a claim of ultimate theoretical superiority for one of them cannot be justified.

Watson, John. Secrets of modern chess strategy: advances since Nimzowitsch. Gambit Publications, 1999. 232-33.