Piece Value - Human vs. Computer

[hgm]

A single game of course means nothing. I always play at least 400 games for any material imbalance. In this case it means less than nothing, because it was not between equally strong players. So of course the stronger player wins. Fischer might well have won if they had swapped colors half-way.

When on top of that the game is selected rather than chosen randomly, it is downright misleading: I could very easily select a GM game where black won, and then claim: "look, this proves it! For those who thought the FIDE opening position was not a zugzwang, this clearly shows black has the advantage!".

[Evert]

We all know that games are won because one player has a good Bishop while the other player has a bad Bishop. Clearly, the good Bishop is worth more than the bad Bishop. Good and bad Bishop have nothing to do with piece value, of course, but just reflect the board position.

It's been said before in this thread: intrinsically, the Bishop is probably a stronger piece than the Knight, but they are close and the Bishop value is depressed by the presence of enemy Knights. Moreover, the evaluation isn't just a sum of piece values, there are other evaluation terms in there and it is well known that some positional features favour a Knight while others favour a Bishop. There are positions where a Knight is superior to a Rook. That does not mean it is worth more in general. All one can conclude from this is that in piece value, Knight and Bishop are very close, practically equal, and it depends on positional features which one is better.

[PK]

concerning knight vs bishop, I have the intuition that the difference of their strength can be related to the probability of exchanging one for the other. The piece that is able to initiate the exchange tends to be stronger.

Take the following scenario from the Sveshnikov Sicilian: a knight on d5 is a monster, but a bit less so if Black has a light squared Bishop. Moreover, what is typical fate of Black's dark squared bishop? It moves from e7 or f6, where it can be hit by a knight, to g5, where it can hit the other knight on e3.

I wonder if a statistical analysis can confirm this way of reasoning. Suppose that we take a set of opening positions in which theory agrees that certain piece is especially good, like g7 bishop in Grunfeld/Benoni or e3/g5 bishop in the Saemisch. Will the notion of the good piece corelate with the ratio of BxN vs NxB in the games starting from the positions in question?

[Evert]

concerning knight vs bishop, I have the intuition that the difference of their strength can be related to the probability of exchanging one for the other. The piece that is able to initiate the exchange tends to be stronger.

Take the following scenario from the Sveshnikov Sicilian: a knight on d5 is a monster, but a bit less so if Black has a light squared Bishop. Moreover, what is typical fate of Black's dark squared bishop? It moves from e7 or f6, where it can be hit by a knight, to g5, where it can hit the other knight on e3.

Sounds reasonable. It's reminiscent of what HGM referred to when he mentioned the cost of a trade-avoid strategy, just worded differently: if the stronger piece (nominally a bishop) cannot avoid being traded for a knight, then in effect it is not worth more than a knight. The same of course applies the other way around. What is then true is that the side that can decide to go for the exchange or not has more options, and is thus better (but that goes beyond simple piece value).