Single Comment

Fwiw, Dutch world chess champ Euwe set Q=R+B+P=10 with R=5.5 and B=3.5.

Indeed, so he used a different scale. Translated to the Q=9 scale this would amount to R=5.05 and B=3.15. Since he did not seem to make a distinction between first and second Bishop, the number he quotes apparently refers to the average of those, which would be 3.25 when we set B=3 and B-pair-bonus=0.5 in the more advanced system. The main difference thus is the value ascribed to the Pawn. Which is a bit meaningless if it doesn't state what is considered the 'reference Pawn', as a 7th-rank passer is easily worth 5 times as much as an unmoved Rook Pawn (say 2.5 vs 0.5).

One should realize, however, that Euwe's values just reflect his personal feelings. And although these must be reasonably good for a world champion, they were not really based on objective criterea like statistical analysis of thousands of games. So they are unlikely to be more accurate than, say, a quarter Pawn.

Chess players have argued whether N is microscopically less than a single B (usually saying yes).

Kaufman found that this depends on the number Pawns that are still present; there was exact equality with 5 Pawns per player; with fewer the Bishop is better, with more the Knight. Of course there is the common lore that it also depends on having Pawns on both wings (which favors the Bishop) vs on a single wing. And there is the 'good Bishop' vs 'bad Bishop' thing as well.

I had a chess master friend that once told me that when Q is vs. 'other material', it was usually critical whether the 'other material' side had 'stickiness', that is that its pieces stuck together and defended each other effectively.

This is very true. A Queen on a sparsely populated board becomes very dangerous, because it can switch the direction of distant attacks quite easily (unlike Chancellor, Archbishop, Griffon, ...) So unprotected pieces get easily forked, and subsequently lost. OTOH, if all pieces can protect each other the Queen can be completely powerless, even unable to defend its own Pawns against and the numerical majority of the lighter pieces.

So we should keep in mind that piece values just reflect the average performance of a piece, and that the actual performance for some imbalances might have a far greater variation than for other imbalances.