Values of pieces
In a comment King of the Spill posted this link to a very important article by IM Larry Kaufman on the values of pieces and material imbalances.
The relative values of bishops and knights are also addressed. Based on evaluation of hundreds of thousands of games the stats shows that bishops and knights are equal, as long as there is no bishop pair. With six and more pawns on both sides the knight has a small edge, with five pawns they are equal, and with less than five pawns the bishop becomes better, but only by 1/8 of a pawn unit.
The question of good and bad bishops is addressed, but not quantified. It is clear, however, that a knight is always better than a bad bishop, and I would guess that a very bad bishop is worth no more than 2 pawns at most.
Kaufman calculated the following average values of pieces and material imbalances:
- P = 1
- B pair = +0.5
- N = 3.25
- B = 3.25
- R = 5
- Q = 9.75