The Evaluation of Material Imbalances
Every novice soon learns a table of [DH: "average"] material value for the pieces, the most popular being 1-3-3-5-9, but with a bit more experience he learns that this table is not always reliable. There are two reasons for this: one is that an accurate table needs fractions, because it would be quite remarkable if the true values of such different types of pieces were all integer multiples of the pawn. The other reason is that the values of the pieces depend somewhat on what other pieces are on the board.
This latter topic has never been addressed comprehensively in the vast literature on chess, to my knowledge. Perhaps this is because the tools to do so properly have only recently become available. Note that the position of the pieces on the board is in general outside the scope of this article; what I am trying to do here is come up with the best possible evaluation of the material on the board. This is very important in actual play, because even though your evaluation of a position depends on the positioning of the pieces, it will be more correct if you first start with a proper evaluation of the material situation.
POSITION OR MATERIAL
There is one case which can be treated as positional or material, namely the rook's pawn, which differs from other pawns in that it can only capture one way instead of two. Since this handicap cannot be corrected without the opponent's help, I regard the rook's pawn as a different piece type, a crippled pawn. Database statistics indicate that it is on average worth about 15% less than a normal pawn. The difference is enough so that it is usually advantageous to make a capture with a rook's pawn, promoting it to a knights pawn, even if that produces doubled pawns and even if there is no longer a rook on the newly opened rook's file. For the rest of this article, I'll treat all pawns the same.