Impossible by Definition
How silly it is to think that there might be such a thing as an absolute value for a chess piece! The very idea is absurd!Here are a couple of reasons:
How well we know that positional and tactical considerations can override vast disparities in material! How thoroughly we have all learned the lesson that one piece in the right place is worth an army in the wrong place! Did you never stop to think that this can also be true in the opening position of the game?
A long, long time ago, I tried to find out how strong the King was (or would be if it didn't have to worry about check). I took off my Knights, put in some non-royal Kings, and played a game against myself. It was horrible; the kings were guillotined.
Then I tried again, but this time I replaced my Bishops with non-royal Kings. It was a fairly even game! Why so different?
Simply put, the short-range King, starting the game on f1 and c1, had no trouble developing to e2 and d2, and then gradually moving forwards to get into the game; but with the Kings on g1 and b1, either one had to spend extra moves or one had to create weaknesses in the Pawn structure in order to get the Kings out of the way.
Therefore, even if a piece does have an absolute value, that value is never its real value; the real value is always affected by its position on the board.
Even if we could calculate the correct value of a piece in isolation, the interaction of each piece with the other pieces on the board affects its relative value.
New May 9 1996: See The Levelling Effect
For example, if the opponent has Rooks, Bishops, and Queens, the weakest pieces on the board get a bonus simply for occupying squares and getting in the enemy's way; the Knight in the standard game benefits from being able to attack any other piece without being counterattacked; and in a sense the Knight is stronger than the Queen because when the N attacks the Q, the Q must move, but not vice-versa!
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