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Ideal Values and Practical Values (part 3). More on the value of Chess pieces.[All Comments] [Add Comment or Rating]

Michael Nelson wrote on Thu, Jul 17, 2003 08:27 PM UTC:

I would not call the magic number arbitrary--it is empirical, it cannot be
deduced from the theory, but I think the concept has an excellent logical
basis. 

For piece values we want to have sometihing that allows for the fact that
the board is never empty, that takes endgame values into account, but is
weighted towards opening and middlegame values. So let's take a weighted
average of the board emptiness at the opening (32/64) and the board
emptiness at its most extreme in the endgame (62/64).  Let's weight them
in a 3:2 ratio to bias the average toward the opening.  This gives a value
of .6875 --  right in the middle of the range of magic number values that
Ralph uses!  The 'correct' value can only be determined by extensive
testing and it might well be .67 or .70 -- but I am quite certain it is
not .59 or .75!

A way to verify this would be to do some value calculations for a board
with a different piece density that FIDE chess, then see if the calculated
magic number for that game yields relative mobility that make sense (as
verified by playtesting).

Sticking to a 64 square board, imagine a game with 12 pieces per side.
This game has a magic number of .7625 -- I predict that the Bishop will be
worth substantially more than the Knight in this game.

Now a game on 64 squares with 20 pieces per side. This game's magic
number is .6125 -- I predict the Knight is stronger than the Bishop in
this game.