Author: Sune Fischer
Date: 16:58:15 01/03/04
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On January 03, 2004 at 17:33:22, Ed Trice wrote: >OK but consider this: your values show an increase in value for the pieces for >an increase in board size, and presumable a decrease is value for a decrease in >board size. > >I maintain the inverse is true. Depends on how you want to define "increase" in value here, I would not be surprised if their value relative to pawns increased. At the same time the board is bigger so there is more material for each side, which means their relative value in relation to total piece set probably decreases. I really wonder if the pawns lose in value though, if the board is 10x8 it means they still have to travel the same distance to promote. One could certainly make the case that e.g. two outside passers would be harder to stop on a wider board. >If you are correct, then that means the metric you use, the pawn value, would >have to change in direct proportion to the area of the board. My values change >linearly (a function of one dimension since the ratio of areas are divided) and >your values change as a function of some power of 2. Such a scaling would tend >to skew results I would imagine. Maybe their value is proportional to some in between fractal dimension :) >You have 2 Knights = 6.0 and the Rook = 5.0. This means your program will >prefer 2 knights to having a Rook. 2 knights cannot force checkmate, but a Rook >can. > >You have bishop + knight = 6.375, but look how hard it is to mate with bishop >and knight when compare to how easy it is for a rook (both pitted against the >sole enemy king.) > >You have a queen = 8.375 which is exactly equal to your Rook + Bishop. A queen >is not merely the sum of its components pieces, it is worth more than this. Why? >The queen can effect the same strength as the Bishop and Rook, but it needs only >1 square to do this, while the other pieces require 2. Yes, and I think that is an important observation. A piece, IMO, is valued in proportion to its maneuverability on an occupied board, not so much on an empty board, for the simple reason that the board is not empty for most of the game. To say that a rook is worth more than two knights because a rook can mate and two knights cannot isn't right, two knights are worth a lot more on the average. -S.
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