Author: Álvaro Begué
Date: 09:12:16 08/03/04
Go up one level in this thread
On August 03, 2004 at 04:54:11, morphy wrote: >Why the valutation is always referred to the material advantage (where a pawn in >more is the unit) and we can't have a valutation in tems of percentage of >probability for winning and drawing? The right score to use is the expected value of the game result. Maximizing the expected value of a utility function is actually the only possible rational behaviour under a very sensible definition of "rational". We can fix the scores of winning and losing to 1 and 0 (in a utility function, an affine transformation with positive slope doesn't alter the decisions taken by maximization of expected value). The value for drawing is typically 0.5, but this is not always the case. Imagine you are playing a 6-game match and after 5 games you are winning 3-2. In this case, the value of a draw is 1 because it is enough to win the match. If we only consider the case were the value of a draw is 0.5, then the material advantage is a reasonable approach to evaluation. To make a model that predicts a result between 0 and 1, a good robust method is to combine several evaluation factors (in our case things like material imbalance, center control, pawn structure, mobility, king safety, passed pawns...) using a linear combination and then pass the result through a sigmoid transfer function, like S(x):=1/(1+exp(-x)). Applying the function at the end can actually be avoided in real play, because S(x) is a monotonically increasing function, and in alpha-beta search we are only concerned with how a score compares with another score.
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.