Sunday, March 16, 2014

Pawn Advantage in iCE

The Texel tuning method tries to minimize the evaluation error for a set of positions. The error is minimal if the score of a position is a good prediction of the outcome of the game the position is from.

There is a formula in the chess programming wiki that helps to translate the score (usually given in fractions of a pawn) into a winning probability. Plotted as graph it looks similar to the one below.
A score of +1 relates to a winning percentage of 79% and +2 to 93%.


I verified whether this distribution applies to the evaluation of iCE and found out that it does not. I used several sets of a million positions each and calculated the function that fits the winning percentage distribution best. The calculated optimal function coefficients were different depending on the set of test positions but when plotted as graph the all were almost identical.


The blue line is the original graph from above, the three others represent the winning probability by score in iCE for three different sets of positions. 

A +2 score only indicates a 72% winning percentage.


I should take that into account in future tuning excercises.