A "study" by Sune Fischer and Pradu Kannan in Dec. 2007 suggested approximate relations between win percentage, pawn advantage, and Elo rating advantage for computer chess. It was found that the the approximate relationship between the winning probability W and the pawn advantage P is

The inverse relationship can be given as

From the above, the relationship between the equivalent Elo rating advantage R and the pawn advantage P can be given as

Data Acquisition

Data was taken from a collection of 405,460 computer games in PGN format. Whenever exactly 5 plys in a game had gone by without captures, the game result was accumulated twice in a table indexed by the material configuration. The data was accumulated twice because it was assumed that material values were equal for both colors. So if there was data for a KPK material configuration, the data was also tallied for the KKP. Only data pertaining to the material configuration was taken. This was considered reasonable because the material configuration is the most important quantity that affects the result of a game.

Data Reduction and Modeling

For each material configuration, a pawn value was computed using conventional pawn-normalized material ratios that are close to those used in strong chess programs (P=1, N=4, B=4.1, R=6, Q=12). The relationship between Win Percentage and Pawn Advantage was assumed to follow a logistic model^{[1]}, namely,

where K is an unknown non-zero constant. When applying the condition that the win probability is 0.5 if there is no pawn advantage, the solution to the above seperable differential equation becomes

For K=4, the proposed logistic model and the data is plotted here for comparison:

Home * Evaluation * Pawn Advantage, Win Percentage and Elo## Table of Contents

A "study" by Sune Fischer and Pradu Kannan in Dec. 2007 suggested approximate relations between win percentage, pawn advantage, and Elo rating advantage for computer chess. It was found that the the approximate relationship between the winning probability W and the pawn advantage P is

The inverse relationship can be given as

From the above, the relationship between the equivalent Elo rating advantage R and the pawn advantage P can be given as

## Data Acquisition

Data was taken from a collection of 405,460 computer games in PGN format. Whenever exactly 5 plys in a game had gone by without captures, the game result was accumulated twice in a table indexed by the material configuration. The data was accumulated twice because it was assumed that material values were equal for both colors. So if there was data for a KPK material configuration, the data was also tallied for the KKP. Only data pertaining to the material configuration was taken. This was considered reasonable because the material configuration is the most important quantity that affects the result of a game.## Data Reduction and Modeling

For each material configuration, a pawn value was computed using conventional pawn-normalized material ratios that are close to those used in strong chess programs (P=1, N=4, B=4.1, R=6, Q=12). The relationship between Win Percentage and Pawn Advantage was assumed to follow a logistic model^{[1]}, namely,where K is an unknown non-zero constant. When applying the condition that the win probability is 0.5 if there is no pawn advantage, the solution to the above seperable differential equation becomes

For K=4, the proposed logistic model and the data is plotted here for comparison:

## See also

## Publications

2007).Visualization and Adjustment of Evaluation Functions Based on Evaluation Values and Win Probability. AAAI 2007, pdf2014).Human and Computer Preferences at Chess. pdf2015).Measuring Level-K Reasoning, Satisficing, and Human Error in Game-Play Data. IEEE ICMLA 2015, pdf preprint2015).Estimating Ratings of Computer Players by the Evaluation Scores and Principal Variations in Shogi. ACIT-CSI## Forum Posts

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