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Volume 25
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Article

On the Value of Chess Squares

by
Aditya Gupta
1,*,
Shiva Maharaj
1,
Nicholas Polson
2 and
Vadim Sokolov
3
1
Chess ED, 729 Colby Ct, Gurnee, IL 60031, USA
2
Booth School of Business, University of Chicago, Chicago, IL 60637, USA
3
Department of Systems Engineering and Operations Research, George Mason University, Fairfax, VA 22030, USA
*
Author to whom correspondence should be addressed.
Entropy 2023, 25(10), 1374; https://doi.org/10.3390/e25101374
Submission received: 13 August 2023 / Revised: 18 September 2023 / Accepted: 22 September 2023 / Published: 24 September 2023
(This article belongs to the Special Issue Learning from Games and Contests)
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Abstract

We propose a neural network-based approach to calculate the value of a chess square–piece combination. Our model takes a triplet (color, piece, square) as the input and calculates a value that measures the advantage/disadvantage of having this piece on this square. Our methods build on recent advances in chess AI, and can accurately assess the worth of positions in a game of chess. The conventional approach assigns fixed values to pieces (= ∞, = 9, = 5, = 3, = 3, = 1). We enhance this analysis by introducing marginal valuations. We use deep Q-learning to estimate the parameters of our model. We demonstrate our method by examining the positioning of knights and bishops, and also provide valuable insights into the valuation of pawns. Finally, we conclude by suggesting potential avenues for future research.
Keywords: AI; AlphaZero; Bayes; chess; deep learning; neural network; chess piece values; knights; bishops; pawns AI; AlphaZero; Bayes; chess; deep learning; neural network; chess piece values; knights; bishops; pawns

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MDPI and ACS Style

Gupta, A.; Maharaj, S.; Polson, N.; Sokolov, V. On the Value of Chess Squares. Entropy 2023, 25, 1374. https://doi.org/10.3390/e25101374

AMA Style

Gupta A, Maharaj S, Polson N, Sokolov V. On the Value of Chess Squares. Entropy. 2023; 25(10):1374. https://doi.org/10.3390/e25101374

Chicago/Turabian Style

Gupta, Aditya, Shiva Maharaj, Nicholas Polson, and Vadim Sokolov. 2023. "On the Value of Chess Squares" Entropy 25, no. 10: 1374. https://doi.org/10.3390/e25101374

APA Style

Gupta, A., Maharaj, S., Polson, N., & Sokolov, V. (2023). On the Value of Chess Squares. Entropy, 25(10), 1374. https://doi.org/10.3390/e25101374

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