# The Value of Chess Squares

arXiv: https://arxiv.org/abs/2307.05330 · HTML: https://mlsanity.com/paper/2307.05330/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 42 references that are in the map.
- First posted on arXiv 8 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [The Uncertainty Bellman Equation and Exploration](https://mlsanity.com/paper/1709.05380/) (2017)
- [Chess AI: Competing Paradigms for Machine Intelligence](https://mlsanity.com/paper/2109.11602/) (2021)
- [A Bellman View of Jesse Livermore](https://mlsanity.com/paper/1407.2642/) (2014)
- [Chess2vec: Learning Vector Representations for Chess](https://mlsanity.com/paper/2011.01014/) (2020)
- [Playing Chess with Limited Look Ahead](https://mlsanity.com/paper/2007.02130/) (2020)
- [Karpov's Queen Sacrifices and AI](https://mlsanity.com/paper/2109.08149/) (2021)

## Built on by (most cited first, 2 of 2)

- [The Growth of E-Bike Use: A Machine Learning Approach](https://mlsanity.com/paper/2308.02034/) (2023)
- [PAWN: Piece Value Analysis with Neural Networks](https://mlsanity.com/paper/2604.15585/) (2026)

## Abstract (arXiv)

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 an 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 (symking=∞, symqueen=9, symrook=5, symbishop=3, symknight=3, sympawn=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.