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arXiv · 2112.09386

An upper bound for the number of chess diagrams without promotion

Daniel Gourion
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Abstract

In 2015, Steinerberger showed that the number of legal chess diagrams without promotion is bounded from above by $2\times 10^{40}$. This number was obtained by restricting both bishops and pawns position and by a precise bound when no chessman has been captured. We improve this estimate and show that the number of legal diagrams is less than $4\times 10^{37}$. To achieve this, we define a graph on the set of diagrams and a notion of class of pawn arrangements, leading to a method for bounding pawn positions with any number of men on the board.

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Daniel Gourion. 2021-12-17. An upper bound for the number of chess diagrams without promotion. https://arxiv.org/abs/2112.09386

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