An upper bound for the number of chess diagrams without promotion

Daniel Gourion (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

The number of legal chess diagrams without promotion is bounded from above by $2 \times 10^{40}$. This number is 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 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 structure, leading to a method for bounding pawn positions with any number of men on the board.

Domaines: Combinatoire [math.CO]; Informatique et théorie des jeux [cs.GT]; Théorie de l'information et codage [math.IT]

Daniel Gourion. An upper bound for the number of chess diagrams without promotion. 2021. ⟨hal-03483904v1⟩