Sequencing Chess

TL;DR

This paper uses Monte Carlo simulation to analyze the structure of chess's state space, revealing that it consists of pockets with rare transitions and that skilled players explore only a small subset of positions, challenging traditional complexity measures.

Contribution

It introduces a novel topological perspective on chess complexity by analyzing state space pockets and transition rarity, providing new insights beyond traditional size estimates.

Findings

State space has multiple pockets with rare transitions between them.

Skilled players explore a small, sparse subset of positions.

Traditional size measures are insufficient to capture game complexity.

Abstract

We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude that the state space consists of several pockets between which transitions are rare. Skilled players explore an even smaller subset of positions that populate some of these pockets only very sparsely. These results suggest that the usual measures to estimate both, the size of the state space and the size of the tree of legal moves, are not unique indicators of the complexity of the game, but that topological considerations are equally important.