Chess Pure Strategies are Probably Chaotic

TL;DR

This paper models chess strategies as a chaotic autonomous system of differential equations, suggesting that the inherent unpredictability explains grandmasters' disagreements and challenges the existence of static evaluation functions.

Contribution

It introduces a novel mathematical framework linking chess strategy to chaos theory, proposing that chess strategies are likely chaotic systems.

Findings

Chess strategy modeled as autonomous differential equations

Conjecture that the system is chaotic

Implication that static evaluators may not exist

Abstract

It is odd that chess grandmasters often disagree in their analysis of positions, sometimes even of simple ones, and that a grandmaster can hold his own against an powerful analytic machine such as Deep Blue. The fact that there must exist pure winning strategies for chess is used to construct a control strategy function. It is then shown that chess strategy is equivalent to an autonomous system of differential equations, and conjectured that the system is chaotic. If true the conjecture would explain the forenamed peculiarities and would also imply that there cannot exist a static evaluator for chess.