Chess God's number grows exponentially

TL;DR

This paper demonstrates that the minimum number of moves required to transition between certain chess positions grows exponentially with the size of the board, revealing complex growth in chess move sequences.

Contribution

It provides an example of two large chess positions connected by a legal move sequence whose length grows exponentially with the board size, highlighting exponential complexity in chess.

Findings

Exponential growth in move sequence length for certain chess positions

Existence of pairs of positions requiring exponentially many moves to connect

Implications for complexity analysis of chess

Abstract

We give an example of two $n\times n$ chess positions, $A$ and $B$, such that (1) there is a sequence $\sigma$ of legal chess moves leading from $A$ to $B$; (2) the length of $\sigma$ cannot be less than $\exp \Theta(n)$.