A position in infinite chess with game value $\omega^4$

TL;DR

This paper constructs a specific position in infinite chess that demonstrates a game value of , significantly advancing the known upper bounds of game complexity in such infinite settings.

Contribution

It introduces a new infinite chess position with a game value of , surpassing previous known values of  and .

Findings

First example of a position with game value  in infinite chess.

Improves the known upper bounds of game complexity in infinite chess.

Demonstrates the potential for even higher game values in infinite combinatorial games.

Abstract

We present a position in infinite chess exhibiting an ordinal game value of $\omega^4$, thereby improving on the previously largest-known values of $\omega^3$ and $\omega^3\cdot 4$.