Advances in finding ideal play on poset games

TL;DR

This paper introduces methods to compute nimbers in poset games, enabling the classification of winning and losing positions, and reveals equivalences of strategies across seemingly unrelated posets.

Contribution

It proposes new techniques for calculating nimbers in poset games, advancing understanding of ideal play beyond special cases.

Findings

Methods to calculate nimbers for poset games.

Classification of winning and losing positions.

Equivalence of strategies across different posets.

Abstract

Poset games are a class of combinatorial game that remain unsolved. Soltys and Wilson proved that computing wining strategies is in \textbf{PSPACE} and aside from special cases such as Nim and N-Free games, \textbf{P} time algorithms for finding ideal play are unknown. This paper presents methods calculate the nimber of posets games allowing for the classification of winning or losing positions. The results present an equivalence of ideal strategies on posets that are seemingly unrelated.