Phutball is PSPACE-hard

TL;DR

This paper proves that determining the winner in the game of Phutball from any given position is a PSPACE-hard problem, highlighting its computational complexity.

Contribution

It establishes the PSPACE-hardness of Phutball, a significant complexity result for this combinatorial game.

Findings

Determining the winner in Phutball is PSPACE-hard.

The complexity holds for any arbitrary position.

The result extends understanding of computational difficulty in combinatorial games.

Abstract

We consider the $n\times n$ game of Phutball. It is shown that, given an arbitrary position of stones on the board, it is a PSPACE-hard problem to determine whether the specified player can win the game, regardless of the opponent's choices made during the game.