thumb|A game of phutball after five men have been placed (the ball has yet to move)
Phutball (short for Philosopher's Football) is a two-player abstract strategy board game described in Elwyn Berlekamp, John Horton Conway, and Richard K. Guy's Winning Ways for your Mathematical Plays.
Rules
Phutball is played on the intersections of a 19×15 grid using one white stone and as many black stones as needed. From the starting position, it is not known whether any player has a winning strategy or both players have a drawing strategy, but there exist other configurations from which both players have drawing strategies.
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Given an arbitrary board position, with initially a white stone placed in the center, determining whether the current player has a winning strategy is PSPACE-hard.