Phutball

Phutball, short for Philosopher's Football, is a two-player abstract strategy board game invented by the mathematicians Elwyn Berlekamp, John Horton Conway and Richard K. Guy and published in their book Winning Ways for your Mathematical Plays. It is typically played on a standard 19 by 19 Go board, using a single white stone to represent the ball and a supply of black stones, called men, that either player may place or use to flip the ball across the board in a chain of jumps toward the opposing goal line. The two sides, traditionally named Ohs and Eks, take turns either adding a new man to the board or moving the ball by jumping it over one or more men in a straight line, and a player wins by getting the ball onto or beyond the opponent's goal line. Despite its simple equipment, the game is notable in combinatorial game theory for being provably hard to analyze, and remains a favorite subject of mathematical study precisely because it resists easy strategic generalization.