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Phutball

Phutball, also known as Philosopher's Football, is a two-player board game first described by Elwyn Berlekamp, John Conway, and Richard Guy, in their book Winning Ways for your Mathematical Plays. Phutball is played on the intersections of a 19 × 15 grid using one white piece and as many black pieces as necessary. The objective is to score goals by using the men (black pieces) to move the football (white piece) onto or over the opponent's goal line, i.e. either rows 1 or 0 or rows 19 and 20 (rows 0 and 20 being off the board. At the start of the game the football is placed on the central point, although a handicapping scheme exists where the ball can start nearer to the stronger player's goal line. Players alternate making moves, which consist either of adding a man to any vacant point on the board or of moving the ball. There is no difference between men played by the two opponents. The football is moved by a series of jumps over adjacent men. One jump is from the football's current point to the first vacant point in a straight line orthogonally or diagonally over one or more men. The jumped men are then removed from the board (before any subsequent jump occurs). Jumping is optional and the can be repeated for as long as there are men available to be jumped and the player desires. In contrast to checkers, multiple men in a row are jumped and removed as a group. If the football ends the move on or over the opponent's goal line then a goal has been scored. If the football passes through your goal line, but ends up elsewhere due to further jumps, the game continues. The game is sufficiently complex that, although theoretically one of the players has a winning strategy, this strategy is not known.