Phutball

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Phutball (also called Philosopher's Football is a board game described in John Conway's "Winning Ways for your Mathematical Plays", a source of many other interesting games.

Phutball is played on a 19 by 15 grid, labeled along the top and bottom by the letters A through P (from left to right from the Ohs player's perspective), and along the right and left side by the numbers (from 1 to 19 from top to bottom from the Eks player's perspective).

The Ohs player tries to move the football to row 19 or row 20 (off the board farthest from the Ohs player). The Eks player at the same time tries to move the football to row 1 or 0 (off the side of the board farthest from the Eks player).

Players alternate making moves. A move is either to add men to the field, or a move is to move the football.

A move that adds men to the field, involves: A man may be added to any position where there isn't a man already. The men added are simply markers, there is no way to tell the difference between men placed by the Eks player or the Ohs player.

A move that moves the football, involves: From the football's initial position, lines of adjacent men are jumped and then removed from the board. The football may jump men diagonally as well as horizontally and as vertically. If the football is moved to the farthest line (your goal line) or past the goal line, the player moving it there is the winner.

Note that in contrast to Checkers, multiple men in a row are jumped as a group.