Philosopher's Football

From MathClub

Philosopher's Football

This game, an invention of our own Professor Conway, is a common pastime in the Fine Hall Common Room. Professor Conway himself is usually up for a game, and he'll give a generous handicap to beginners so that the game isn't too short.

How to Play

The game is played on a standard 19x19 Go board (or on a 19x15 modified Go board, although this doesn't matter very much, and 19x19 is more convenient). Necessary pieces are a single white stone and many black stones. The white stone is the "ball" and the black stones are the "men."

At the start of the game, the ball is at the center of the board, and the board is otherwise empty. If one player is significantly better than the other, the stronger player can give a handicap by allowing the ball to start one or more ranks closer to his own goal. The first move is also an advantage.

On a player's turn, there are two options.

• One move is to add a man to the board. A man may be added to any empty space. Once a man is on the board, he may be used by either player.
• The other move is a sequence of jumps. In a jump, the player may move the ball in a straight line over a man or a sequence of adjacent men. The ball must land in the first available space. The player may make as many legal jumps as he wants in a row, but the ball cannot change direction mid-jump, only between jumps. After the ball jumps over a man (or men), those men are immediately removed and cannot be jumped over again, even in the same turn.

A player wins when he moves his ball to the farthest rank from him on the board, or jumps beyond it. After a player places a man, he should announce "Shot!" if (assuming the opponent doesn't stop him) he will win on his next move.

More detailed rules are available on Wikipedia or from an experienced player (to be found in the math common room).

The League

The Math Club will maintain player rankings on this website. This is an informal Phutball league, and rated games need not be supervised. To report a game, email nsavir@ with the names of both players and the result.

The rating system will be similar to the USCF rating system, but much simpler. Suppose the two players have ratings M and N, and player M wins. Suppose further that player M has played k games and N has played j games. Then the rating changes will be:

New players will be assigned a rating of 1000. The factor at the end is the provisional rating factor: the more games one plays, the less this matters. Scores will be rounded to the nearest integer after each game.