Mathematical Go using Tokens

Abstract

Additional Rules

• The last player to make a legal move is the winner.
• Passing is only allowed if a player has one or more prisoners. Free one of your prisoners to pass.
• As their move, a player may place a token of their colour on any empty intersection they completely surround.
• An intersection cannot contain more than one token, other than that, an intersection containing a token is considered empty.
• A token is captured by a play on the intersection containing the token that also captures stones.
• Captured tokens are treated as prisoners.
• If k points of komi are being used, k (rounded down) prisoners are given to white at the start of the game.
• In an n stone handicap game, white is given n-1 stones as prisoners at the start of the game.
• A token does not change the board state for superko.

Optional Rules

• Recommended A player may not place a stone on an intersection that contains a token of their colour. (This shortens the game and makes the choice of objects to use as tokens easier, since they do not need to co-exist on the same point as a stone.)
• Prisoner amnesty. If both playes have prisoners, reduce both players' prisoners so that the player with the least has no prisoners.
• The board state (for superko) includes all symmetries of the square. This only makes a difference on very small boards (eg 2 x 2 or 1 x 5), but it seems obvious that these symetric operations preserve board state.

Notes