Positions and Games on 2x2


Number of positions

On a 2x2 board, there are 3^4 = 81 possible positions:


An enumeration of all possible positions on 2x2. Illegal positions crossed out

Of these, there are 16 that have 4 stones and are illegal, and another 8 that have three stones and are illegal, which leaves 57 that are legal. The illegal positions have been crossed out.

This gives an overal percentage of 70% for valid positions, on bigger boards this percentage is much lower.

Note: The first row or column gives all the positions for the 1x2 board.

Number of games

John Tromp had calculated the number of possible games on a 2x2 board (under the Tromp-Taylor rules of go) as being 386,356,909,593

Positions and Games on 2x2 last edited by willemien on December 18, 2009 - 09:59
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