The anti-pattern game Håkon Robbestad Gylterud
Here is a small game I though of when taking a course on modal logic. It is a bit too tedious to be played by humans, but I had great fun finding a winning stategy for it – and there are still simple questions about this game I cannot answer.
The rules
The anti-pattern game is a two-player game. It is played using black and white pebbles (like Go). These pebbles are placed in sequence on a line. On their turn the player has a simple choice: to continue the sequence with a white or a black pebble.
A player loses if they put down a pebble such that the sequence contains a pattern. A pattern is a sequence of pebbles repeated three times in a row.
A player wins if the other player loses.
Example
Here is a simlpe game won by player 1:
● ● ○ ○ ● ● ○ ○ ● ● ○ ● ● ○ ● ○ ○ ● ● ○ ○ ● ● ○ ○ ● 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
Player two lost because after their final turn, the sequence ended with the pattern: ● ○ ○ ● repeated trice.
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