What is Misère Tic-Tac-Toe?
Misère Tic-Tac-Toe, also called reverse, inverse or avoidance tic-tac-toe and toe-tac-tic, keeps the board and the moves of the standard game and turns the goal around. X moves first, the players take turns marking an empty square, and the player who completes a line of three of their own marks, across, down or diagonally, loses at once. If the board fills without a line, the game is a draw.
You cannot pass, so the game becomes a struggle not to run out of safe squares. Late in the game a player can find that every empty square completes one of their own lines, and then the game is lost whatever they do.
With perfect play the game is a draw, as in the standard game, but the first player has only one safe opening: the centre. A computer search of every position shows that any other first move loses against best play. After taking the centre, X can never lose by answering each of O's moves with the square directly opposite it through the centre, because any line X could complete that way is the mirror image of a line O has already completed.
Rule changes
| Rule | Standard Tic-Tac-Toe | Misère Tic-Tac-Toe |
|---|---|---|
| How to win | Standard Tic-Tac-ToeComplete a line of three of your marks, across, down or diagonally. | Misère Tic-Tac-ToeMake your opponent complete a line of three of their marks. Complete one yourself and you lose at once. |
| Draws | Standard Tic-Tac-ToeA full board without a line is a draw. | Misère Tic-Tac-ToeThe same: a full board without a line is a draw. |
| Perfect play | Standard Tic-Tac-ToeA draw. Every first move keeps the draw. | Misère Tic-Tac-ToeAlso a draw, but only the centre is a safe first move. Any other opening loses. |
| Board and options | Standard Tic-Tac-ToeA 3×3 board. The table setup also offers 4×4 and 5×5 boards, where four in a row wins. | Misère Tic-Tac-ToeAny board size: on 4×4 and 5×5, completing four in a row loses. Misère also combines with Wild and gravity. |
History
Losing versions of games are called misère, from the French word for destitution. In card games such as Boston, whose rules from the late 18th century are the earliest recorded use, a misère bid promises to take no tricks at all. The name later spread to any game played under its normal rules but played to lose, and in combinatorial game theory a misère game is one in which the normal winner loses.
Misère tic-tac-toe has no known inventor. It appears in books and articles on recreational mathematics under several names, including avoidance tic-tac-toe and toe-tac-tic. The centre-and-mirror strategy for the first player is described by Solomon Golomb and Alfred Hales in a 2002 paper on tic-tac-toe.