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Game Theory 7.0/10

Misère Tic-Tac-Toe Openings

Misère tic-tac-toe is played on the usual 3×3 grid by X (moving first) and O, but a player who completes a line of three of their own marks loses. If the grid fills with no such line, the game is a draw. For each of the nine possible opening squares for X, consider the game under optimal play by both sides afterwards. For how many opening squares does X lose? Answer with an integer.

Related problems & prerequisites

Worth solving first

Source: Misère tic-tac-toe ('toe-tac-tic') is a recreational folklore variant; no traceable original source. Statement written for AxiomIQ.