The game of tic-tac-toe as an arena: Opponent starts, Proponent plays X. Occupancy and terminal positions are arena legality, so every strategy is automatically a legal playing policy. Perfect play is minimax; it never loses.
Enabling structure of the arena (each move drawn once). Hover a move for its role. Enabling.
Minimax. Never loses with X.
Trace against auto. (stuck — Ω)
P-view
Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.
Take the centre if free, otherwise the first empty cell.
Trace against auto. (stuck — Ω)
P-view
Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.
Always the first empty cell (row-major).
Trace against auto. (stuck — Ω)
P-view
Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.
The empty strategy Ω: Proponent never moves.
Trace against auto. (stuck — Ω)
P-view
Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.