Consider a computer-refereed game of tic-tac-toe (or any other game which a computer can play perfectly), where if a player fails to convert a winning position, then that player loses.
This allows one player to sort of "gamble" a drawn position by playing a losing move, and if the opponent does not reply with the winning move, then the gambler wins. Whoever makes the first mistake giving away a win loses, as adjudicated by the computer. (An alternative would be last mistake.)
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