Zermelo's Theorem

Zermelo's Theorem states that in any finite, turn-based game with perfect information—meaning both players know everything about the game state—there exists a strategy for the player who moves first to guarantee at least a tie, and if a winning strategy exists, they can always achieve a win. This implies that such games are determined; one can analyze all possible moves to find the optimal strategy. The theorem underpins strategic thinking in games like chess or checkers, confirming that optimal play can be theoretically identified and guarantees outcomes given perfect play.