Signals: two players, alternating turns, both play optimally, determine winner or optimal score. State design: represent the game position. Include whose turn it is if not inferrable.
Track any parameters that affect valid moves. Transition: current player picks the move that maximizes their outcome. Opponent's outcome becomes your loss (in zero-sum games). Common patterns: interval games (pick from ends), pile games (remove stones), graph games (move pieces). The DP structure adapts to each.