First-player and second-player win
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In game theory, a two-player deterministic perfect-information turn-based game is first-player-win if a perfect player who plays first can always force a win. Similarly, a game is second-player-win if a perfect player who plays second can always force a win. When winning is not possible with perfect play by both opposing sides, the game is a draw.
Some games with relatively small game trees have been proven to be first or second player wins. For example, the game of nim with the classic 3–4–5 starting position is a first-player-win game. However, Nim with the 1-3-5-7 starting position is a second-player-win game. The classic game of Connect Four has been mathematically proven to be first-player-win.
- Strategy-stealing argument
- Forced draw
- Combinatorial game theory
- First-mover advantage
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