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.

The first player in checkers, can only guarantee themselves a draw under perfect play.[1] Another example of a draw game is tic-tac-toe.

It remains a matter of conjecture as to whether other games such as chess are first-player-wins; see the article first-move advantage in chess for more on this.

See also[edit]


  1. ^ "Checkers Is Solved". Science. 317: 1518–1522. doi:10.1126/science.1144079. Retrieved 2008-11-24.