First-player and second-player win

In game theory, a two-player turn-based game is a first-player-win if a perfect player can always force a win.

Some games with relatively small game trees have been proven to be first player wins. For example, the game of Nim with the classic 3–4–5 starting position is an example of a first-player-win game. 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. The first player in Checkers, however, can only guarantee themselves a draw under perfect play.

See also

• Strategy-stealing argument
• Second player win
• Forced draw
• Zugzwang
• Determinacy
• Combinatorial game theory