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. The game of Nim with the classic 3-4-5 starting position is an example of a first player win game.

Some games with relatively small game trees have been proven to be first player wins. 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

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