In [[game theory]], a two-player deterministic [[perfect- information]] [[Sequential game|turn-based game]] is a '''first-player-win''' if awith [[optimalSolved game#Perfect play|perfect playerplay]] who playsthe first player to move can always force a win. Similarly, a game is '''second-player-win''' if with perfect play the second player to move can always force a win. With perfect play, if neither side can force a win, the game is a '''draw'''.
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 tree]]s 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 [[English draughts|checkers]], can only guarantee themselves a draw under perfect play.<ref>{{cite journal|url=http://www.sciencemag.org/cgi/content/abstract/1144079 |title=Checkers Is Solved |date= |accessdate=2008-11-24 |doi=10.1126/science.1144079 |volume=317 |journal=Science |pages=1518–1522}}</ref>
Another example of a draw game is [[tic-tac-toe]].
