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.