In game theory, perfect play is the behavior or strategy of a player which leads to the best possible outcome for that player, and if there are multiple options with the same outcome perfect play is usually considered the fastest method for getting a good result, or the slowest time for a bad result. Game theory is a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ...

For example, we can say that the game of tic tac toe ends in a tie with perfect play by both sides, because the game is simple enough to analyze completely. Games like nim also admit of a rigorous analysis using combinatorial game theory. Tic-tac-toe, also called noughts and crosses, hugs and kisses, and many other names, is a pen-and-paper game for two players, O and X, who take turns to mark the spaces in a 3×3 grid. ... Nim is a two-player mathematical game of strategy in which players take turns removing objects from distinct heaps. ... Combinatorial game theory (CGT) is a mathematical theory that only studies two-player games which have a position which the players take turns changing in defined ways or moves to achieve a defined winning condition. ...

Perfect play is meaningful only in scenarios with perfect information and no chance, since otherwise it is impossible to determine with certainty what the outcome of a given strategy will be. Perfect information is a term used in economics and game theory to describe a state of complete knowledge about the actions of other players that is instantaneously updated as new information arises. ...

In practice, the optimal strategy might be impossible to determine even when there is perfect information, since there might be too many possibilities for a human or even a computer to exhaustively analyze. For example, this is the case in the opening stages of a game of chess, but not necessarily in the (often much simpler) endgame positions, thousands of which have indeed had perfect play calculated, with the results being included in computer chess programs (see endgame tablebase). Chess is an abstract strategy board game and mental sport for two players. ... In chess, the endgame (or end game or ending) refers to the stage of the game when there are few pieces left on the board. ... 1990s Pressure-sensory Chess Computer with LCD screen The idea of creating a chess-playing machine dates back to the eighteenth century. ... In chess, an endgame tablebase or endgame database is a database of all possible endgame positions with small groups of material. ...

In recent years some games previously thought to be too complex to analyze exhaustively have been "solved" using computers and clever algorithms. A two-player game can be solved on several levels. ...

See also

• Game complexity
• Solved board games