Perfect play

From Academic Kids

In game theory, perfect play is the behavior or strategy of a player which leads to the best possible outcome for that player.

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.

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.

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.

In recent years some games previously thought to be too complex to analyze exhaustively have been "solved" using computers and clever algorithms.

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