Editing Solved game (section)

==Perfect play==

In [[game theory]], '''perfect play''' is the behavior or strategy of a player that leads to the best possible outcome for that player regardless of the response by the opponent. Perfect play for a game is known when the game is solved.<ref name="Allis"/> Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw). By [[backward chaining|backward reasoning]], one can recursively evaluate a non-final position as identical to the position that is one move away and best valued for the player whose move it is. Thus a transition between positions can never result in a better evaluation for the moving player, and a perfect move in a position would be a transition between positions that are equally evaluated. As an example, a perfect player in a drawn position would always get a draw or win, never a loss. If there are multiple options with the same outcome, perfect play is sometimes considered the fastest method leading to a good result, or the slowest method leading to a bad result.

Perfect play can be generalized to non-[[perfect information]] games, as the strategy that would guarantee the highest minimal [[expected value|expected outcome]] regardless of the strategy of the opponent. As an example, the perfect strategy for [[rock paper scissors]] would be to randomly choose each of the options with equal (1/3) probability. The disadvantage in this example is that this strategy will never exploit non-optimal strategies of the opponent, so the expected outcome of this strategy versus any strategy will always be equal to the minimal expected outcome.

Although the optimal strategy of a game may not (yet) be known, a game-playing computer might still benefit from solutions of the game from certain [[Chess endgame|endgame]] positions (in the form of [[endgame tablebase]]s), which will allow it to play perfectly after some point in the game. [[Computer chess]] programs are well known for doing this.