In game theory, perfect play is the behavior or strategy of a player which leads to the best possible outcome for that player regardless of the response by the opponent. Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw). By backward reasoning, one can recursively evaluate a non-final position as identical to that of 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 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 endgame positions (in the form of endgame tablebases), which will allow it to play perfectly after some point in the game. Computer chess programs are well known for doing this.
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Famous quotes containing the words perfect and/or play:
“There was an artist in the city of Kouroo who was disposed to strive after perfection. One day it came into his mind to make a staff. Having considered that in an imperfect work time is an ingredient, but into a perfect work time does not enter, he said to himself, It shall be perfect in all respects, though I should do nothing else in my life.”
—Henry David Thoreau (18171862)
“The playing adult steps sideward into another reality; the playing child advances forward to new stages of mastery....Childs play is the infantile form of the human ability to deal with experience by creating model situations and to master reality by experiment and planning.”
—Erik H. Erikson (20th century)