minimax

[′min·ə‚maks] (mathematics) The minimum of a set of maxima. In the theory of games, the smallest of a set of maximum possible losses, each representing the most unfavorable outcome of a particular strategy.

Minimax

in mathematics, the value of the expression

of a real function f(x,y) of two variables. The concept of maximin equal to max_y min_xf(x, y) is related to the concept of minimax. In the theory of zero-sum games, the fundamental optimality principle is the minimax principle, which consists in the attempt of a player to minimize his loss, assuming that his opponent’s strategy takes the most unfavorable form.

minimax

(games)An algorithm for choosing the next move in a twoplayer game. A player moves so as to maximise the minimumvalue of his opponent's possible following moves. If it is myturn to move, I give a value to each legal move I might make.If the result of a move is an immediate win for me I give itpositive infinity and, if it is an immediate win for you,negative infinity. The value to me of any other move is theminimum of the values resulting from each of your possiblereplies.

The above algorithm will give every move a value of positiveor negative infinity since the value of every move will be thevalue of some final winning or losing move. This can beextended if we can supply a heuristic evaluation functionwhich gives values to non-final game states withoutconsidering all possible following complete sequences. We canthen limit the minimax algorithm to look only a certain numberof moves ahead. This number is called the "look-ahead" or"ply".

See also alpha/beta pruning.

单词	minimax
释义	minimax min·i·max M0315900 (mĭn′ə-măks′)adj. Of or relating to the strategy in game theory that minimizes the maximum risk for a player. [mini(mum) + max(imum).] minimax (ˈmɪnɪˌmæks) n1. (Mathematics) maths the lowest of a set of maximum values2. (Statistics) (in game theory, etc) the procedure of choosing the strategy that least benefits the most advantaged member of a group. Compare maximin[C20: from mini(mum) + max(imum)] minimax minimax [′min·ə‚maks] (mathematics) The minimum of a set of maxima. In the theory of games, the smallest of a set of maximum possible losses, each representing the most unfavorable outcome of a particular strategy. Minimax in mathematics, the value of the expression of a real function f(x,y) of two variables. The concept of maximin equal to max_y min_xf(x, y) is related to the concept of minimax. In the theory of zero-sum games, the fundamental optimality principle is the minimax principle, which consists in the attempt of a player to minimize his loss, assuming that his opponent’s strategy takes the most unfavorable form. minimax (games)An algorithm for choosing the next move in a twoplayer game. A player moves so as to maximise the minimumvalue of his opponent's possible following moves. If it is myturn to move, I give a value to each legal move I might make.If the result of a move is an immediate win for me I give itpositive infinity and, if it is an immediate win for you,negative infinity. The value to me of any other move is theminimum of the values resulting from each of your possiblereplies. The above algorithm will give every move a value of positiveor negative infinity since the value of every move will be thevalue of some final winning or losing move. This can beextended if we can supply a heuristic evaluation functionwhich gives values to non-final game states withoutconsidering all possible following complete sequences. We canthen limit the minimax algorithm to look only a certain numberof moves ahead. This number is called the "look-ahead" or"ply". See also alpha/beta pruning.
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