Minimax

adj. of or pertaining to game strategy

Minimax (sometimes minmax) is a method in decision theory for minimizing the maximum possible loss. Alternatively, it can be thought of as maximizing the minimum gain (maximin). It started from two player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves. It has also been extended to more complex games and to general decision making in the presence of uncertainty.
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<games> An algorithm for choosing the next move in a two player game. A player moves so as to maximise the minimum value of his opponent's possible following moves. If it is my turn 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 it positive infinity and, if it is an immediate win for you, negative infinity. The value to me of any other move is the minimum of the values resulting from each of your possible replies.
The above algorithm will give every move a value of positive or negative infinity since the value of every move will be the value of some final winning or losing move. This can be extended if we can supply a heuristic evaluation function which gives values to non-final game states without considering all possible following complete sequences. We can then limit the minimax algorithm to look only a certain number of moves ahead. This number is called the "look-ahead" or "ply".
See also alpha/beta pruning.
[Is "maximin" used? Is it significantly different?]
(2000-12-07)

An algorithm to assign linear scaling coefficients for a set of numbers. The minimum and maximum of the set are found, and scaling factors selected so that these are mapped to desired minimum and maximum values.
See also, Neural Networks.

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