# Minimax

[min-uh-maks] /ˈmɪn əˌmæks/

**noun**

1.

a strategy of game theory employed to minimize a player’s possible loss.

/ˈmɪnɪˌmæks/

**noun**

1.

(maths) the lowest of a set of maximum values

2.

(in game theory, etc) the procedure of choosing the strategy that least benefits the most advantaged member of a group Compare maximin

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)

Tagged: m

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