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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.



in mathematics, the value of the expression

of a real function f(x,y) of two variables. The concept of maximin equal to maxy minxf(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.


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.

References in periodicals archive ?
Li, "A modified SQP algorithm for minimax problems," Journal of Mathematical Analysis and Applications, vol.
Ahmad: Second order symmetric duality for nonlinear minimax mixed integer programming problems, Eur.
By taking into account the above, we propose a classification model using the minimax and minimin strategies for situations when a part of features are observed and there are precise values of the features corresponding to different classified classes, but our initial information about other parts of features is restricted by mean values of the features for every class.
Both MiniMax finals were punctuated early on by the all course yellow and black quarter flags for pile ups at the bottom hairpin, Dave Wooder quick to pass Lando Norris and pull away in the first final only to be sidelined by an electrical fault.
[12] presented a unifying view of the pathology in the minimax and single-agent searches.
Thus, to overcome the limitations of MV model, alternative risk measures such as Mean Absolute Deviation (MAD), minimax (MM) and lower partial moment (LPM) have been proposed.
The Astec EarthPro Series DD-65 MiniMax horizontal directional drill is small enough to work among obstacles in existing landscapes or in tight work areas such as against walls or buildings.
Continuing the development of its MINIMAX small engine line, Yanmar Industrial Engines said that the 3TNM72 diesel is now available.
The appointments of Rory and Alex is part of a strategic move by the management to grow and develop the services offered by the company, which recently launched MiniMax for smaller machinery users and invested in a new stores unit, with parts immediately available.
The school district spent $2,000 to $2,500 per classroom, including the APWMayville MiniMax cabinets, a Cisco eight-port data switch and wiring.
But Hungarian cablers may prove a more noteworthy buying force at Nip behind such niche cable nets as Minimax (children), HBO Hungary (movies), TV Paprika (food) and Viva (music) to name a few.
It also launched its new MiniMax division in June this year.

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