AI News, Artificial Intelligence/Search/Adversarial search/Minimax Search

Artificial Intelligence/Search/Adversarial search/Minimax Search

The minimax search is especially known for its usefulness in calculating the best move in two player games where all the information is available, such as chess or tic tac toe (Muller, 2001).

Theoretically, this search algorithm is based on von Neumann’s minimax theorem which states that in these types of games there is always a set of strategies which leads to both players gaining the same value and that seeing as this is the best possible value one can expect to gain, one should employ this set of strategies (Kulenovic, 2008).

Each level of the tree alternates between player 1’s move, who is trying to maximize her score, and player 2’s move, who is trying to minimize player 1's score in order to undermine her success.

If the level above the terminal nodes represents player 2’s possible moves, then the value of the nodes will be the lowest value among those of their children, the minimum.

Moreover, representing all the possible moves for simple games like tic tac toe is not so difficult but with games like chess, it becomes computationally expensive to represent them all.

Another way of cutting down the search space is to only go to a certain depth, treat the moves at that level as makeshift terminal nodes and determine their values using heuristics.

epl341-minimax-algorithm

Minimax is a decision rule algorithm, which is represented as a game-tree. It has applications in decision theory, game theory , statistics and philosophy.

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