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## Minimax Search

### Minimax Search Algorithm

The standard algorithm for two-player perfect-information games such as chess, checkers or othello is minimax search with heuristic static evaluation. The minimax search algorithm searches forward to a fixed depth in the game tree, limited by the amount of time available per move. At this search horizon, a heuristic function is applied to the frontier nodes. In this case, a heuristic evaluation is a function that takes a board position and returns a number that indicates how favourable that position is for one player relative to the other. For example, a very simple heuristic evaluator for chess would count the total number of pieces on the board for one player, appropriately weighted by their relative strength, and subtract the weighted sum of the opponent’s places. Thus, large positive values would correspond to strange positions for one player called MAX, whereas large negative values would represent advantageous situation for the opponent called MIN.

Given the heuristic evaluations of the frontier nodes, minimax search algorithm recursively computes the values for the interior nodes in the tree according to the maximum rule. The value of a node where it is MAX’s turn to move is the maximum of the values of its children, while the value of the node where MIN is to move is the minimum of the values of its children. Thus at alternative levels of the tree, the maximum values of the children are backed up. This continues until the values of the immediate children of the current position are computed at which point one move to the child with the maximum or minimum value is made depending on whose turn it is to move.