minmax Searching algorithm

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nMinmax algorithm

Minimax is an algorithm used to determine the score in a zero-sum game after a certain number of moves, with best play according to an evaluation function.

The algorithm can be explained like this: In a one-ply search, where only move sequences with length one are examined, the side to move (max player) can simply look at the evaluation after playing all possible moves. The move with the best evaluation is chosen. But for a two-plysearch, when the opponent also moves, things become more complicated. The opponent (min player) also chooses the move that gets the best score. Therefore, the score of each move is now the score of the worst that the opponent can do.

function minimax(node, depth, maximizingPlayer)  if depth = 0 or node is a terminal node
       return the heuristic value of node
 if maximizingPlayer
     bestValue := -∞
     for each child of node
           val := minimax(child, depth - 1, FALSE)
           bestValue := max(bestValue, val)
           return bestValue
 else
         bestValue := +∞
         for each child of node
             val := minimax(child, depth - 1, TRUE)
             bestValue := min(bestValue, val);
       return bestValue
(* Initial call for maximizing player *) minimax(origin, depth, TRUE)