minimax search procedure.pptx

# minimax search procedure.pptx - MINIMAX SEARCH PROCEDURE...

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MINIMAX SEARCH PROCEDURE

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TOPICS Minimax Tree Creation of Minimax Tree And-Or Graph Examples Algorithm for minimax search procedure Limitations of minimax procedure
Minimax Search Procedure 1. The minimax search procedure is a depth-first, depth limited search procedure. 2. The idea is to start at the current position and use the plausible-move generator to generate the set of possible successor positions. 3. By applying static evaluation functions to those positions we can choose the best one. 4. After that, we can back that value up to the starting position to represent our evaluation of it. 5. The starting position is exactly as good as the position generated by the best move we can make next. 6. Here we assume that the static evaluation function returns large values to indicate good situations for us, so our goal is to maximize the value of the static evaluation function of the next board position.

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The game begins from a specified initial state and ends in position that can be declared win for one, loss for other or possibly a draw . Game tree is an explicit representation of all possible plays of the game. The root node is an initial position of the game. Its successors are the positions that the first player can reach in one move, and Their successors are the positions resulting from the second player's replies and so on. Terminal or leaf nodes are represented by WIN, LOSS or DRAW. Each path from the root to a terminal node represents a different complete play of the game.
A B C D 8 3 -2 One ply Search

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An example of this operation is shown in above figure. It assumes a static evaluation function that returns values ranging from -10 to 10, with 10 indicating a win for us, -10 a win for the opponent, and 0 an even match. Since our goal is to maximize the value of the heuristic function, we choose to move to B. Backing B’s value up to A, we can conclude that A’s value is 8, since we know we can move to a position with a value of 8. But since we know that the static evaluation function is not completely accurate, we would like to carry the search farther ahead than one ply. This could be very important, for example, in a chess game in which we are in the middle of a piece exchange. After our move, the situation would appear to be very good, but, if we look one move ahead, we will see that one of our pieces also gets captured and so the situation is not as favorable as it seemed. So we would like to look ahead to see what will happen to each of the new game positions at the next move which will be made by the opponent. Instead of applying the static evaluation function to each of the positions that we just generated, we apply the plausible-move generator, generating a set of successor positions for each position. If we wanted to stop here, at two ply look ahead, we could apply the static evaluation function to each of these positions, as shown in below figure.
E J A B D C G F H I K 9 0 -8 -2 8 -4 -3 Two Ply Search

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• Spring '19
• Dr. Anjali Mathur
• Minimax, L. Manevitz

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