Minimax

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Minimax

• COT 4810
• Lorn Miller

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Minimax

• What is it?
• Game play algorithm
• How do you use it?
• Search a game state tree
• How efficient is it?
• Well see!

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Minimax

• What is it?
• Game play algorithm
• Used to select the next move
• Useful in avoiding traps
• Ex Chess

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Minimax

• How do you use it?
• Create a game state tree
• Assign state values to every leaf
• Use a heuristic
• Use the Minimax algorithm to select next move

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Minimax
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Minimax

• The Minimax Algorithm
• Indirect recursion
• Max function and Min function
• Max
• If values are known, pick the largest
• Otherwise ask min what the values should be for
  each option
• Min
• If values are known, pick the smallest
• Otherwise ask max what the values should be
• Call one of the functions on the root of the tree

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Minimax
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Minimax
8
102
1
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Minimax
102
8
102
1
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Minimax

• How Efficient is it?
• Depends on size of search tree
• Imagine Tic-Tac-Toe

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Minimax

• 9 Possible Initial moves
• 8 possible second moves
• 7 possible third moves
• 9! Possible states
• (9!362880)

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Minimax

• 9! States
• 1 bit to show if square is occupied
• 1 bit to show who occupies square
• 9 squares
• 18 bits per state to describe board

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Minimax

• 9! States
• 18 bits to define state
• Integer to hold heuristic value (4 bytes)
• 32 bits to hold heuristic for state

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Minimax

• 9! States
• 183250 bits per state
• 9! 50 18144000 bits
• 18144000 bits 2268000 bytes
• 2268000 bytes 2214.84375 KB
• 2214.84375 KB 2.162933349609375 MB

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Minimax

• More than 2.16 MB of search space for Tic Tac Toe!

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Minimax

• What to do?
• Searching larger state makes searching slower
• Only generate a few levels
• Modify Minimax to run faster

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Minimax

• Modification of Minimax Alpha and Beta Pruning
• Prevents processing unnecessary states
• Effectively shrinks search space

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Minimax
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Minimax
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Minimax
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102
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Minimax
102
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1
102
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Minimax
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Minimax
412
87
102
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Minimax
87
412
87
102
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Minimax

• Questions?