Minimax Algorithm
Atacan KULLABCI
140144035
Kubilay BEKTAŞ
130144010
Ankara/2017
• The initial state and the legal moves for
each side define the game tree for the game.
• First player (MAX)
• Second player (MIN)
• The number on each leaf node indicates the utility
value of the terminal state from the point of view of
MAX
Example: Strategy Game Solved by Minimax Algorithm
• Let’s assume this strategic game with two players: MAX (black area) and MIN (white area).
• The army can move up, down, right and left.
• The utility function is given as: (points of first move of MAX) - (points of first move of MIN)
Check if MAX player’s armies can move up, down, right and left. If so, find the possible moves.
There are 2 possible moves
Option1
Option2
Check if MIN player’s armies can move up, down, right and left. If so, find the possible moves.
There are 3 possible moves for Option1 and 2 possible moves for Option2
For Option1
Moves1
Moves2
For Option2
Moves1
Moves2
Let’s analyze Minimax algorithm by combining all the possible options(moves)
+4
-10
-10
+4
-4
-10
-10
MAX
MIN
MAX
-6
MIN
-6
-6
-6
-6
0
-6
-6
Minimax Algorithm Analysis
• The minimax algorithm performs a complete depth-first exploration of the
game tree.
• If the maximum depth of the tree is m and there are b legal moves at each
point,
The time complexity of the minimax algorithm is O(b m).
The space complexity is O(bm) for an algorithm that generates all actions at
once, or O(m) for an algorithm that generates actions one at a time.
• For real games, of course, the time cost is totally impractical, but this
algorithm serves as the basis for the mathematical analysis of games and for
more practical algorithms.
References
• https://en.wikipedia.org/wiki/Minimax
• http://www.code2learn.com/2012/01/minimax-algorithmtutorial.html
• http://neverstopbuilding.com
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