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- Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for mini mizing the possible loss for a worst case (max imum loss) scenario. When dealing with gains, it is.
Inartificial intelligence, minimax is a decision-making strategy under gametheory, which is used to minimize the losing chances in a game and tomaximize the winning chances. This strategy is also known as ‘Minmax,’ ’MM,’or ‘Saddle point.’ Basically, it is a two-player game strategy where ifone wins, the other loose the game. This strategy simulates those gamesthat we play in our day-to-day life. Like, if two persons are playing chess, theresult will be in favor of one player and will unfavor the other one. Theperson who will make his best try,efforts as well as cleverness, will surelywin.
Wecan easily understand this strategy via game tree– where the nodesrepresent the states of the game and edges represent the moves made by theplayers in the game. Players will be two namely:
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- MIN: Decrease the chances of MAX to win the game.
- MAX: Increases his chances of winning the game.
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Theyboth play the game alternatively, i.e., turn by turn and following the abovestrategy, i.e., if one wins, the other will definitely lose it. Both playerslook at one another as competitors and will try to defeat one-another, givingtheir best.
Inminimax strategy, the result of the game or the utility value is generated by aheuristic function by propagating from the initial node to the rootnode. It follows the backtracking technique and backtracks to find thebest choice. MAX will choose that path which will increase its utility valueand MIN will choose the opposite path which could help it to minimize MAX’sutility value.
MINIMAX Algorithm
MINIMAXalgorithm is a backtracking algorithm where it backtracks to pick the best moveout of several choices. MINIMAX strategy follows the DFS(Depth-firstsearch) concept. Here, we have two players MIN and MAX, and the gameis played alternatively between them, i.e., when MAX made a move, thenthe next turn is of MIN. It means the move made by MAX is fixed and, hecannot change it. The same concept is followed in DFS strategy, i.e., we followthe same path and cannot change in the middle. That’s why in MINIMAX algorithm,instead of BFS, we follow DFS.
- Keep on generating the game tree/ search tree till a limit d.
- Compute the move using a heuristic function.
- Propagate the values from the leaf node till the current position following the minimax strategy.
- Make the best move from the choices.
Forexample, in the above figure, the two players MAX and MIN arethere. MAX starts the game by choosing one path and propagating all thenodes of that path. Now, MAX will backtrack to the initial node andchoose the best path where his utility value will be the maximum. After this,its MIN chance. MIN will also propagate through a path and againwill backtrack, but MIN will choose the path which could minimize MAXwinning chances or the utility value.
So, if the level is minimizing, the node will accept the minimum valuefrom the successor nodes. If the level is maximizing, the node will accept themaximum value from the successor.
Note: The time complexity of MINIMAX algorithm is O(bd) where b is the branching factor and d is the depth of the search tree.