Mini-Max Algorithm in Artificial Intelligence.pptx

Mini-Max Algorithm in Artificial Intelligence.pptx

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  1 TriaRight: The New Eraof Learning Welcome To PACK 365
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  2 Module 03
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  3 Mini-Max Algorithm in ArtificialIntelligence
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  4 Mini-Max Algorithm inArtificial Intelligence Mini-Max algorithm is a decision-making algorithm used in artificial intelligence, particularly in game theory and computer games. It is designed to minimize the possible loss in a worst-case scenario(hence "min") and maximize the potential gain (therefore "max").
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  5 Minimax Algorithm –An Introduction  Minimax Algorithm is used in Artificial Intelligence in computer games  It's at the heart of almost every computer board game  Minimax chooses the path which maximizes the gain of the current player, while minimizing the gain of the adversary  A search tree is generated, depth-first, starting with the current game position up to the end game position.  Can work in real time(i.e.- not turn based) with timer (iterative deepening, later)
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  6 Where is thealgorithm used ?  Applies to games where: • Players take turns • Have perfect information • Chess, Checkers, Tactics  Most widely used in logic games. These games are also called as zero sum games i.e. a game in which gain of player’s move is exactly balanced by loss incurred by opponent’s move  Used in economic situations  Used in social situations
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  7 Minimax Algorithm-Components  Searchtree : • Squares represent decision states (i.e.- after a move) • Branches are decisions (i.e.- the move) • Start at root • Nodes at end are leaf nodes  Unlike binary trees can have any number of children • Depends on the game situation  Levels usually called plies (a ply is one level) • Each ply is where "turn" switches to other player  Players called Min and Max
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  8 Minimax Algorithm-Description(1)  Assignpoints to the outcome of a game • Ex: Tic-Tac-Toe: X wins, value of 1. O wins, value -1.  Max (X) tries to maximize point value, while Min (O) tries to minimize point value  Assume both players play to best of their ability • Always make a move to minimize or maximize points  So, in choosing, Max will choose best move to get highest points, assuming Min will choose best move to get lowest points
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  9 Maximizing Player (Max): •Aims to maximize their score or utility value. • Chooses the move that leads to the highest possible utility value, assuming the opponent will play optimally. Minimizing Player (Min): • Aims to minimize the maximizer's score or utility value. • Selects the move that results in the lowest possible utility value for the maximizer, assuming the opponent will play optimally.
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  10 How is Minimaxtree generated ? Step 1:Creation of a MAX node Step 2:Generation of children nodes (MIN) using DFS A1 Step 3:Node A1 is generated. Step 4:Children of a A1 are generated Step 5:Node evaluation takes place using evaluation function. Values are filled in nodes Step 6:Now A1 chooses the minimum of the (two) child node values Step 7:Repeat steps 3 to 6 till all children of main nodes (A1,A2,A3) are generated and filled Step 8:The Main mode chooses the max value of the child node values and this tells us the best possible move that we should take A2 A3 7 3 15 1 12 20 3 15 1 15 MIN MAX
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  11 Properties Of MinimaxAlgorithm • Complete? • Yes (if tree is finite) • Optimal? • Yes (against an optimal opponent). • Can it be beaten by an opponent playing sub-optimally? • No • Time complexity? • O(bm ) ,where m is depth and b is branching factor • Space complexity? • O(bm) (depth-first search, generate all actions at once) • O(m) (backtracking search, generate actions one at a time)
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  13 Steps involved inthe Mini-Max Algorithm • The Min-Max algorithm involves several key steps, executed recursively until the optimal move is determined. Here is a step-by-step breakdown:  Step 1: Generate the Game Tree • Objective: Create a tree structure representing all possible moves from the current game state. • Details: Each node represents a game state, and each edge represents a possible move.  Step 2: Evaluate Terminal States • Objective: Assign utility values to the terminal nodes of the game tree. • Details: These values represent the outcome of the game (win, lose, or draw).
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  14  Step 3:Propagate Utility Values Upwards • Objective: Starting from the terminal nodes, propagate the utility values upwards through the tree. • Details: For each non-terminal node: • If it's the maximizing player's turn, select the maximum value from the child nodes. • If it's the minimizing player's turn, select the minimum value from the child nodes.  Step 4: Select Optimal Move • Objective: At the root of the game tree, the maximizing player selects the move that leads to the highest utility value.
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  15 9 18 10 7 1230 max min Normal Minimax ( CPU with max move) 9 7 12 12 Perfect move calculated every time Human error not taken into account No randomness *Numbers illustrate evaluation score of the game board i.e. game state
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  16 9 18 10 7 1230 10 7 12 10 Random Minimax ( CPU with random move) Case 1: Θ->infinity optimal minimax strategy (previous example) Case 2: Θ->0 random strategy (current example) CPU move Wrong move !! Correct move !! Note that CPU does not play optimal move because of Rminimax *Numbers illustrate evaluation score of the game board i.e. game state
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  17 THANK YOU