Mini-Max Algorithm in Artificial Intelligence.pptx
- 1. 1 TriaRight: The New Era of Learning Welcome To PACK 365
- 2. 2 Module 03
- 3. 3 Mini-Max Algorithm in Artificial Intelligence
- 4. 4 Mini-Max Algorithm in Artificial 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").
- 5. 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)
- 6. 6 Where is the algorithm 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
- 7. 7 Minimax Algorithm-Components Search tree : • 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
- 8. 8 Minimax Algorithm-Description(1) Assign points 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
- 9. 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.
- 10. 10 How is Minimax tree 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
- 11. 11 Properties Of Minimax Algorithm • 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. 13 Steps involved in the 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).
- 14. 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.
- 15. 15 9 18 10 7 12 30 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
- 16. 16 9 18 10 7 12 30 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
- 17. 17 THANK YOU