1. What is the Min-Max Algorithm?

   • The Min-Max algorithm is a decision-making algorithm used in artificial intelligence, particularly in two-player games.
   • It aims to minimize the possible loss in a worst-case scenario (hence “min”) while maximizing the potential gain (therefore “max”).
   • In a two-player game:
     • The maximizer seeks to maximize their score or utility value.
     • The minimizer aims to minimize the maximizer’s score.
   • The algorithm evaluates all possible moves for both players, predicts the opponent’s responses, and selects the optimal move to achieve the best possible outcome.

2. How Does the Min-Max Algorithm Work?

   • The process involves several key steps:
     • Generate the Game Tree:
       • Create a tree structure representing all possible moves from the current game state.
     • Evaluate Terminal States:
       • Assign utility values (e.g., +1 for Max win, -1 for Min win, 0 for a draw) to the terminal nodes (end game states).
     • Propagate Utility Values Upwards:
       • Starting from the terminal nodes, propagate utility values upward through the tree:
         • If it’s the maximizing player’s turn, select the maximum value from child nodes.
         • If it’s the minimizing player’s turn, select the minimum value from child nodes.
     • Select Optimal Move:
       • At the root of the game tree, the maximizing player chooses the move leading to the highest utility value.

3. Min-Max Formula:

   • The Min-Max value of a node in the game tree is calculated recursively:
     • Maximizing Player’s Turn:

       • text{Max-Value}(node) = max(text{Min-Value}(child_1), text{Min-Value}(child_2), ldots)Max-Value(node)=max(Min-Value(child1​),Min-Value(child2​),…)

     • Minimizing Player’s Turn:

       • text{Min-Value}(node) = min(text{Max-Value}(child_1), text{Max-Value}(child_2), ldots)Min-Value(node)=min(Max-Value(child1​),Max-Value(child2​),…)

The Min-Max algorithm helps AI agents make strategic decisions by considering both maximizing their own gains and minimizing the opponent’s gains in a game.