MiniMax Search Algorithm in Artificial Intelligence with Solved Example || Game Playing

Introduction

This tutorial guides you through the MiniMax search algorithm, a fundamental concept in artificial intelligence, particularly in game playing. By the end of this tutorial, you will understand how the MiniMax algorithm works and how to implement it with a solved example.

Step 1: Understand the MiniMax Algorithm Fundamentals

The MiniMax algorithm is designed for two-player games, where players take turns to make moves. The goal is to minimize the possible loss for a worst-case scenario.

• Players:
  • Maximizing Player (e.g., Player 1)
  • Minimizing Player (e.g., Player 2)
• Objective:
  • Maximizing Player aims for the highest score.
  • Minimizing Player aims to minimize the score of the Maximizing Player.

Step 2: Structure of the Game Tree

A game can be represented as a tree structure where:

• Each node represents a game state.
• Each edge represents a player's move.
• Leaf nodes represent terminal states with scores.

Key Points:

• Start from the root node, which represents the initial game state.
• Expand each node by adding child nodes for possible moves by the current player.

Step 3: Implementing the MiniMax Algorithm

Algorithm Steps:

1. Evaluate Terminal Nodes:

   • Assign a score to each terminal state.
   • Use a heuristic function if necessary for non-terminal states.

2. Recursive MiniMax Function:

   • If it's the Maximizing Player's turn, choose the child node with the maximum score.
   • If it's the Minimizing Player's turn, choose the child node with the minimum score.

Pseudocode:

function miniMax(node, depth, isMaximizingPlayer):
    if depth == 0 or node is a terminal node:
        return evaluate(node)

    if isMaximizingPlayer:
        bestScore = -∞
        for each child in node.children:
            score = miniMax(child, depth - 1, false)
            bestScore = max(score, bestScore)
        return bestScore
    else:
        bestScore = +∞
        for each child in node.children:
            score = miniMax(child, depth - 1, true)
            bestScore = min(score, bestScore)
        return bestScore

Step 4: Solved Example

Example Setup:

Consider a simple game tree with three levels:

• Level 1: Maximizing Player's turn
• Level 2: Minimizing Player's turn
• Level 3: Terminal states with assigned scores

Example Execution:

1. Start at the root node.
2. Recursively evaluate child nodes.
3. Choose the optimal move based on the MiniMax values calculated.

Example Scores:

• Leaf Node Scores:
  • A: 3
  • B: 5
  • C: 2
  • D: 9
  • E: 0
  • F: -1
  • G: 6
  • H: -3

Result:

• The algorithm identifies the best move for the Maximizing Player based on the calculated scores.

Conclusion

The MiniMax algorithm is a powerful tool for developing AI in game playing scenarios. By understanding its structure, implementing the recursive function, and practicing with examples, you can effectively utilize this algorithm in various applications. Next steps could include exploring alpha-beta pruning to optimize the MiniMax algorithm for larger game trees.