The Min Max & Alpha Beta Prunning

Mohan Kumar / January 2022

759 Words, 5 Minutes

Minimax is a type of adversarial search algorithm for generating and exploring game trees. It is mostly used to solve zero-sum games where one side’s gain is equivalent to other side’s loss, so adding all gains and subtracting all losses end up being zero.

Introduction

In the realm of artificial intelligence and game theory, the Min-Max algorithm and its optimization technique, Alpha-Beta Pruning, play a crucial role in decision-making processes. These techniques are widely used in creating intelligent agents, such as chess-playing AI engines, that are capable of making optimal choices in complex, competitive environments. In this article, we will delve into the concepts of the Min-Max algorithm and Alpha-Beta Pruning, accompanied by practical examples implemented in C++.

Min-Max Algorithm: The Basics

The Min-Max algorithm is a decision-making approach used in two-player games with perfect information, where players alternate turns and have full knowledge of the game’s state. The primary objective of the algorithm is to maximize the gain while minimizing potential loss. In the context of games like chess, one player aims to maximize their advantage (score) while the other tries to minimize it.

Consider a simple example of a tic-tac-toe game. The algorithm recursively evaluates all possible moves and outcomes, assigning scores to each possible game state. It then makes decisions based on these scores, aiming to maximize its own score while minimizing the opponent’s.

Alpha-Beta Pruning: Optimizing Min-Max

While the Min-Max algorithm provides a systematic approach to making decisions, it can be computationally expensive for games with deep decision trees. This is where Alpha-Beta Pruning comes in. Alpha-Beta Pruning is an optimization technique that reduces the number of nodes evaluated in the search tree by eliminating branches that are guaranteed to be irrelevant to the final decision.

The technique maintains two values, α (alpha) and β (beta), which represent the minimum score that the maximizing player is assured of and the maximum score that the minimizing player is assured of, respectively. If the algorithm finds a move that leads to a score worse than α (for the maximizing player) or better than β (for the minimizing player), it can prune the rest of the branch, as it would not influence the final decision.

C++ Examples: Chess AI

Let’s consider a simplified chess AI implementation using the Min-Max algorithm and Alpha-Beta Pruning. In this example, we’ll focus on evaluating possible moves for a chess engine to make informed decisions.

#include <iostream>
#include <vector>
#include <algorithm>

// Evaluation function (returns a simple score)
int evaluateBoard(char board[8][8]) {
    // Implementation of the evaluation logic
    // Return a positive score for an advantageous position and a negative score for disadvantageous positions
}

int minimax(char board[8][8], int depth, bool maximizingPlayer, int alpha, int beta) {
    if (depth == 0) {
        return evaluateBoard(board);
    }

    if (maximizingPlayer) {
        int maxScore = INT_MIN;
        // Generate possible moves and iterate through them
        for (auto move : generateMoves(board)) {
            // Simulate the move
            int score = minimax(newBoard, depth - 1, false, alpha, beta);
            maxScore = std::max(maxScore, score);
            alpha = std::max(alpha, score);
            if (beta <= alpha) {
                break; // Beta cutoff
            }
        }
        return maxScore;
    } else {
        int minScore = INT_MAX;
        // Generate possible moves and iterate through them
        for (auto move : generateMoves(board)) {
            // Simulate the move
            int score = minimax(newBoard, depth - 1, true, alpha, beta);
            minScore = std::min(minScore, score);
            beta = std::min(beta, score);
            if (beta <= alpha) {
                break; // Alpha cutoff
            }
        }
        return minScore;
    }
}

int main() {
    char chessBoard[8][8]; // Representing the chess board
    int depth = 4; // Depth of the search tree
    int bestMoveScore = minimax(chessBoard, depth, true, INT_MIN, INT_MAX);
    std::cout << "Best move score: " << bestMoveScore << std::endl;
    return 0;
}

Conclusion

The Min-Max algorithm and Alpha-Beta Pruning are fundamental techniques in the realm of artificial intelligence, particularly in creating intelligent game-playing agents. These techniques allow for strategic decision-making while optimizing computational resources. By combining these concepts with programming languages like C++, we can create efficient and powerful AI engines capable of playing complex games like chess at a high level.