What Is Minimax AI?

Minimax is a fundamental decision-making algorithm in artificial intelligence, particularly used in game theory and two-player zero-sum games. This article provides an in-depth look at the Minimax algorithm, its applications, and its significance in AI.

What is Minimax?

Minimax is an algorithmic approach designed to minimize the possible loss for a worst-case scenario. In the context of two-player games, it assumes that one player aims to maximize their score (the “maximizing” player), while the other aims to minimize it (the “minimizing” player).

How Minimax Works

1. Game Tree Construction: The algorithm builds a game tree representing all possible moves and their outcomes.
2. Recursive Evaluation: It recursively evaluates each node in the tree, assigning scores based on the game state.
3. Backtracking: The algorithm works backwards from the end states, alternating between choosing the maximum and minimum scores.
4. Decision Making: The initial player chooses the move that leads to the highest score, assuming optimal play by both sides.

Pseudocode

python

def minimax(node, depth, maximizingPlayer):

    if depth == 0 or node is terminal:

        return static evaluation of node

    if maximizingPlayer:

        value = -∞

        for child in node.children:

            value = max(value, minimax(child, depth – 1, False))

        return value

    else:

        value = +∞

        for child in node.children:

            value = min(value, minimax(child, depth – 1, True))

        return value

Applications

1. Chess Engines: Many chess AI systems, including IBM’s Deep Blue, use Minimax as a core algorithm.
2. Game AI: It’s used in various two-player games like tic-tac-toe, checkers, and Connect Four.
3. Decision Theory: Minimax principles are applied in economics and decision-making under uncertainty.

Limitations and Enhancements

• Computational Complexity: The algorithm’s efficiency decreases with game complexity.
• Alpha-Beta Pruning: An enhancement that reduces the number of nodes evaluated in the search tree.
• Depth Limitation: Practical implementations often limit the search depth to manage computational resources.

Conclusion

Minimax remains a cornerstone algorithm in game AI and decision theory. While more advanced techniques have been developed, understanding Minimax is crucial for anyone interested in game theory or AI decision-making processes.