Minimax Algorithm - Interactive Lesson

What is Minimax?

Minimax is a decision-making algorithm used in two-player, zero-sum games like chess, checkers, and tic-tac-toe. It works by simulating all possible moves and choosing the one that minimizes the maximum loss (hence "mini-max"). The algorithm assumes both players play optimally.

Interactive Demo

Current Step:

Click "Run Minimax" to start

Key Concepts:

Maximizer: Player trying to maximize score
Minimizer: Player trying to minimize score
Terminal States: End game positions with scores
Backpropagation: Values bubble up from leaves to root

How Minimax Works:

Build the game tree: Represent all possible moves
Evaluate leaf nodes: Assign scores to terminal states
Propagate values upward:
- MAX nodes choose the highest value from children
- MIN nodes choose the lowest value from children
Choose best move: Root picks child with best value

function minimax(node, depth, isMaximizing):
    if node is terminal or depth == 0:
        return evaluate(node)

    if isMaximizing:
        maxEval = -∞
        for each child of node:
            eval = minimax(child, depth-1, false)
            maxEval = max(maxEval, eval)
        return maxEval
    else:
        minEval = +∞
        for each child of node:
            eval = minimax(child, depth-1, true)
            minEval = min(minEval, eval)
        return minEval

Real-World Applications:

♟️ Chess Engines

Evaluating millions of positions to find the best move

🎮 Game AI

Creating challenging opponents in strategy games

🤖 Decision Making

Optimal choices in competitive scenarios

📊 Game Theory