Minimax is a recursive algorithm used in two-player games (such as Tic-Tac-Toe, Chess, and Checkers). The name comes from its core philosophy:
- Max: You attempt to maximize your chances of winning.
- Min: Your opponent attempts to minimize your chances of winning.
How it works in practice
The central idea is simple: choose the best move assuming your opponent is also playing at their absolute best. To decide where to move, the machine follows three mental steps:
1. Future Simulation
The machine doesn’t just look at the current board. It simulates: “If I move here, my opponent might move there, and then I’ll move here…”. It does this for every empty cell until the game ends (victory, defeat, or draw).
2. Scoring (Heuristics)
To determine if a move is good, the machine assigns values to the final outcomes:
- Win (+1): The best-case scenario for the machine.
- Loss (-1): The worst-case scenario (human victory).
- Draw (0): A neutral scenario.
3. The Intelligent Choice
The machine assumes you are a smart player.
- On its turn, it chooses the move with the highest score.
- On your turn (simulated), it chooses the move that would be worst for it (the lowest score), because it knows you are trying to win.
In the end, the machine selects the path that leads to the best possible guaranteed result.
A Bit of History: From Math to the Board
The concept of Minimax wasn’t born in computing but in Game Theory. It was originally formulated by John von Neumann in 1928 as part of his fundamental theorem of Game Theory. Von Neumann proved the “Minimax Theorem,” stating that in two-player, zero-sum games with perfect information (where nothing is hidden), there is always a strategy that allows both players to minimize their maximum possible loss. Later, in 1950, Claude Shannon suggested this algorithm as the foundation for chess-playing computers, paving the way for modern AI.
Why do we call this AI?
Many associate AI only with neural networks, but Minimax is a prime example of Deterministic AI. Unlike machine learning, Minimax doesn’t “learn” to play; it “knows” the game perfectly through mathematics. It doesn’t just react; it projects the system’s state into the future and makes a present decision based on a final goal.
- Rational Agent: Acts to achieve the best result (or best expected result).
- Heuristic: Uses logic to evaluate situations without real-time human intervention.
Recursive Simplicity
function minimax(board, depth, isMaximizing) {
// 1. Is the game over? Return the score (+1, -1, or 0)
let winner = getWinner();
if (winner !== null) return scores[winner];
if (isMaximizing) {
let bestScore = -Infinity;
// Simulating machine moves (O) seeking the maximum value
for (let i = 0; i < 9; i++) {
if (board[i] === '') {
board[i] = 'O';
let score = minimax(board, depth + 1, false);
board[i] = '';
bestScore = Math.max(score, bestScore);
}
}
return bestScore;
} else {
let bestScore = Infinity;
// Simulating human moves (X) seeking the minimum value
for (let i = 0; i < 9; i++) {
if (board[i] === '') {
board[i] = 'X';
let score = minimax(board, depth + 1, true);
board[i] = '';
bestScore = Math.min(score, bestScore);
}
}
return bestScore;
}
}
Algorithm Limitations
Pure Minimax has one major drawback: it analyzes every single possibility. While this works perfectly for simple games like Tic-Tac-Toe, the number of possibilities in complex games like Chess grows exponentially (combinatorial explosion).
To solve this, optimizations like Alpha-Beta Pruning were developed, which "cut" branches of the tree that don't need to be analyzed, significantly reducing processing time without losing decision quality.
Conclusion:
The machine never loses. If you play perfectly, the game will always end in a draw.
