What is minimax?

Minimax is a decision‑making algorithm used in two‑player turn‑based games (like chess or tic‑tac‑toe). It assumes both players play perfectly: one tries to maximize their own score while the other tries to minimize it. The algorithm looks ahead at possible moves, builds a tree of game states, and picks the move that leads to the best worst‑case outcome.

Let's break it down

  • Game tree: Imagine every possible move creates a new branch. The root is the current board, each level alternates between the two players.
  • Leaf nodes: At the far ends of the tree are positions where the game ends (win, lose, draw) or where we stop looking ahead.
  • Evaluation: Each leaf gets a numeric value (e.g., +1 for a win, -1 for a loss, 0 for a draw).
  • Back‑propagation: Starting from the leaves, we move upward. When it’s our turn, we pick the maximum value among child nodes (we want the best). When it’s the opponent’s turn, we pick the minimum value (they will try to hurt us).
  • Root decision: The value that reaches the root tells us which first move gives the best guaranteed result.

Why does it matter?

Minimax gives a clear, mathematically sound way to choose moves when you can’t predict the opponent’s exact actions. It guarantees that, if both players play optimally, you’ll never do worse than the algorithm predicts. This makes it a cornerstone for building AI that can play classic board games and for teaching concepts like game theory and search algorithms.

Where is it used?

  • Classic board games: chess, checkers, tic‑tac‑toe, Connect Four.
  • Video game AI for turn‑based strategy titles.
  • Decision‑making in puzzles and some economic models.
  • Teaching tools in computer science courses to illustrate recursion, tree traversal, and adversarial search.

Good things about it

  • Optimality: Provides the best possible move under the assumption of perfect play.
  • Simplicity: Conceptually easy to understand and implement with recursion.
  • Generality: Works for any two‑player, zero‑sum, turn‑based game.
  • Foundation: Basis for more advanced techniques (alpha‑beta pruning, Monte‑Carlo Tree Search).

Not-so-good things

  • Computationally heavy: The number of possible game states grows exponentially (the “branching factor”), making raw minimax impractical for complex games like chess without enhancements.
  • Assumes perfect play: Real opponents make mistakes; minimax may over‑estimate the difficulty of a position.
  • Memory usage: Storing large game trees can consume a lot of RAM.
  • Limited to deterministic, turn‑based games: Doesn’t handle randomness (dice, cards) or simultaneous moves without modifications.