Minimax Algorithm
Description
The Minimax Algorithm is a decision-making algorithm used in two-player games (like Tic-Tac-Toe, Chess, or Checkers). It assumes both players play optimally:
- >
- One player (Max) tries to maximize their score.
- The other player (Min) tries to minimize the opponent’s score.
The algorithm evaluates possible moves by exploring the game tree and choosing the move that leads to the best possible outcome assuming the opponent is also playing optimally.
Examples (Code)
Below is a simple example of AI using python to create a basic decision-making system:
# Minimax algorithm for Tic-Tac-Toe
def minimax(board, depth, is_maximizing):
score = evaluate(board)
if score == 10 or score == -10:
return score
if is_draw(board):
return 0
if is_maximizing:
best = -float('inf')
for move in get_available_moves(board):
make_move(board, move, 'X')
best = max(best, minimax(board, depth + 1, False))
undo_move(board, move)
return best
else:
best = float('inf')
for move in get_available_moves(board):
make_move(board, move, 'O')
best = min(best, minimax(board, depth + 1, True))
undo_move(board, move)
return best
Real-World Applications
Chess Engines
Used to evaluate best moves by exploring future game states up to a certain depth.
Tic-Tac-Toe AI
Minimax can be used to create an unbeatable Tic-Tac-Toe opponent.
Game Bots
Used in various two-player board or video games to simulate intelligent opponents.
AI Education
Serves as a foundational algorithm for teaching AI game theory and adversarial search.
Where the Topic Is Applied
Game | Use of Minimax |
---|---|
Chess | Evaluates best move by simulating opponent's best response |
Tic-Tac-Toe | Simple case for building a perfect AI using full game tree |
Connect Four | Minimax is used to build winning strategies |
Checkers | Game tree search helps avoid traps and make smart moves |
Resources
Additional resources
Interview Questions with Answers
What is the Minimax algorithm?
It is a backtracking algorithm used in decision making and game theory to minimize the possible loss for a worst-case scenario.
In what kind of games is Minimax used?
Minimax is used in two-player, zero-sum games like Tic-Tac-Toe, Chess, Checkers, and Connect Four.
What is the role of 'Max' and 'Min' in the algorithm?
'Max' tries to choose the move that maximizes the outcome, while 'Min' tries to minimize the outcome, assuming both play optimally.
What are the limitations of the Minimax algorithm?
It can be computationally expensive for games with a large search space. Alpha-Beta pruning is often used to optimize it.
What is Alpha-Beta pruning?
It is an optimization technique for the Minimax algorithm that eliminates branches that won't affect the final decision, reducing computation time.