Minimax Algorithm in AI

The Minimax Algorithm in AI is a backtracking algorithm used in decision-making, game theory, and artificial intelligence. It is mainly applied in two-player turn-based games such as Chess, Tic-Tac-Toe, Checkers, and Go. The goal of minimax is to determine the optimal move for a player, assuming that the opponent also plays optimally.

Backtracking Concept

A backtracking algorithm works by building a solution incrementally, step by step. If a candidate step cannot lead to a valid solution, it is abandoned immediately, and the algorithm backtracks to try other possibilities.

How Minimax Works

• There are two players: Max (trying to maximize the score) and Min (trying to minimize Max’s score).
• The algorithm constructs a game tree where each node represents a possible state of the game.
• Minimax evaluates all possible moves, assuming both players play optimally, and chooses the move with the best guaranteed outcome for Max.

Example: Tic-Tac-Toe

Consider the current board (X = Max, O = Min):

           X | O | X
           O | X |  
             |   | O
            

Minimax evaluates all empty positions to determine the best move for Max.

Game Tree Representation

                     Max
                   /  |  \
                 O    O    O
                / \       / \
              X     X   X     X
             / \   / \ / \   / \
            +1  0 0 -1 +1 0 0 -1
            

Explanation of Scores:

• +1 → Max wins
• -1 → Min wins
• 0 → Draw

Max chooses the path with the highest score (+1 if possible), while Min tries to choose paths that minimize Max’s advantage. This ensures Max plays optimally, even against a perfect opponent.