Table of Contents
Implementing an Unbeatable Tic-Tac-Toe AI with Minimax Algorithm
Overview of the Minimax Algorithm
The Minimax algorithm is a recursive decision-making algorithm primarily used in AI programming for games like Tic-Tac-Toe. It simulates all possible moves in a game, considers each player’s best move, and determines the optimal strategy for the AI, ensuring it cannot lose.
Why Minimax is Ideal for Tic-Tac-Toe
- Perfect Information Game: Tic-Tac-Toe is a game with complete visibility of the state, making it suitable for Minimax, which relies on full game tree exploration.
- Deterministic Gameplay: The game’s deterministic nature ensures that with Minimax, the AI explores all configurations and assures optimal play.
Implementing Minimax in Unity
public int Minimax(char[] board, int depth, bool isMaximizing) { int score = Evaluate(board); if (score == 10) return score; if (score == -10) return score; if (IsMovesLeft(board) == false) return 0; if (isMaximizing) { int best = -1000; for (int i = 0; i < 9; i++) { if (board[i] == '_') { board[i] = 'X'; best = Math.Max(best, Minimax(board, depth + 1, !isMaximizing)); board[i] = '_'; } } return best; } else { int best = 1000; for (int i = 0; i < 9; i++) { if (board[i] == '_') { board[i] = 'O'; best = Math.Min(best, Minimax(board, depth + 1, !isMaximizing)); board[i] = '_'; } } return best; }}Optimizing Minimax with Alpha-Beta Pruning
Alpha-Beta Pruning enhances Minimax by eliminating branches that won’t improve the final decision. It maintains two bounds, alpha and beta, representing the maximum and minimum score that the maximizing and minimizing players can respectively assert.
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- Efficiency Gains: Reduces the time complexity from O(bd) to O(b^(d/2)), where b is the branching factor and d is the depth of the tree.
Conclusion
By implementing Minimax with Alpha-Beta Pruning, you create a performant and unbeatable AI for your Tic-Tac-Toe game in Unity, leveraging optimal decision-making at every turn.