Ultimate Tic Tac Toe with Minimax

Ministry of Truth Programming
4 Jun 202312:58

TLDRIn this video, Winston teaches how to implement the minimax algorithm in Ultimate Tic Tac Toe, a game with a 3x3 global board consisting of nine 3x3 local boards. The first move dictates the local board for the opponent. The game ends when a player gets three in a row on any local board or when all squares are filled with no winner. Winston explains the minimax function, considering depth due to computational limits, and an evaluation function that assigns scores to board positions to determine the best move, aiming to maximize the chances of winning.

Takeaways

  • 🎮 Ultimate Tic Tac Toe is played on a global board with nine smaller local boards, each with a 3x3 grid.
  • 🔄 The first move determines which local board the opponent must play on, creating a strategic layer to the game.
  • 🚫 If a local board is fully occupied or won by a player, the next player can choose any available local board.
  • 🏁 The game ends when a player gets three in a row on a local board, or when all squares are filled with no winner.
  • 💡 The minimax algorithm is implemented to make the AI's moves, considering both offensive and defensive strategies.
  • 📊 The minimax function uses a depth parameter to limit the search to a manageable number of moves ahead, preventing resource exhaustion.
  • 📈 The scoring system evaluates the board state, with different weights for center, corner, and edge squares, influencing AI decision-making.
  • 🔢 Scores are adjusted based on board positions and potential wins, with significant points for winning a local board or the game.
  • 💻 The AI's depth of lookahead varies by device, with mobiles set to a maximum of four moves ahead and PCs up to six.
  • 🔍 The minimax algorithm explores possible moves and countermoves, with the aim of maximizing the score for the current player.
  • 🏆 Despite the AI's capabilities, there's still a chance for human players to win by thinking several moves ahead of the AI.

Q & A

  • What is the game 'Ultimate Tic Tac Toe'?

    -Ultimate Tic Tac Toe is a variation of the classic Tic Tac Toe game, featuring a global board with nine smaller local boards. Players make moves on the local boards, and the choice of move determines which local board the opponent can play on.

  • How does the gameplay of Ultimate Tic Tac Toe work?

    -In Ultimate Tic Tac Toe, players take turns making moves on the local boards. The first move is free, but subsequent moves are restricted to the local board where the opponent's last move was made. If a local board is fully occupied or won by a player, the next player can choose any available local board.

  • What determines the winner in Ultimate Tic Tac Toe?

    -A player wins Ultimate Tic Tac Toe by getting three 'O's or 'X's in a row on any local board. If no player can achieve this by the end of the game, it results in a draw.

  • Why is the minimax algorithm used in the game?

    -The minimax algorithm is used to create an AI opponent for Ultimate Tic Tac Toe. It helps the AI to choose the best possible move by simulating all possible outcomes of the game and selecting the one that maximizes its chances of winning.

  • What is the purpose of the alpha-beta pruning in the minimax algorithm?

    -Alpha-beta pruning is used to reduce the number of nodes the minimax algorithm needs to evaluate. It eliminates branches of the game tree that cannot possibly influence the final decision, thus saving computational resources.

  • How does the AI determine the best move in Ultimate Tic Tac Toe?

    -The AI uses the minimax algorithm with alpha-beta pruning to explore the game tree up to a certain depth, evaluating each move based on a scoring system that considers the position of pieces on the board and the potential to win on a local board.

  • What is the significance of the center square in Ultimate Tic Tac Toe?

    -The center square is the most important square in Ultimate Tic Tac Toe because it has the highest position score. Controlling the center can influence the play on multiple local boards, giving the player a strategic advantage.

  • How does the AI score different board positions in Ultimate Tic Tac Toe?

    -The AI assigns scores to different board positions based on the potential to win on a local board. For example, having three in a row is highly scored, while having two of the same symbol with an empty square is less favorable, and thus scored lower.

  • What is the impact of winning a local board on the game score?

    -Winning a local board significantly impacts the game score. The score for the board is adjusted by the position scores multiplied by 150, which strongly encourages the AI to win local boards.

  • Can the AI in Ultimate Tic Tac Toe be beaten?

    -Yes, the AI in Ultimate Tic Tac Toe can be beaten. Since the minimax function does not explore the entire game tree and is limited in the depth it searches (four steps for mobile devices, six for PCs), a player who can think several steps ahead may outsmart the AI.

Outlines

00:00

🎲 Introduction to Minimax and Automated Tic-Tac-Toe

In the first paragraph, Winston introduces the concept of Minimax and its application in an automated version of Tic-Tac-Toe. He explains the basic rules of the game, highlighting the global board with nine local boards and how a player's move restricts the opponent's next move to a specific local board. Winston also discusses the game's progression, where players are initially free to choose any local board but later must choose from available ones, and the conditions for winning or ending in a draw. The paragraph concludes with an overview of the coding structure used to represent the game board and the Minimax function's role in determining the best moves.

05:01

🤖 AI Strategy and Scoring Mechanism

The second paragraph delves into the AI's strategy, with Winston setting a maximum depth for the AI's lookahead in the game tree, varying between four for mobile devices and six for PCs or laptops. The depth determines how many future moves the AI considers. The paragraph introduces the concept of a scoring system that evaluates the entire board, not just individual moves, and is influenced by the game's progress. Scores are assigned based on the importance of board positions, with higher values for central and corner squares. The scoring system also accounts for specific game situations, such as having three in a row or two of one player's marks with an empty square, which can either favor the maximizing or minimizing player. The paragraph emphasizes the significance of these scores in guiding the AI's decisions.

10:02

🏆 Winning Conditions and Game Evaluation

In the final paragraph, Winston discusses the impact of winning a local board on the game's score, with a substantial multiplier applied to the position scores. He explains that a win results in a significant score increase, encouraging the player to secure victories. The paragraph also covers the game's end conditions, where a player with three in a row wins, and the final score is adjusted by 50,000 points, heavily favoring the winning player. Winston concludes by encouraging viewers to try the game, suggesting that the AI can be beaten if a player can look ahead more than the AI's lookahead limit. He also mentions that the Minimax function does not explore the entire game tree, leaving room for human strategy and the possibility of outsmarting the AI.

Mindmap

Keywords

💡Ultimate Tic Tac Toe

Ultimate Tic Tac Toe is a variant of the classic Tic Tac Toe game. It is played on a larger 'global' board that contains nine smaller 'local' boards. The game introduces a strategic layer where each move on the global board restricts the opponent to a specific local board. This concept is central to the video's theme as it sets the stage for the discussion on implementing the minimax algorithm within this game's unique structure.

💡Minimax

The minimax algorithm is a decision-making strategy used in artificial intelligence, particularly in the context of two-player, zero-sum games like Ultimate Tic Tac Toe. It involves simulating all possible moves and outcomes to determine the optimal move for a player. In the video, the minimax algorithm is implemented to create an AI that can play Ultimate Tic Tac Toe, aiming to maximize its chances of winning while minimizing the opponent's.

💡Global Board

The 'global board' in Ultimate Tic Tac Toe refers to the larger board that encompasses all nine local boards. Each cell on the global board corresponds to a local board, and a player's move on the global board dictates which local board the opponent must play on next. This concept is crucial for understanding the video's explanation of how moves are restricted and how the game progresses.

💡Local Board

A 'local board' is one of the nine smaller boards within the global board of Ultimate Tic Tac Toe. Each local board operates like a standard Tic Tac Toe game, and the outcome of each local board can influence the overall game. The video explains how the first move on the global board determines which local board the opponent can play on, showcasing the interplay between the global and local boards.

💡Alpha-Beta Pruning

Alpha-beta pruning is an optimization technique for the minimax algorithm that reduces the number of nodes evaluated in the search tree. This technique helps to improve the efficiency of the AI by avoiding the exploration of branches that are unlikely to influence the final decision. The video mentions alpha-beta pruning as a method to prevent the AI from exhausting computational resources, making it a key concept in the implementation of the minimax algorithm for Ultimate Tic Tac Toe.

💡Depth

In the context of the minimax algorithm, 'depth' refers to the number of moves ahead the AI considers during its decision-making process. The video discusses setting a maximum depth for the AI's search tree to balance computational efficiency and strategic planning. A depth of four is suggested for mobile devices, while six is recommended for more powerful devices like PCs or laptops.

💡Evaluation Function

An 'evaluation function' is a critical component of the minimax algorithm that assigns a score to a particular board configuration. This score helps the AI determine the most advantageous move. The video explains how the evaluation function takes into account the position of pieces on the board, the state of the local boards, and the overall game state to calculate a score that guides the AI's decision-making.

💡Position Score

The 'position score' is a numerical value assigned to each square on the board based on its strategic importance. In Ultimate Tic Tac Toe, the center square is typically given the highest score, followed by corner squares, and then edge squares. The video uses the concept of position scores to explain how the evaluation function prioritizes certain moves over others, influencing the AI's strategy.

💡Winning Condition

The 'winning condition' in Ultimate Tic Tac Toe is when a player manages to get three 'O's or 'X's in a row on any local board. The video script mentions this condition as part of explaining how the game is won, which is essential for the AI to know when to aim for a win or to block the opponent's win.

💡Draw

A 'draw' in Ultimate Tic Tac Toe occurs when all squares on the global board are filled, and no player has won on any local board. The video script includes this scenario to illustrate the end of the game when no further moves can lead to a win, which is an important consideration for the AI's strategy to avoid losing.

Highlights

Introduction to Ultimate Tic Tac Toe and its rules

Explanation of the global board and nine local boards

How a player's move determines the opponent's playing board

Strategy of choosing moves in local boards

Winning condition of Ultimate Tic Tac Toe

Code representation of the global and local boards

Implementation of the minimax algorithm for decision-making

Alpha-beta pruning to optimize the minimax algorithm

Setting the maximum depth for AI's lookahead

Scoring system to evaluate board positions

Importance of center and corner squares in scoring

Scoring for different in-game situations like rows and local board wins

Impact of winning a local board on the overall score

Final game score determination and its significance

Encouraging strategic play with high scores for winning moves

AI's limitations and how players can still outsmart it

Invitation to viewers to try the game and challenge the AI