Coding an UNBEATABLE Tic Tac Toe AI (Game Theory Minimax Algorithm EXPLAINED)

Kylie Ying
20 Jan 202014:59

TLDRThis video explains how to create an unbeatable Tic Tac Toe AI using the minimax algorithm. The presenter demonstrates the algorithm's effectiveness by pitting it against a random player and another AI, showing the minimax player never loses. The script covers the game's finite states, the utility function, and how to implement the minimax algorithm in a Tic Tac Toe game, including coding examples for different player types and the minimax function itself.

Takeaways

  • 🎮 The video demonstrates coding an unbeatable Tic Tac Toe AI using the minimax algorithm.
  • 🔢 The Tic Tac Toe board has nine squares, leading to approximately 20,000 possible game states.
  • 🧠 The minimax algorithm is a decision-making process used to find the optimal move by simulating all possible game outcomes.
  • 🏆 The AI is designed to always maximize its chances of winning, while the opponent tries to minimize their loss.
  • 📊 A utility function is used to assign a value to each game state, helping determine the most favorable position.
  • 🔄 The algorithm works by recursively evaluating the best and worst possible outcomes at each step of the game.
  • 👾 The video includes a demonstration where the AI plays against a random player and another AI to test its effectiveness.
  • 💡 The script explains how to implement the minimax algorithm in a Tic Tac Toe game, including handling game states and moves.
  • 👨‍💻 The video creator implemented different player types: human, random computer, and smart computer (minimax) player.
  • 🌐 The final game implementation allows for various player combinations, such as human vs. computer or computer vs. computer.

Q & A

  • What is the primary algorithm used to create an unbeatable Tic Tac Toe AI?

    -The primary algorithm used is the minimax algorithm, which is a decision-making algorithm used in game theory to find the optimal move for a player, assuming that the opponent is also playing optimally.

  • How many squares are on a standard Tic Tac Toe board?

    -A standard Tic Tac Toe board has nine squares.

  • What is the approximate number of total possible states in Tic Tac Toe?

    -The approximate number of total possible states in Tic Tac Toe is 20,000, which is calculated as three to the ninth power (3^9).

  • Why is the calculated number of states in Tic Tac Toe an overestimate?

    -The calculated number of states is an overestimate because it includes states that are not reachable through realistic play between two players.

  • How does the utility function in the minimax algorithm contribute to the AI's decision-making process?

    -The utility function measures the value of the final result in the game tree, helping the AI to determine the most optimal move by assigning positive or negative values based on whether a move leads to a win, loss, or draw.

  • What is the purpose of the 'Maximizer' and 'Minimizer' in the minimax algorithm?

    -The 'Maximizer' aims to maximize the player's chance of winning, while the 'Minimizer' seeks to minimize the opponent's chance of winning. They work together to find the best possible move for the current player.

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

    -The AI determines the best move by trying out all possible moves and evaluating their outcomes using the minimax algorithm and the utility function, then selecting the move that leads to the most optimal outcome.

  • What is the significance of the 'empty squares' function in the AI's gameplay?

    -The 'empty squares' function checks for any remaining empty spaces on the board, which is crucial for the AI to know where it can make moves and for the minimax algorithm to explore all possible game states.

  • How does the AI handle different types of players in the game?

    -The AI handles different types of players by implementing a superclass called 'player' and creating subclasses for human, random computer, and smart computer players, each with their own methods for making moves.

  • What is the role of the 'winner' function in the Tic Tac Toe AI?

    -The 'winner' function checks if a player has won after each move by evaluating rows, columns, and diagonals for three identical consecutive marks.

  • How does the AI use the minimax algorithm to play against itself?

    -The AI uses the minimax algorithm to play against itself by alternating between the 'Maximizer' and 'Minimizer' roles, simulating both the current player's and the opponent's moves to find the optimal strategy.

Outlines

00:00

🎮 Coding Tic-Tac-Toe AI

The speaker shares their experience coding a tic-tac-toe game and teaching their computer to play it. They created a weak player for comparison and tested it against a smart AI player. The smart AI never loses, demonstrating the effectiveness of the minimax algorithm. The speaker explains the game's finite number of states and how the minimax algorithm can be used to make the computer unbeatable. They discuss the algorithm's Maximizer and Minimizer concepts and provide an example using a partially completed game of tic-tac-toe, highlighting the utility function's role in determining the most optimal move.

05:02

🧠 Understanding the Minimax Algorithm

The speaker delves deeper into the minimax algorithm, explaining how it works through a decision tree to find the best move. They discuss the utility function's importance in evaluating game states and how it's used to propagate values back up the tree to determine the optimal path. The speaker also describes their implementation of tic-tac-toe, including the game's class structure, board initialization, and move validation. They detail the winner function, which checks for winning conditions, and the available moves function, which identifies empty spaces on the board. The speaker outlines the different types of players, including human, random computer, and smart computer players, and explains how the smart computer player uses the minimax algorithm to make strategic decisions.

10:04

💻 Implementing and Playing Tic-Tac-Toe

The speaker concludes by discussing the implementation of the minimax function in their tic-tac-toe game. They explain how the function is used recursively to evaluate game states and determine the best move. The speaker also describes the play function, which orchestrates the game by alternating turns between players and checking for a winner. They demonstrate how to set up a game with different types of players and how to play the game with or without visual output. The speaker emphasizes the game's adaptability, allowing for human versus computer or computer versus computer matches, and invites viewers to try different player configurations to experience the game.

Mindmap

Keywords

Tic-Tac-Toe

Tic-Tac-Toe, also known as Noughts and Crosses, is a classic paper-and-pencil game for two players, X and O, who take turns marking the spaces in a 3x3 grid. The objective of the game is to be the first to place three of their marks in a horizontal, vertical, or diagonal row. In the context of the video, the game is used to demonstrate the application of the minimax algorithm, where an AI is taught to play the game optimally, ensuring it can never be defeated.

Minimax Algorithm

The minimax algorithm is a recursive algorithm used in decision-making and game theory, particularly in two-player games with perfect information. It involves simulating all possible moves and outcomes to determine the optimal strategy. In the video, the minimax algorithm is used to create an unbeatable Tic-Tac-Toe AI by evaluating all possible game states and choosing the move that minimizes the maximum possible loss, effectively maximizing the chances of winning.

Maximizer and Minimizer

In game theory, the Maximizer is the player who aims to maximize their gains, while the Minimizer seeks to minimize their losses. These concepts are central to the minimax algorithm. The video explains how, in Tic-Tac-Toe, the AI (Maximizer) tries to maximize its chances of winning while assuming the opponent (Minimizer) will try to minimize the AI's gains, leading to a strategy that ensures the AI's victory.

Utility Function

A utility function is a mathematical function that measures the value or utility of different outcomes in a game. It is used in the minimax algorithm to assign scores to different game states, helping to determine the most advantageous move. In the video, the utility function is used to assign positive values for winning positions, negative values for losing positions, and zero for draws, guiding the AI's decision-making process.

Game State

A game state refers to the configuration of the game at a particular point in time, including the positions of all pieces or markers. In the context of the video, the Tic-Tac-Toe board represents a game state, with each square's status (empty, X, or O) contributing to the overall state. The minimax algorithm evaluates the game state to predict future outcomes and choose the best move.

Recursion

Recursion is a method in programming where a function calls itself to solve smaller instances of the same problem. In the video, recursion is used in the minimax algorithm to explore each possible move and its resulting game states, effectively building a decision tree to find the optimal strategy. This allows the AI to simulate the entire game from any given state to its conclusion.

Backpropagation

Backpropagation is the process of passing information back through a system, such as a neural network or decision tree, to update or improve its structure. In the video, backpropagation is used to pass the results of the utility function up the decision tree after each move is simulated. This helps the AI to determine the best move by comparing the values of different branches of the tree.

Random Player

A random player is a type of player in a game that makes moves without any strategic consideration, choosing actions at random. In the video, a weak player that randomly selects a spot on the Tic-Tac-Toe board is created to test the AI's capabilities. The AI's consistent victory against this random player demonstrates the effectiveness of the minimax algorithm in creating a superior strategy.

Computer Player

A computer player is a program that plays a game, following a set of rules or algorithms to make decisions. In the video, the smart computer player uses the minimax algorithm to make strategic moves in Tic-Tac-Toe. This contrasts with the random computer player, which makes moves randomly, and the human player, who inputs their moves manually.

Game Theory

Game theory is a mathematical framework used to model and analyze strategic situations where players have interdependent interests. It is the basis for the minimax algorithm and is central to the video's theme. The video demonstrates how game theory can be applied to create an unbeatable Tic-Tac-Toe AI by predicting and simulating all possible moves and outcomes.

Highlights

Coding a Tic Tac Toe AI that can't be defeated using the minimax algorithm.

Creating a weak player to test the AI's effectiveness.

The smart AI player never loses against the weak player.

Tic Tac Toe has a finite number of states, making it suitable for the minimax algorithm.

There are approximately 20,000 possible states in Tic Tac Toe.

Many game states are unreachable in realistic play, reducing the number of possible states.

The minimax algorithm is based on a Maximizer and Minimizer concept.

The utility function measures the value of the final result in the game tree.

The goal is to maximize wins while minimizing losses.

An example is provided to illustrate how the minimax algorithm works in Tic Tac Toe.

The utility function is used to assign values to game outcomes.

The minimax algorithm is used to find the best move by trying all possible moves.

The algorithm propagates utility values back up the game tree to find the optimal path.

The implementation of Tic Tac Toe includes a class with methods for board management.

The game checks for a winner after each move.

Different player types are implemented: human, random computer, and smart computer.

The smart computer player uses the minimax algorithm to make decisions.

The minimax function is explained in detail, including its recursive nature.

The game is played by alternating between X and O players.

The game ends when there is a winner or a tie.

The final implementation allows for different player combinations and game visualization.