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

Kylie Ying
20 Jan 202014:59

TLDRThis video tutorial demonstrates how to create an unbeatable Tic Tac Toe AI using the minimax algorithm, a decision-making process used in game theory. The script explains the concept of game states, utility functions, and how to implement the minimax algorithm to ensure the AI always makes the best move. The video also covers the coding of different player types, including a smart AI player, and concludes with a demonstration of the AI playing against itself and a human, showcasing its unbeatable strategy.

Takeaways

  • 😲 The video demonstrates coding an unbeatable Tic Tac Toe AI using the minimax algorithm.
  • 🎲 The Tic Tac Toe board has nine squares and can generate approximately 20,000 unique game states.
  • 🧠 The minimax algorithm is used to determine the best move by simulating all possible game outcomes.
  • 🔢 A utility function is introduced to assign a value to each game state, helping to decide optimal moves.
  • 🏆 The AI is programmed to maximize its own wins while minimizing the opponent's chances of winning.
  • 💡 The script explains how to implement a recursive minimax function to find the best move in a game tree.
  • 👾 The video includes a demonstration of the AI playing against a random player and another AI to test its effectiveness.
  • 📝 The implementation details of the Tic Tac Toe game, including board initialization and move validation, are covered.
  • 🤖 Different player types are created: human, random computer, and smart computer using the minimax algorithm.
  • 🔄 The minimax function is explained with a focus on how it handles game states and propagates utility values back up the game tree.
  • 🌐 The final game setup allows for various player combinations, enabling human vs. AI or AI vs. AI gameplay.

Q & A

  • What is the minimax algorithm and how is it used in Tic Tac Toe?

    -The minimax algorithm is a decision-making algorithm used in game theory, particularly for two-player, zero-sum games like Tic Tac Toe. It's designed to minimize the maximum possible loss, or maximize the minimum possible gain. In Tic Tac Toe, it's used by the AI to simulate all possible moves and outcomes to determine the best move that will either lead to a win or prevent a loss.

  • How many total possible states are there in a game of Tic Tac Toe?

    -There are approximately 20,000 possible states in a game of Tic Tac Toe, calculated by raising 3 to the power of 9 (3^9), considering each square on the board can be empty, have an 'X', or have an 'O'.

  • What is a utility function in the context of the minimax algorithm?

    -A utility function is a scoring system used in the minimax algorithm to evaluate the desirability of different game states. It assigns a numerical value to each possible outcome, with positive values for wins, negative for losses, and zero for draws, allowing the algorithm to choose the optimal move.

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

    -The AI determines the best move by exploring all possible moves from the current game state, evaluating each using the utility function, and choosing the move that maximizes its own utility (i.e., leads to a win or minimizes loss) while assuming the opponent will play optimally.

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

    -In the minimax algorithm, the 'Maximizer' is the player trying to maximize their own score, while the 'Minimizer' is the opponent trying to minimize the Maximizer's score. The algorithm alternates between these two roles as it explores the game tree to find the optimal move.

  • How does the AI handle a tie in Tic Tac Toe?

    -In Tic Tac Toe, if the board is full and neither player has won, the game is a tie. The AI handles this by assigning a utility value of zero to such a state, indicating neither a win nor a loss, and it will aim to avoid moves that lead to a tie if a winning move is available.

  • What is the significance of the number of remaining squares in the utility function?

    -The number of remaining squares is significant in the utility function because it helps to prioritize moves that lead to a win sooner rather than later. A win achieved with fewer moves is considered more valuable, so the utility function often includes a factor that increases with the number of remaining squares.

  • How does the AI handle the first move in a game of Tic Tac Toe?

    -For the first move in Tic Tac Toe, the AI can either choose a random move or follow a heuristic that suggests certain moves are slightly more advantageous, such as the center square. However, since the game is symmetric at the start, any move is theoretically optimal in the first turn.

  • What are the different types of players implemented in the Tic Tac Toe AI?

    -The Tic Tac Toe AI implementation includes different types of players: a Human player, a Random Computer player, and a Smart Computer player. The Human player takes user input for moves, the Random Computer player chooses moves randomly, and the Smart Computer player uses the minimax algorithm to make optimal moves.

  • How does the AI know when the game has been won?

    -The AI checks for a win by looking for three consecutive 'X's or 'O's in any row, column, or diagonal after each move. If such a sequence is found, the current player is declared the winner, and the game ends.

Outlines

00:00

🎮 Tic-Tac-Toe AI Algorithm

The speaker shares their experience coding a Tic-Tac-Toe game and developing an AI that can't be defeated. They explain the game's mechanics, the finite number of possible states, and how the minimax algorithm is used to teach the computer to play optimally. The minimax algorithm is described as a decision-making process involving a Maximizer and a Minimizer, aiming to maximize wins while minimizing losses. A utility function is introduced as a measure of the value of the game's outcome. The speaker provides an example of how the minimax algorithm is applied in a partially completed game of Tic-Tac-Toe, detailing the process of evaluating each move and propagating utility values to determine the best path to victory.

05:02

💻 Implementation of Tic-Tac-Toe

The speaker discusses the implementation of the Tic-Tac-Toe game, including the creation of a class for the game board and functions for printing the board, making moves, and checking for a winner. They explain how the game board is initialized and how moves are made, including checks for valid moves and winner determination. The speaker also introduces a superclass called 'Player' and subclasses for different types of players, including human, random computer, and smart computer players. The smart computer player utilizes the minimax algorithm to make optimal moves. The minimax function is described in detail, including its recursive nature and how it evaluates the best move by considering all possible game outcomes.

10:04

👾 Playing the Game with Different Players

The speaker concludes by discussing how to play the Tic-Tac-Toe game with different types of players, including humans and various AI players. They explain how to set up the game with different player configurations and how the game progresses, alternating between players until the board is full or a winner is declared. The speaker also mentions the option to print the game's progress for visual tracking. The video ends with a demonstration of playing a game and the outcome, highlighting the effectiveness of the smart AI player.

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, Tic Tac Toe serves as the basis for demonstrating the application of the minimax algorithm to create an unbeatable AI player.

💡Minimax Algorithm

The minimax algorithm is a recursive algorithm used in decision-making and game theory, particularly in two-player games with perfect information, to minimize the maximum possible loss. In the video, the minimax algorithm is used to create an unbeatable Tic Tac Toe AI by simulating all possible moves and outcomes to determine the best move for the AI to make, ensuring it always plays optimally.

💡Maximizer and Minimizer

In game theory, the Maximizer is the player who aims to maximize their gains or minimize their losses, while the Minimizer is the player who aims to minimize their opponent's gains. The video explains that in the context of Tic Tac Toe, the AI (Maximizer) tries to maximize its chances of winning, while the opponent (Minimizer) tries to minimize the AI's chances of winning.

💡Utility Function

A utility function is a mathematical representation used to determine the value of a game state to a player. In the video, the utility function is used to assign a positive or negative value to the game's outcome, with positive values indicating a win for the AI and negative values indicating a win for the opponent. This helps the minimax algorithm to evaluate which move is most advantageous.

💡Game State

A game state refers to the configuration of the game board at any given moment during a game. The video mentions that Tic Tac Toe has a finite number of possible game states, which allows the minimax algorithm to evaluate all possible moves and outcomes. Understanding game states is crucial for the AI to make informed decisions.

💡Recursive Algorithm

A recursive algorithm is one that calls itself in order to solve smaller instances of the same problem. The minimax algorithm is an example of a recursive algorithm, as it repeatedly calls itself to evaluate different game states and their outcomes. The video explains how this recursive nature allows the AI to explore all possible moves and their consequences.

💡Backtracking

Backtracking is a form of recursion where the algorithm retraces its steps to find all possible solutions. In the context of the minimax algorithm, backtracking is used to explore each potential move, evaluate the outcome, and then undo the move to explore other possibilities. The video demonstrates how backtracking allows the AI to simulate and evaluate different game scenarios.

💡Optimal Move

An optimal move is a decision that leads to the best possible outcome for a player. In the video, the minimax algorithm is used to determine the optimal move for the AI in Tic Tac Toe by evaluating all possible game states and selecting the one that maximizes the AI's chances of winning.

💡Human Player

A human player is a participant in a game who makes decisions based on their own strategy and intuition. The video script mentions the creation of a 'human player' class to allow a human to play against the AI, providing a comparison between human strategy and the AI's minimax-based strategy.

💡Random Computer Player

A random computer player is a non-strategic AI that makes moves at random, without considering the game's state or the consequences of its moves. In the video, a 'random computer player' is created to serve as a weak opponent, demonstrating the effectiveness of the minimax algorithm by comparing its performance against random moves.

💡Smart Computer Player

A smart computer player is an AI that uses advanced algorithms, like minimax, to make strategic decisions. In the video, the 'smart computer player' represents the AI that employs the minimax algorithm to always play optimally, ensuring it cannot be defeated in a game of Tic Tac Toe.

Highlights

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

Creating a weak player to test the AI against, ensuring the smart AI never loses.

Exploring the total number of possible game states in Tic Tac Toe.

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

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

Using a utility function to measure the value of the final result in the game tree.

Maximizing the win for X and minimizing the loss for O in the utility function.

Mapping out all possible scenarios of gameplay to find the most optimal path.

Propagating utility values back up the game tree to find the best move.

Implementing a Tic Tac Toe class with a board and current winner.

Defining a function to check for a winner after each move.

Creating interchangeable player types: human, random computer, and smart computer.

The smart computer player uses minimax for optimal move selection.

The minimax function checks if the previous move was a winner and returns the utility of it.

Setting up the game to play with different player combinations.

Playing a game and visually tracking the moves and outcomes.