Minimax Algorithm for Tic Tac Toe (Coding Challenge 154)

The Coding Train
11 Dec 201926:33

TLDRIn this coding challenge, the presenter explores the implementation of the Minimax algorithm in a Tic-Tac-Toe game. Initially, the game involved random moves by the AI. The presenter then introduces the Minimax algorithm, a recursive strategy for optimizing decision-making, aiming for the AI to play a perfect game. The video explains the algorithm's concept using a tree diagram, illustrating possible game outcomes and scores. The presenter refactors the game's code to incorporate Minimax, resulting in an AI that consistently plays optimally, often leading to a tie or victory against a human player. The video concludes with suggestions for further exploration, such as alpha-beta pruning, applying the algorithm to larger boards or different games, and considering game depth in scoring.

Takeaways

  • 😀 The video is a coding challenge focused on implementing the Minimax algorithm for a Tic Tac Toe game.
  • 🎮 The presenter initially created a basic two-player Tic Tac Toe game with random moves and later adjusted it for human play.
  • 👨‍💻 The Minimax algorithm is introduced as a search algorithm to find the optimal move for the AI player in the game.
  • 🌐 Two resources are recommended for further understanding: a video by Sebastian Lague and a three-part series on geeksforgeeks.org.
  • 📚 Minimax is typically visualized as a decision tree, with the root representing the current game state and branches for each possible move.
  • 🏆 The algorithm assigns scores to each game outcome: +1 for X wins, -1 for O wins, and 0 for a tie.
  • 🔄 Minimax involves alternating between a maximizing player (trying to maximize their score) and a minimizing player (trying to minimize the opponent's score).
  • 💡 The presenter suggests that Minimax can be applied to a variety of scenarios beyond Tic Tac Toe, such as chess, but acknowledges the complexity of such applications.
  • 🛠️ The video includes a live coding session where the presenter writes the Minimax function and integrates it into the Tic Tac Toe game.
  • 🔍 The presenter discusses potential improvements and variations, such as alpha-beta pruning, larger game boards, and applying the algorithm to other games like Connect Four.

Q & A

  • What is the main topic of the video?

    -The main topic of the video is the implementation of the Minimax algorithm for the game Tic Tac Toe.

  • What was the initial version of the Tic Tac Toe game like?

    -The initial version of the Tic Tac Toe game was a mess and played with two players picking random spots.

  • What adjustments were made to the Tic Tac Toe game to allow human play?

    -A mouse pressed function was added to place the human player's mark on the board, and the next turn function was adjusted to allow the AI to pick a random spot.

  • What are the two resources recommended for learning more about the Minimax algorithm?

    -The two resources recommended are a video by Sebastian Lague explaining the Minimax algorithm and alpha-beta pruning, and a three-part series on geeksforgeeks.org about the Minimax algorithm.

  • How is the Minimax algorithm typically visualized?

    -The Minimax algorithm is typically visualized as a tree, with the root of the tree being the current state of the game board.

  • What does the Minimax algorithm aim to do in the context of Tic Tac Toe?

    -The Minimax algorithm aims to find the optimal next move for the AI player in Tic Tac Toe to either win the game or at least tie.

  • What are the three possible scores in the Tic Tac Toe game according to the script?

    -The three possible scores in the Tic Tac Toe game are: plus 1 for X wins, negative 1 for O wins, and 0 for a tie.

  • What is the role of the 'maximizing player' in the Minimax algorithm?

    -The 'maximizing player' in the Minimax algorithm aims to maximize their score, typically represented by X in Tic Tac Toe.

  • What is the role of the 'minimizing player' in the Minimax algorithm?

    -The 'minimizing player' in the Minimax algorithm aims to minimize the score of the maximizing player, typically represented by O in Tic Tac Toe.

  • What is the significance of the 'depth' in the Minimax algorithm?

    -The 'depth' in the Minimax algorithm refers to the number of moves from the current position, and it can be used to prioritize quicker wins or to limit the search depth in more complex games.

  • What is the purpose of the 'Best Move' function in the script?

    -The 'Best Move' function is designed to determine the optimal move for the AI by using the Minimax algorithm to evaluate all possible board positions and selecting the one with the highest score.

  • What is the final outcome when two AI players using the Minimax algorithm play against each other in Tic Tac Toe?

    -When two AI players using the Minimax algorithm play against each other in Tic Tac Toe, the game will always result in a tie, as the game is solved and the AI will always choose the optimal move.

Outlines

00:00

🎮 Introduction to the Tic-Tac-Toe Minimax Algorithm

The speaker begins by introducing a coding challenge to improve a previously created Tic-Tac-Toe game by implementing the Minimax algorithm. They recount their initial creation of a two-player random spot picker game and how they adjusted it for human play. The goal is to enhance the AI to play optimally, either winning or tying. The speaker suggests resources for learning about the Minimax algorithm and alpha-beta pruning, which they do not implement but recommend for further study. They describe the algorithm visually as a tree, explaining the root and branches representing the game's current and future states, and how the algorithm helps determine the best move for the AI player.

05:01

🌳 Understanding the Minimax Algorithm with Tree Diagrams

The speaker delves into the specifics of how the Minimax algorithm works using tree diagrams. They illustrate possible moves for the game piece 'X' and how each move leads to different game outcomes, marking the win conditions for 'X' in green and losses for 'O' in red. The explanation includes the concept of 'maximizing' and 'minimizing' players, where 'X' aims to maximize its chances of winning, and 'O' tries to minimize 'X's chances. The speaker discusses the recursive nature of the Minimax algorithm, suggesting that it involves a function calling itself to evaluate all possible game outcomes.

10:02

💻 Coding the Minimax Algorithm for Tic-Tac-Toe

The speaker transitions into the coding phase, aiming to replace the random move picker with a function named 'Best Move' that will use the Minimax algorithm. They outline the process of evaluating all possible board positions and choosing the move with the highest score. The speaker discusses the importance of not altering the global board state and suggests making a copy or undoing moves to maintain the game's integrity. They also touch upon the need to handle the alternating turns between the maximizing and minimizing players within the algorithm.

15:02

🔍 Debugging and Refining the Minimax Implementation

The speaker encounters issues while implementing the Minimax function, such as incorrect variable names and logic errors. They discuss the need to check for a game's terminal state before proceeding with recursive calls. The debugging process includes fixing mistakes like incorrect return statements and ensuring that the algorithm correctly identifies the best move by comparing scores. The speaker also considers refactoring the code for readability and efficiency, emphasizing the importance of proper bracketing and logical flow in the algorithm.

20:04

🏁 Testing and Tweaking the AI's Performance

After implementing the Minimax algorithm, the speaker tests the AI's performance in the game. They observe the AI making suboptimal moves initially due to errors in the code but eventually correct these issues. The speaker highlights the AI's ability to learn and adapt, playing moves that lead to ties or wins against the human player. They also experiment with the AI going first and note that the game is 'solved,' meaning the AI will always result in a tie or a win, demonstrating the effectiveness of the Minimax algorithm in a deterministic game like Tic-Tac-Toe.

25:06

🚀 Expanding the Minimax Algorithm's Application

The speaker concludes by suggesting potential enhancements and applications of the Minimax algorithm. They propose ideas such as creating two AI players, adjusting the score to account for game depth, expanding the game board, introducing more players, or even applying the algorithm to other games like Connect Four. They also touch upon the concept of alpha-beta pruning to improve efficiency and the possibility of using heuristics for games with more complex or larger search spaces. The speaker invites viewers to share their own creative implementations and join the coding community for support and collaboration.

Mindmap

Keywords

💡Minimax Algorithm

The Minimax Algorithm is a recursive algorithm used in decision-making and game theory, particularly for zero-sum games. It involves minimizing the potential maximum loss in the worst case. In the context of the video, the Minimax Algorithm is implemented to improve the AI's gameplay in Tic-Tac-Toe by calculating the optimal move, considering all possible outcomes. The script describes how the algorithm is used to ensure the AI, playing as 'X', can either win or force a tie against a human player or another AI, making it play a 'perfect' game.

💡Tic-Tac-Toe

Tic-Tac-Toe is a classic paper-and-pencil game for two players, X and O, who take turns marking the spaces in a 3x3 grid. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row wins the game. The video uses Tic-Tac-Toe as a practical example to demonstrate the application of the Minimax Algorithm, showing how the AI can be programmed to make strategic moves against a human player.

💡Recursive Algorithm

A recursive algorithm is a function that calls itself in order to solve smaller instances of the same problem. In the video, the Minimax Algorithm is inherently recursive as it explores all possible game states by simulating each move and its subsequent countermove, effectively 'thinking' multiple steps ahead. This approach is crucial for the AI to evaluate the best move in a game like Tic-Tac-Toe.

💡Game Theory

Game Theory is a mathematical model that deals with strategic interactions among rational decision-makers. The video touches on game theory by implementing the Minimax Algorithm, which is a concept used to determine the optimal strategy in a game. It assumes that all players are rational and will play to maximize their gains or minimize their losses.

💡Alpha-Beta Pruning

Alpha-Beta Pruning is an optimization technique for the Minimax Algorithm that reduces the number of nodes evaluated in the decision tree. It eliminates branches that cannot possibly influence the final decision. Although not implemented in the video's Tic-Tac-Toe example, the script mentions it as a potential next step for optimization, suggesting that viewers could explore its application in more complex scenarios or games.

💡Tree Diagram

A tree diagram, as mentioned in the video, is a graphical representation used to visualize the branching of possible moves in a game. Each node represents a game state, and branches represent possible moves from that state. The Minimax Algorithm uses tree diagrams to explore all possible game outcomes from the current state, helping the AI to choose the best move.

💡Terminal State

In the context of the video, a terminal state refers to a game state where no more moves are possible, typically because one player has won, or the game is a tie. The Minimax Algorithm evaluates the score of these terminal states to determine the best course of action from the current game state.

💡Optimal Move

The optimal move is the decision that leads to the best possible outcome for a player. The video's central focus is on using the Minimax Algorithm to calculate the AI's optimal move in Tic-Tac-Toe. It involves evaluating all possible moves and choosing the one that maximizes the AI's chance of winning or ensures a tie against an optimal human opponent.

💡Global Variable

A global variable is a variable that is defined and can be accessed from any part of the program. In the script, the AI's interaction with the game board is mentioned, where global variables might be used to track the state of the game. The video discusses the need to manage these variables carefully, especially when making and undoing moves to explore different game scenarios.

💡Heuristic

A heuristic is a technique designed for solving problems that is practical but not necessarily optimal. While not directly discussed in the video, the concept is alluded to when suggesting future enhancements to the algorithm. For more complex games like chess, where calculating every possible move is impractical, heuristics can be used to estimate the value of a game state and guide the AI's decision-making process.

Highlights

Introduction to a coding challenge on implementing the Minimax algorithm for Tic Tac Toe.

Discussion of a previous coding challenge where a two-player random Tic Tac Toe game was created.

Explanation of adjustments made to allow human players to interact with the game.

Introduction of the Minimax algorithm as a method to find the optimal move for AI in games.

Recommendation of resources for learning more about the Minimax algorithm and its application.

Description of the Minimax algorithm as a decision-making process visualized as a tree.

Explanation of the algorithm's approach to evaluating game states and choosing the best move.

Illustration of how to score different game outcomes in the Minimax algorithm.

Introduction to the concept of 'maximizing' and 'minimizing' players within the algorithm.

Discussion on the implementation of the Minimax algorithm in code using recursion.

Explanation of how to handle game states and the use of a 'check winner' function.

Demonstration of coding the Minimax function with proper terminal conditions.

Exploration of handling different player turns within the algorithm and the concept of depth.

Identification of errors and refinement of the Minimax function to ensure correct scoring.

Testing the algorithm and observing its behavior in making optimal moves.

Discussion on potential improvements and variations of the Minimax algorithm.

Suggestion to try the algorithm with different game parameters or more complex games like Chess.

Encouragement for viewers to create their own versions of the Tic Tac Toe game with the Minimax algorithm.