Beating Connect 4 with Monte Carlo Tree Search! | Explanation + Code

Introduction

In this article, we will explore the Monte Carlo Tree Search (MCTS) algorithm and its application in beating the game of Connect 4. MCTS is a reinforcement learning algorithm commonly used in multiplayer games to make optimal decisions based on heuristics and game experience.

Introduction to Monte Carlo Tree Search

The goal of MCTS is to choose the best actions that lead to a state with the highest probability of winning. The algorithm simulates multiple games from a given state by randomly selecting actions. Through the law of large numbers, the algorithm determines which states are more favorable for winning. The agent then selects the action that leads to the best chance of winning based on the simulations.

Understanding the Monte Carlo Tree Search Algorithm

The MCTS algorithm consists of four stages: select, expand, simulate, and back propagate. These stages are repeated multiple times to refine the agent's strategy. Let's delve into each stage:

1. Select: In this stage, the algorithm selects a leaf node that has either not been explored or has a high value according to the Upper Confidence Bound (UCT) function. The UCT function balances exploration and exploitation by considering the probability of winning (Q/N) and an exploration variable. The algorithm traverses the tree by selecting child nodes with the highest UCT value until it reaches a leaf node.

2. Expand: Once a leaf node is reached, the algorithm checks if it is an expandable state (i.e., the game is not over and legal moves are available). If it is expandable, the algorithm adds children nodes to the leaf node, representing the possible actions. One of these children is randomly selected for further simulation.

3. Simulate (Rollout): In this stage, the algorithm simulates a random game from the selected child node. The game is played out until a terminal state is reached (a win, loss, or draw).

4. Back Propagate: After simulating the game, the algorithm tracks the results and propagates them back up the tree to update the Q (total games won) and N (total games played) values of each node. The rewards are added accordingly, with a +1 reward for a win and a 0 reward for a loss. The process continues recursively until the root node is reached.

By repeating these stages, the algorithm builds a tree of nodes representing states and their associated values. The agent then selects the action corresponding to the node with the highest UCT value from the root node.

Implementation of MCTS in Connect 4

To apply the MCTS algorithm to beat Connect 4, we will use a board representation, game logic, and the MCTS class. The board keeps track of the game state, players, height per column, and the last move played. The MCTS class includes functions for selecting, expanding, simulating, and back propagating in accordance with the MCTS algorithm.

The MCTS agent simulates games within a time limit, running the four stages of MCTS repeatedly until the time budget is exhausted. The agent selects nodes, expands the tree, simulates games, and updates the game statistics. Finally, the agent chooses the best move based on the most explored state.

Code Explanation and Execution

You can find the complete code for implementing MCTS in Connect 4 on my website. The code is well-documented and provides instructions for running the game. The MCTS agent has a budget of 5 seconds to simulate and make moves. The code allows you to play against the MCTS agent, testing your skills against its optimized decision-making.

To execute the code, instantiate the game state and MCTS agent. You can then take turns making moves with the MCTS agent, and the game will continue until a win or loss occurs. The MCTS agent will optimize its moves based on simulations and heuristics.

Keyword

Monte Carlo Tree Search, Reinforcement Learning, Connect 4, Game Playing, Upper Confidence Bound, Exploration vs. Exploitation, Simulations, Optimized Decision-Making.

FAQ

Q: What is Monte Carlo Tree Search? A: Monte Carlo Tree Search (MCTS) is a reinforcement learning algorithm used to make optimal decisions in games. It balances exploration and exploitation by simulating random games from a given state and selecting actions that lead to states with the highest probability of winning.

Q: How does MCTS work in Connect 4? A: In Connect 4, MCTS builds a tree of game states and their associated values. It selects the most promising moves based on the Upper Confidence Bound (UCB) formula, expands the tree by adding children nodes to unexplored states, simulates random games to determine the outcome, and back propagates the results to update the values of each node.

Q: Can MCTS be used in other games? A: Yes, MCTS can be applied to other games as well. It has been successfully used in games like Tic-Tac-Toe and Go. In more complex games, MCTS can be combined with deep learning techniques for improved performance.

Q: How can MCTS be optimized for faster execution? A: MCTS can be optimized by implementing efficient state evaluation functions, pruning less promising branches of the search tree, and optimizing the selection strategy. Additionally, using parallelization techniques and exploiting hardware acceleration can speed up the execution of MCTS algorithms.

Q: Can MCTS be used for non-game applications? A: Yes, MCTS can be applied to various domains outside of games, such as decision-making processes, optimization problems, and resource allocation. Its ability to balance exploration and exploitation makes it a powerful tool for solving complex problems in different domains.