# Minimax with Alpha Beta Pruning

TLDRThis video tutorial explains the minimax algorithm with alpha-beta pruning, focusing on a detailed worked example. It starts by illustrating the minimax algorithm without pruning, then demonstrates the efficiency gains from alpha-beta pruning. The example shows how the algorithm navigates a game tree, updating alpha and beta values to prune unpromising branches, ultimately determining the best move for the maximizing player.

### Takeaways

- 😀 The minimax algorithm is used in decision-making processes, particularly in two-player games, to find the optimal move by considering all possible outcomes.
- 🔍 Alpha-beta pruning is an enhancement to the minimax algorithm that reduces the number of nodes evaluated in the decision tree, thus improving efficiency.
- 🎯 The minimax algorithm assumes that both players, Max and Min, play optimally, with Max aiming to maximize the score and Min aiming to minimize it.
- 🌳 The algorithm operates on a game tree, where each node represents a game state, and each branch represents a possible move.
- 🔢 Alpha represents the best score that Max can ensure, given the choices of Min, while beta represents the best score that Min can ensure, given the choices of Max.
- 📉 Alpha-beta pruning eliminates branches of the search tree that are unlikely to contain better moves, based on the current values of alpha and beta.
- 🛠️ The algorithm uses mutually recursive functions, max_value and min_value, which are called from the root node down to the leaf nodes of the game tree.
- 🔄 The process involves iteratively updating alpha and beta as better moves are found, which can lead to earlier termination of the search in some branches.
- 🏁 The algorithm's goal is to reach a terminal node (end of the game) to calculate the utility, which is then propagated back up the tree to determine the best move at the root.
- 📝 The video provides a worked example to demonstrate how the minimax algorithm with alpha-beta pruning operates and how it can prune the search space effectively.

### Q & A

### What is the minimax algorithm?

-The minimax algorithm is a decision-making strategy used in artificial intelligence, particularly in two-player, zero-sum games. It involves evaluating the possible moves a player can make, assuming that the opponent will play optimally to minimize the player's gains.

### What is the role of the 'Max' and 'Min' agents in the minimax algorithm?

-In the minimax algorithm, 'Max' is the agent trying to maximize the reward, while 'Min' is the agent trying to minimize the reward. They take turns making decisions, and the algorithm assumes that 'Min' will play optimally to minimize 'Max's reward.

### How does alpha beta pruning improve the minimax algorithm?

-Alpha beta pruning is an optimization technique that reduces the number of nodes evaluated in the minimax algorithm by eliminating branches of the game tree that cannot possibly influence the final decision. It uses the alpha and beta values to determine if further exploration of a branch is necessary.

### What are the three parameters used in the minimax algorithm?

-The three parameters used in the minimax algorithm are the state of the game, the alpha value (best alternative for 'Max'), and the beta value (best alternative for 'Min').

### What is the significance of the alpha and beta values in alpha beta pruning?

-Alpha represents the best score that 'Max' can achieve so far, while beta represents the best score that 'Min' can achieve so far. These values are used to prune branches of the game tree that are not promising, thus reducing the number of nodes evaluated.

### How does the minimax algorithm handle the terminal nodes?

-Terminal nodes are the end points of the game tree where the game is over, and their values are calculated based on the game's outcome. The minimax algorithm uses these values to evaluate the best move from the current state.

### What is the purpose of the 'max value' and 'min value' functions in the minimax algorithm?

-The 'max value' function is used to evaluate the best move for 'Max', while the 'min value' function is used to evaluate the best move for 'Min'. They are mutually recursive and are called in an alternating fashion to traverse the game tree.

### How does the algorithm decide which move to make when there are multiple children with the same value?

-When multiple children have the same value, the minimax algorithm typically chooses the first one encountered in the search order. However, in practice, other strategies might be used to break ties, such as choosing the move that leads to the most diverse game states.

### Can you explain the pruning process in alpha beta pruning with an example?

-In the pruning process, if a 'Max' node has a value greater than or equal to 'Min's beta value, then 'Min' would prefer that branch, and the algorithm prunes the subtree below that 'Max' node because it cannot lead to a better outcome for 'Min'. Conversely, if a 'Min' node has a value less than or equal to 'Max's alpha value, then 'Max' would prefer that branch, and the subtree below that 'Min' node is pruned.

### What is the impact of alpha beta pruning on the efficiency of the minimax algorithm?

-Alpha beta pruning significantly improves the efficiency of the minimax algorithm by reducing the search space. It eliminates the need to explore branches that cannot possibly affect the final decision, thus saving computational resources.

### Outlines

### 🌟 Introduction to Minimax Algorithm and Alpha-Beta Pruning

This paragraph introduces the minimax algorithm with alpha-beta pruning, focusing on a practical example. The minimax algorithm is used in decision-making and game theory, where two players, Max and Min, alternate moves. Max aims to maximize the game's utility (reward), while Min tries to minimize it. The algorithm assumes that both players play optimally. The video will demonstrate the algorithm without alpha-beta pruning first, then with it, to show the efficiency gains. The minimax algorithm uses a game tree and involves recursive functions: max_value and min_value, which pass parameters like game state, alpha (best alternative for Max), and beta (best alternative for Min). Alpha-beta pruning is a technique to reduce the number of nodes evaluated in the tree, thus improving search efficiency.

### 📚 Detailed Walkthrough of Alpha-Beta Pruning

This paragraph delves into the mechanics of alpha-beta pruning with a step-by-step example. It begins with Max's perspective, evaluating the first child node and updating alpha if a better value for Max is found. The algorithm checks if the current node's value exceeds beta; if so, it prunes the search because Min would prefer a path leading to beta. The example continues with Min's perspective, updating the node's value and checking for pruning opportunities based on alpha. The process demonstrates how alpha-beta pruning can eliminate branches of the game tree that do not contribute to finding the optimal move, thus saving computational resources.

### 🔍 Conclusion and Assignment on Alpha-Beta Pruning

The final paragraph summarizes the benefits of alpha-beta pruning by showing how it prunes the search space effectively. It sets the stage for an assignment where viewers will apply what they've learned to find pruning points in a similar example. The paragraph reinforces the idea that alpha-beta pruning is crucial for optimizing the minimax algorithm's performance, especially in games with large search spaces. It concludes with an invitation for viewers to practice and solidify their understanding of the concept through hands-on application.

### Mindmap

### Keywords

### Minimax Algorithm

### Alpha Beta Pruning

### Game Tree

### Utility

### Max and Min Agents

### Recursive Functions

### Terminal Nodes

### Backtracking

### Search Space

### Pruning

### Highlights

Introduction to the minimax algorithm with alpha beta pruning.

Explanation of the minimax algorithm using a game tree.

Role of Max and Min agents in the minimax algorithm.

Assumption of logical play by the Min agent.

Recursive nature of the max value and min value functions.

Parameters of the minimax algorithm: state, alpha, and beta.

Purpose of alpha and beta values in pruning the search tree.

Demonstration of the minimax algorithm without alpha beta pruning.

Example of calculating max value and min value without pruning.

Illustration of how alpha beta pruning improves search efficiency.

Process of updating alpha and beta values during the algorithm.

Explanation of when to prune the search based on alpha and beta values.

Pruning the search tree to reduce computational complexity.

How alpha beta pruning affects the decision-making of Max.

Practical example of alpha beta pruning in a game tree.

Assignment for viewers to apply alpha beta pruning to a given example.