# Algorithms Explained – minimax and alpha-beta pruning

TLDRThis video explains the minimax algorithm and alpha-beta pruning, crucial for creating AI capable of playing turn-based games like chess. The minimax algorithm evaluates potential game moves by considering the best and worst outcomes, while alpha-beta pruning optimizes the process by eliminating branches that won't affect the final decision. The video uses a tree structure to illustrate how these techniques can efficiently determine the optimal move, even in complex games.

### Takeaways

- 😀 The minimax algorithm is a decision-making process used in artificial intelligence, particularly for two-player, zero-sum games like chess.
- 🔍 Minimax explores all possible moves in a game by creating a game tree, where each node represents a game state and each branch represents a possible move.
- 🏁 The algorithm uses static evaluation to estimate the value of a game state without making further moves, favoring the maximizing player (usually white).
- 🔄 Minimax alternates between maximizing and minimizing players, with white aiming to maximize the evaluation and black aiming to minimize it.
- 🌳 The algorithm is implemented recursively, evaluating each possible move and its consequences to determine the best move from the current position.
- 📉 Alpha-beta pruning is an optimization technique for the minimax algorithm that reduces the number of nodes evaluated by eliminating branches that cannot possibly influence the final decision.
- 🔄 Alpha and beta are values that represent the best possible scores for the maximizing and minimizing players, respectively, and are updated as the algorithm explores the game tree.
- 🏁 Pruning occurs when the minimax algorithm recognizes that further evaluation of a branch is unnecessary because a better alternative has already been found.
- 🔍 The order of move evaluation can significantly impact the efficiency of pruning; ideally, moves should be ordered from best to worst for the current player.
- 💡 The minimax algorithm with alpha-beta pruning is a powerful tool for game-playing AI, as it allows for more efficient searching of game trees and better decision-making.

### Q & A

### What is the purpose of a search algorithm in turn-based games?

-A search algorithm in turn-based games is used to look ahead at possible future positions before deciding on a move in the current position, allowing the program to make more informed decisions.

### How does the minimax algorithm decide which move to make?

-The minimax algorithm decides which move to make by evaluating all possible moves and their outcomes, choosing the move that leads to the highest evaluation for the maximizing player and the lowest evaluation for the minimizing player.

### What is a static evaluation in the context of the minimax algorithm?

-A static evaluation is an estimation of how good a position is for one side without making any more moves, often done by summing the values of the remaining pieces.

### Why does the minimax algorithm use recursion?

-The minimax algorithm uses recursion to explore all possible move sequences from the current position, evaluating each branch to determine the best move.

### What is the role of the 'maximizing player' and 'minimizing player' in the minimax algorithm?

-The 'maximizing player' aims to find the move that yields the highest evaluation, while the 'minimizing player' seeks to find the move that results in the lowest evaluation, simulating the adversarial nature of turn-based games.

### How does alpha-beta pruning improve the efficiency of the minimax algorithm?

-Alpha-beta pruning improves the efficiency of the minimax algorithm by eliminating branches of the search tree that cannot possibly influence the final decision, thus saving computational resources.

### What are the initial values of alpha and beta in the minimax algorithm with alpha-beta pruning?

-The initial values of alpha and beta are negative infinity and positive infinity, respectively, representing the worst possible score for the maximizing player and the best possible score for the minimizing player.

### Why is it beneficial to order the moves in the minimax algorithm?

-Ordering the moves can lead to more efficient pruning, as moves that are likely to be good for the player whose turn it is can be explored first, potentially leading to earlier pruning opportunities.

### How does the minimax algorithm handle game positions where the game is over?

-When the minimax algorithm encounters a game position where the game is over, it returns the static evaluation of that position without further recursion.

### What is the significance of the minimax algorithm in the history of computer chess?

-The minimax algorithm is significant in the history of computer chess because it was used in the first computer program to defeat a reigning world champion in classical time controls.

### Outlines

### 😀 Introduction to Minimax Algorithm

The paragraph introduces the concept of the minimax algorithm used in turn-based games like chess. It explains how the algorithm allows a program to look ahead at possible future positions and make decisions based on a search tree. The tree is expanded until the end of the game or a predefined depth is reached. At the end of the tree, static evaluations are performed to estimate the position's value for one side. The algorithm alternates between maximizing and minimizing players, with white aiming to maximize the evaluation and black aiming to minimize it. The paragraph uses an example to demonstrate how the algorithm assigns values to positions based on the evaluations of child nodes.

### 🔍 Implementing Minimax with Recursion

This section delves into the implementation of the minimax algorithm through a recursive function. The function takes the current position, search depth, and a boolean indicating the maximizing player. It first checks if the depth is zero or the game is over, returning the static evaluation in these cases. For the maximizing player, the algorithm seeks the highest evaluation by initializing a variable to negative infinity and recursively calling minimax on child nodes. For the minimizing player, it initializes to positive infinity and recursively finds the lowest evaluation. The algorithm alternates between these two processes, returning the best evaluation found for the current position.

### 🏁 Enhancing Minimax with Alpha-Beta Pruning

The paragraph discusses how the minimax algorithm can be optimized using alpha-beta pruning. This technique eliminates branches in the search tree that cannot possibly influence the final decision. The algorithm uses two parameters, alpha and beta, to track the best scores achievable by the maximizing and minimizing players, respectively. As the algorithm traverses the tree, it updates these parameters and prunes branches that are guaranteed not to be explored due to better alternatives being available. The paragraph provides an example to illustrate how pruning works in practice, showing how it can significantly reduce the number of nodes evaluated and thus speed up the search process.

### 🌟 Conclusion and Historical Context

The final paragraph concludes the discussion on the minimax algorithm and its enhancement through pruning. It highlights the importance of the algorithm in the context of game-playing AI, mentioning a historical milestone where a computer defeated a reigning world chess champion using these techniques. The paragraph leaves the audience with a sense of the algorithm's significance and its impact on the development of AI in games.

### Mindmap

### Keywords

### 💡minimax

### 💡alpha-beta pruning

### 💡search algorithm

### 💡static evaluation

### 💡turn-based game

### 💡recursion

### 💡maximizing player

### 💡minimizing player

### 💡game tree

### 💡depth

### Highlights

Explaining the minimax algorithm used in game theory for turn-based games like chess.

The algorithm allows the program to look ahead at possible future positions before making a move.

Each position has two possible moves, visualized as branches leading to new positions.

The tree of moves is expanded until the end of the game or a stopping criterion is met.

Static evaluation estimates the position's goodness without further moves.

White aims to maximize the evaluation, while Black aims to minimize it.

The minimax function is introduced, which takes the current position, search depth, and the maximizing player into account.

If the depth is zero or the game is over, the position's static evaluation is returned.

Max evaluation is initialized to negative infinity for the maximizing player.

For each child position, a recursive minimax call is made, decrementing the depth.

Max eval is updated to the greatest value found among child positions.

Mini eval is set to positive infinity for the minimizing player, with a similar process to max eval.

The algorithm uses recursion to search through the tree of possible moves.

Alpha-beta pruning is introduced to speed up the minimax algorithm.

Pruning eliminates branches that cannot affect the outcome based on better options available.

Alpha and beta values track the best scores either side can achieve, assuming optimal play from the opponent.

Alpha is updated when a better score for the maximizing player is found.

Beta is updated when a better score for the minimizing player is found.

Pruning occurs when beta is less than or equal to alpha, indicating a better move is available.

The order of moves can affect the efficiency of pruning; ideally, moves should be ordered from best to worst.

The minimax algorithm with alpha-beta pruning is a powerful tool for decision-making in games.