# Algorithms Explained β minimax and alpha-beta pruning

TLDRThis video explains the minimax algorithm with alpha-beta pruning, used in turn-based games like chess. It describes how the algorithm evaluates game positions by considering all possible future moves to determine the best current move. The minimax function is introduced, which recursively explores game positions to maximize or minimize scores based on the player's turn. Alpha-beta pruning is then explained as a method to optimize the search process by eliminating branches that cannot influence the final decision, thus saving computational resources.

### Takeaways

- π The minimax algorithm is used for decision-making in two-player, zero-sum games like chess, where one player's gain is another's loss.
- π Minimax works by simulating all possible moves from the current game state to evaluate the best possible outcome.
- π³ It constructs a game tree where each node represents a game state and branches represent possible moves.
- π Minimax uses static evaluation to estimate the value of a game state without making further moves.
- π The algorithm alternates between maximizing and minimizing players to simulate decision-making at each level of the tree.
- π For the maximizing player (e.g., white in chess), the algorithm selects the move that leads to the highest evaluation.
- π½ Conversely, the minimizing player (e.g., black) chooses the move that results in the lowest evaluation for the opponent.
- π Minimax is implemented recursively, with the function calling itself for each child node in the game tree.
- β± Alpha-beta pruning is an optimization technique that reduces the number of nodes evaluated in the minimax algorithm by eliminating branches that cannot possibly influence the final decision.
- π Alpha represents the lowest score the maximizing player can guarantee, while beta represents the highest score the minimizing player can ensure.
- π‘ Pruning occurs when the minimax function identifies that further evaluation of a branch will not change the decision at a higher level of the tree.
- π The effectiveness of alpha-beta pruning depends on the order of move evaluation; ideally, moves should be ordered from best to worst for the maximizing player.

### Q & A

### What is the purpose of a search algorithm in a turn-based game like chess?

-A search algorithm in a turn-based game like chess allows the program to look ahead at possible future positions before deciding on the best move in the current position.

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

-A static evaluation estimates how good a position is for one side without making any more moves, often based on factors like material count in chess.

### How does the minimax algorithm decide which move to choose for white and black?

-White, the maximizing player, chooses the move that leads to the highest evaluation, while black, the minimizing player, selects the move with the lowest evaluation.

### What role does recursion play in the minimax algorithm?

-Recursion allows the minimax algorithm to evaluate deeper levels of the game tree by calling itself to assess future moves, passing the control between maximizing and minimizing players.

### How does alpha-beta pruning optimize the minimax algorithm?

-Alpha-beta pruning skips the evaluation of branches that won't affect the final decision, saving computation time by not exploring suboptimal moves.

### In the example where a position evaluates to +5, why doesn't black explore the other branch?

-Black doesn't explore the other branch because he already has a better option available, which means evaluating the second branch won't affect the outcome.

### What are alpha and beta values in the context of alpha-beta pruning?

-Alpha represents the best score that the maximizing player (white) can guarantee, and beta represents the best score that the minimizing player (black) can guarantee. These values help determine when to prune branches.

### What happens when beta becomes less than or equal to alpha in alpha-beta pruning?

-When beta is less than or equal to alpha, it indicates that the current branch won't improve the outcome for the player, so the branch is pruned to save computation.

### Why is move ordering important for effective pruning?

-Move ordering is important because pruning occurs more efficiently if the moves are ordered from best to worst for the player, allowing for earlier prunes in the game tree.

### How is the final game outcome affected by alpha-beta pruning?

-Alpha-beta pruning does not change the final outcome of the game; it simply speeds up the decision-making process by ignoring branches that wonβt impact the final result.

### Outlines

### π° Introduction to the Minimax Algorithm

The paragraph introduces the concept of a search algorithm in turn-based games like chess. It explains that the algorithm allows a program to look ahead at possible future positions before deciding on a move. The white dot symbolizes a game position with two possible moves, visualized as branches leading to new positions. The tree of moves is expanded until the end of the game or a predetermined depth is reached. At the end of the tree, static evaluation is performed to estimate the position's value for one side without further moves. The example uses a simple chess evaluation where the sum of the values of remaining pieces determines the position's value. The player whose turn it is (white in this case) aims to maximize the evaluation, while the opponent aims to minimize it. The paragraph concludes with a basic implementation of the minimax function, which includes checking for game end or maximum depth, and recursive calls to evaluate child positions.

### π Enhancing Minimax with Pruning

This paragraph delves into optimizing the minimax algorithm through pruning, which eliminates branches that cannot affect the final decision. The example starts by evaluating a position and marking it as a minimum or maximum based on the player's perspective. If a player has a guaranteed better option, branches leading to worse outcomes are pruned, saving computational resources. The paragraph illustrates how pruning works in a tree structure, where certain positions are not evaluated because they are overshadowed by better alternatives. The concept of move ordering is introduced as a strategy to increase the chances of pruning by exploring the most promising moves first. The paragraph concludes with a brief mention of implementing pruning in code by adding alpha and beta parameters to track the best scores that can be achieved, allowing for early termination of unproductive branches.

### π The Impact of Minimax and Pruning in Chess

The final paragraph emphasizes the practical application of the minimax algorithm and pruning in chess, highlighting their significance in computer chess programs. It mentions a historical event where a computer defeated a reigning world champion in classical time controls, attributing part of the success to the efficiency of the minimax algorithm with pruning. The paragraph serves as a conclusion, reinforcing the importance of these techniques in achieving strategic depth in artificial intelligence for games.

### Mindmap

### Keywords

### π‘minimax

### π‘alpha-beta pruning

### π‘turn-based game

### π‘search algorithm

### π‘static evaluation

### π‘maximizing player

### π‘minimizing player

### π‘game tree

### π‘recursion

### π‘depth

### Highlights

The minimax algorithm is a search algorithm used in decision-making and game theory to find the optimal move for a player.

Alpha-beta pruning is a technique to reduce the number of nodes evaluated in the minimax algorithm.

A static evaluation function estimates the value of a game position without making further moves.

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

The minimax function is called recursively to evaluate game positions at different depths.

The algorithm checks if the game is over or if the maximum search depth is reached before making a static evaluation.

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

Mini evaluation is initialized to positive infinity for the minimizing player.

The algorithm loops through all children of a position to find the best move.

Alpha-beta pruning eliminates branches of the search tree that cannot possibly influence the final decision.

Alpha is updated to the highest value encountered for the maximizing player.

Beta is updated to the lowest value encountered for the minimizing player.

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

The order of moves can affect the efficiency of alpha-beta pruning.

Moves should ideally be ordered from best to worst for the player whose turn it is.

The minimax algorithm with alpha-beta pruning is used to find the best move in games like chess.

The algorithm's efficiency is demonstrated through a step-by-step example of a game tree.

Pruning can significantly reduce the computational effort required by the minimax algorithm.