# Algorithms Explained – minimax and alpha-beta pruning

TLDRThis video explains the minimax algorithm and alpha-beta pruning, focusing on their application in turn-based games like chess. It introduces how the minimax algorithm evaluates possible future positions to make the best move by recursively analyzing the game tree. The video also demonstrates how alpha-beta pruning speeds up the process by eliminating branches that won't affect the outcome, saving computational resources. The explanation includes examples, a step-by-step breakdown of the algorithm, and insights into how both strategies help improve game performance.

### Takeaways

- 🧠 Minimax is a search algorithm used for turn-based games like chess, allowing a program to predict future positions and determine the best move.
- 🌳 The game positions are visualized as a decision tree, with each move expanding into new positions for the opponent's turn.
- 🔍 At the end of each branch, a static evaluation is performed to estimate how favorable the position is for one player without making further moves.
- 🔄 White tries to maximize the evaluation, while Black attempts to minimize it. This alternating strategy forms the core of the minimax algorithm.
- 🧮 The algorithm assigns values to positions based on their potential outcomes, with White selecting moves that lead to the highest values and Black choosing those with the lowest values.
- 💻 The minimax algorithm uses recursion to evaluate game positions and moves, continually comparing child positions to update the maximum or minimum evaluation.
- ✂️ Alpha-beta pruning improves minimax efficiency by eliminating branches that cannot influence the final decision, saving computational time.
- 🚫 Pruning occurs when a move is determined to be suboptimal compared to other options, allowing the algorithm to skip further evaluation of certain branches.
- 🔄 The order of moves can impact pruning effectiveness, with better results achieved when likely strong moves are evaluated first.
- 📉 Alpha (best score for maximizing player) and Beta (best score for minimizing player) are used in the algorithm to track potential best outcomes and decide when to prune branches.

### Q & A

### What is the main purpose of the minimax algorithm?

-The minimax algorithm helps a program make decisions in turn-based games by simulating possible future positions and selecting the optimal move based on evaluations of those positions.

### How does the minimax algorithm work in terms of evaluation?

-It evaluates the static positions at the leaves of a game tree. White, as the maximizing player, selects moves that maximize the evaluation, while Black, as the minimizing player, selects moves that minimize the evaluation.

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

-A static evaluation is an estimate of how favorable a game position is for one side, without considering further moves. In chess, for example, it could involve adding up the values of all remaining pieces on both sides.

### How does the algorithm decide which moves to pick?

-At each turn, White (the maximizing player) picks the move with the highest evaluation, while Black (the minimizing player) picks the move with the lowest evaluation.

### What is the role of recursion in the minimax algorithm?

-Recursion is used to evaluate game positions at deeper levels of the game tree, passing evaluations back up the tree until the best move for the current position is found.

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

-Alpha-beta pruning reduces the number of positions the minimax algorithm needs to evaluate by eliminating branches of the game tree that can't affect the final decision, thus speeding up the search.

### When does pruning occur in alpha-beta pruning?

-Pruning occurs when the algorithm finds a move that guarantees a better result than a previously evaluated move, allowing it to skip the evaluation of certain branches in the game tree.

### What are alpha and beta in alpha-beta pruning?

-Alpha is the best score that the maximizing player can guarantee so far, while beta is the best score that the minimizing player can guarantee. If beta becomes less than or equal to alpha, further exploration of that branch is pruned.

### Why is move ordering important in alpha-beta pruning?

-Move ordering can affect the efficiency of alpha-beta pruning. If moves are ordered from best to worst for the current player, more pruning can occur, reducing the number of positions evaluated.

### What is the significance of alpha being greater than beta?

-If alpha becomes greater than beta at any point, it means that one player has a guaranteed better move, and further exploration of that branch is unnecessary, leading to pruning.

### Outlines

### ♟️ Understanding Game Search Algorithms in Turn-Based Games

This section introduces how search algorithms are used in turn-based games like chess to evaluate future positions before making a move. The example uses a simple scenario where two possible moves are explored for each position. It explains the concept of static evaluation, where the position is assessed based on the material advantage (e.g., piece values). White tries to maximize the evaluation, while Black aims to minimize it. The process continues with each player selecting the best move until the game ends or the search is cut off due to time constraints.

### 🔄 The Minimax Algorithm Explained

This paragraph explains the Minimax algorithm in detail. It describes how the algorithm is implemented with a recursive function that considers the current position, depth of the search, and whether it is the maximizing player’s turn. The goal is for the maximizing player (White) to find the highest evaluation, while the minimizing player (Black) seeks the lowest. The paragraph provides an example of how positions are recursively evaluated and how the best move is chosen based on the evaluations of future positions.

### ⏩ Speeding Up with Pruning in Minimax

The concept of pruning in the Minimax algorithm is introduced to improve efficiency. The example shows that once a move is found that is better than an opponent’s available options, further exploration of certain branches is unnecessary. By pruning these branches, computation is reduced without affecting the final outcome. The paragraph walks through an example of how pruning can eliminate unnecessary evaluations in the game tree, helping to speed up decision-making.

### Mindmap

### Keywords

### 💡Minimax Algorithm

### 💡Static Evaluation

### 💡Maximizing Player

### 💡Minimizing Player

### 💡Game Tree

### 💡Recursion

### 💡Alpha-Beta Pruning

### 💡Alpha

### 💡Beta

### 💡Depth

### Highlights

The minimax algorithm helps a program playing a turn-based game (like chess) look ahead at future positions before deciding on a move.

A static evaluation function estimates the position's strength without further moves, such as summing up the values of pieces in chess.

White aims to maximize the evaluation score, while Black tries to minimize it in the game decision tree.

The recursive nature of minimax evaluates child positions by alternating between maximizing (White) and minimizing (Black) players.

The algorithm stops either when a certain depth is reached or the game ends, returning a static evaluation of the position.

Alpha-beta pruning speeds up minimax by cutting off branches that won’t affect the final outcome based on earlier evaluations.

Pruning occurs when a player finds a move better than any remaining possibilities, saving computational resources.

Alpha represents the best score that the maximizer (White) can guarantee, and beta represents the best score that the minimizer (Black) can guarantee.

If beta becomes less than or equal to alpha during the search, further exploration down that path is halted (pruned).

The order in which moves are explored affects pruning efficiency—ideally, the best moves should be considered first to maximize pruning.

Moves like capturing pieces in chess should be prioritized as they're likely good moves, which can help initiate pruning early.

Even without pruning, the minimax algorithm ensures that both players will choose the best move available to them at each step.

Pruning only occurs when the order of the moves leads to a branch that won't be chosen due to an earlier better move.

Alpha-beta pruning ensures that the game tree search is more efficient, leading to faster decisions in complex games like chess.

The practical example of pruning in chess showed how it can significantly reduce the number of nodes evaluated while maintaining accuracy.