# Minimax Algorithm in Artificial Intelligence | Minimax Algorithm Explained | AI Tutorial|Simplilearn

TLDRThe video tutorial from Simplilearn's YouTube channel delves into the Minimax algorithm, a pivotal decision-making tool in AI, particularly within Game Theory. It's utilized in two-player games like chess and tic-tac-toe, aiming to select the optimal move assuming both players will act optimally. The video covers the algorithm's properties, including completeness and optimality, and discusses its time and space complexity. A detailed walkthrough of the pseudocode and a practical example illustrate how the algorithm functions to minimize the maximum possible loss, constructing a game tree to evaluate all potential moves and outcomes.

### Takeaways

- 😀 The Minimax algorithm is a decision-making algorithm used in AI, particularly for two-player games like chess, checkers, and tic-tac-toe.
- 🔍 It operates on the principle of minimizing the maximum possible loss by considering all possible moves and outcomes.
- 🌐 The algorithm is based on a backtracking approach that uses depth-first search to explore all nodes of a game tree.
- 🏁 Minimax assumes that both players will play optimally, aiming to maximize their gains while minimizing their losses.
- 📊 It has properties like completeness, optimality, and specific time and space complexity measures related to the depth of the search and branching factor of the game tree.
- 📝 The pseudocode for Minimax involves a function that takes the current game state, search depth, and player type (maximizing or minimizing) as arguments.
- 🔄 If the node is terminal or maximum depth is reached, the function returns a heuristic value; otherwise, it continues to explore recursively.
- 🔝 For a maximizing player, the algorithm initializes the best value to negative infinity and looks for the maximum value among child nodes.
- 🔽 Conversely, for a minimizing player, the best value starts at positive infinity, seeking the minimum value among possible moves.
- 🎯 The algorithm constructs a game tree starting from the current game state, helping to determine the best move for a player in a given game state.
- 💡 The example provided illustrates how Minimax works through a series of moves and countermoves, choosing the path that leads to the optimal outcome.

### Q & A

### What is the Minimax algorithm in AI?

-The Minimax algorithm is a decision-making algorithm used in artificial intelligence, particularly in game theory and decision theory. It is a backtracking algorithm that employs depth-first search to evaluate all possible moves in a game, aiming to minimize the maximum possible loss for the player making the move.

### In which areas of AI is the Minimax algorithm commonly used?

-The Minimax algorithm is commonly used in two-player games such as chess, checkers, and tic-tac-toe, where it helps to determine the best move for a player assuming the opponent will also play optimally.

### What are the properties of the Minimax algorithm?

-The properties of the Minimax algorithm include completeness, optimality, time complexity, and space complexity. Completeness means it will find a solution if it exists. Optimality refers to the algorithm's ability to make optimal moves if both players are playing optimally. Time complexity is of the order of B^M, where B is the branching factor and M is the maximum depth of the game tree. Space complexity is of the order of B*M, following the same principle as depth-first search.

### What is the time complexity of the Minimax algorithm?

-The time complexity of the Minimax algorithm is of the order of B^M, where B is the branching factor of the game tree and M is the maximum depth of the tree.

### How does the Minimax algorithm work in a game tree?

-The Minimax algorithm works by constructing a tree of all possible moves and their outcomes starting from the current game state. It evaluates each move by comparing the values of terminal nodes, with the maximizer choosing the maximum value and the minimizer choosing the minimum value, to determine the best move for the current player.

### What is the role of heuristics in the Minimax algorithm?

-Heuristics play a role in the Minimax algorithm by providing a method to evaluate the value of a node when a terminal node is reached or the maximum search depth is reached. This helps in determining the utility or score for the current player's position.

### How does the Minimax algorithm handle different players' turns?

-The Minimax algorithm handles different players' turns by alternating between maximizing and minimizing values. When it's the maximizer's turn, it sets the best value to negative infinity and looks for the maximum value among child nodes. Conversely, when it's the minimizer's turn, it sets the best value to positive infinity and looks for the minimum value.

### What is the significance of the 'max player' variable in the Minimax algorithm's pseudocode?

-The 'max player' variable in the Minimax algorithm's pseudocode is a Boolean that indicates whether the current player is trying to maximize or minimize their score. It determines the direction of the search: maximizing for the maximizer and minimizing for the minimizer.

### Can you provide an example of how the Minimax algorithm selects the best move in a game?

-In the provided example, the maximizer starts by setting the best value to negative infinity and compares each terminal node's value, choosing the maximum. The minimizer then sets the best value to positive infinity and chooses the minimum value among the remaining options. This process continues until the algorithm reaches the root node, selecting the move that results in the best outcome for the maximizer.

### How does the Minimax algorithm ensure that both players are playing optimally?

-The Minimax algorithm assumes that both players are playing optimally by always choosing the best response to the opponent's move. It simulates all possible game outcomes and selects the move that minimizes the maximum possible loss for the current player, thus ensuring an optimal strategy against an optimal opponent.

### Outlines

### 🎮 Introduction to the Minimax Algorithm in AI

The video introduces the Minimax algorithm, a decision-making strategy in AI, particularly used in game theory and decision theory. It operates as a backtracking algorithm that employs depth-first search to explore all possible moves in a game. The algorithm is designed for two-player games like chess, checkers, and tic-tac-toe. Its goal is to select the best move for the current player, assuming the opponent will also play optimally. The video outlines the agenda for the session, which includes understanding the algorithm, its properties, pseudocode, and its working mechanism. It also promotes a professional certificate program in AI and ML for those interested in mastering these skills.

### 🔍 Deep Dive into Minimax Algorithm's Properties and Pseudocode

This section delves into the properties of the Minimax algorithm, such as completeness, optimality, and its time and space complexity. Completeness ensures a solution is found if it exists, while optimality means the algorithm will find the best move if both players play optimally. The time complexity is expressed as O(B^M), where B is the branching factor and M is the maximum depth of the game tree. The space complexity mirrors that of depth-first search. The pseudocode of the algorithm is explained, detailing how it functions with three arguments: the current node, depth, and whether the current player is maximizing or minimizing. The recursive nature of the algorithm is highlighted, showing how it evaluates nodes and chooses the best move by comparing values against positive or negative infinity, depending on the player's role.

### 🌳 Understanding the Working of the Minimax Algorithm

The video explains the working of the Minimax algorithm through the construction of a game tree, which represents all possible moves and outcomes starting from the current game state. It uses a game tree to analyze and solve games, determining the best move for a player or predicting game outcomes. An example is provided with two players, Max and Min, to illustrate how the algorithm works through the layers of the game tree. The example shows how Max aims to choose the maximum value, while Min seeks to minimize the outcome. The video challenges viewers to find the optimal value in the provided game tree and encourages engagement through comments. It concludes with a call to action for subscriptions and notifications to stay updated with more educational content.

### Mindmap

### Keywords

### 💡Minimax Algorithm

### 💡Game Theory

### 💡Decision Theory

### 💡Backtracking Algorithm

### 💡Depth First Search

### 💡Completeness

### 💡Optimality

### 💡Time Complexity

### 💡Space Complexity

### 💡Game Tree

### Highlights

The Minimax algorithm is a popular decision-making algorithm in AI used in Game Theory and decision Theory.

It is a backtracking algorithm that uses depth-first search to evaluate all possible moves.

The algorithm is commonly used in two-player games like chess, checkers, and tic-tac-toe.

The main goal is to choose the best move for the current player, assuming the opponent also plays optimally.

The algorithm has properties such as completeness, optimality, and specific time and space complexity.

The time complexity is O(B^M), where B is the branching factor and M is the maximum depth of the game tree.

The space complexity is O(B^M), following the same principle as depth-first search.

The pseudocode of the Minimax algorithm includes a function with three arguments: node, depth, and max player.

The algorithm checks if the current node is terminal or if the maximum search depth has been reached.

For the max player, the best value is initialized to negative infinity and updated with the maximum of recursive calls.

For the min player, the best value is initialized to positive infinity and updated with the minimum of recursive calls.

The algorithm constructs a tree of all possible moves and outcomes starting from the current game state.

A game tree is a graphical representation of different moves and results in a game.

Game trees are used to analyze and solve games, determining the best move for a player.

The algorithm strategy involves minimizing the maximum possible loss.

The working of the Minimax algorithm is demonstrated through an example with two players, Max and Min.

The algorithm compares utility values or scores for the maximizer and minimizer at each step.

The optimal move is chosen based on the highest value for the maximizer and the lowest for the minimizer.

The video concludes with a question for viewers to find the optimal value in a provided game tree.

The video encourages viewers to subscribe and engage with the content for more learning opportunities.