### Game Tree AnalysisThe diagram presented is a game tree used to illustrate the minimax algorithm, which is a decision-making algorithm used in artificial intelligence, particularly in game theory.#### Structure of the Game Tree- **Levels of Nodes:** - The tree consists of four levels. - **Top Level (Root):** A single square node. - **Second Level:** Circle nodes. - **Third Level:** Square nodes. - **Bottom Level:** Contains numerical values.- **Leaf Nodes (Bottom Level):** - Numerical values from left to right are: 7, 4, 2, 3, -1, -2, 3, -1, 4, 5, 5, 7, 8.- **Nodes Explanation:** - **Circles** represent MAX nodes, aiming to maximize the value. - **Squares** represent MIN nodes, aiming to minimize the value.### Questions1. **Maximizing Strategy:** - "If the circles are MAX nodes and the squares are MIN nodes, what is the minimax value of this game tree?" - Respond with the calculated minimax value.2. **Position Analysis:** - "Does it look like a position that is more likely to be a win for MAX or for MIN?" - Select between MAX or MIN as the favorable position.3. **Reversed Strategy:** - "If instead the squares are MAX nodes and the circles are MIN nodes, what is the minimax value of this game tree?" - Provide the alternative minimax value.### Analysis Instructions- Analyze the tree from the bottom up, determining the MAX and MIN values at each level.- Apply the minimax algorithm accordingly, switching between maximization and minimization at each level transition.This visual representation serves to understand the intricacies of decision-making in competitive environments and illustrates basic principles of AI strategy formulation.

If the circles are MAX nodes and the squares are MIN nodes, the minimax value is 4. It looks like a…

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If the circles are MAX nodes and the squares are MIN nodes, what is the minimax value of this game tree?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

### Game Tree Analysis

The diagram presented is a game tree used to illustrate the minimax algorithm, which is a decision-making algorithm used in artificial intelligence, particularly in game theory.

#### Structure of the Game Tree
- **Levels of Nodes:**
- The tree consists of four levels.
- **Top Level (Root):** A single square node.
- **Second Level:** Circle nodes.
- **Third Level:** Square nodes.
- **Bottom Level:** Contains numerical values.

- **Leaf Nodes (Bottom Level):**
- Numerical values from left to right are: 7, 4, 2, 3, -1, -2, 3, -1, 4, 5, 5, 7, 8.

- **Nodes Explanation:**
- **Circles** represent MAX nodes, aiming to maximize the value.
- **Squares** represent MIN nodes, aiming to minimize the value.

### Questions

1. **Maximizing Strategy:**
- "If the circles are MAX nodes and the squares are MIN nodes, what is the minimax value of this game tree?"
- Respond with the calculated minimax value.

2. **Position Analysis:**
- "Does it look like a position that is more likely to be a win for MAX or for MIN?"
- Select between MAX or MIN as the favorable position.

3. **Reversed Strategy:**
- "If instead the squares are MAX nodes and the circles are MIN nodes, what is the minimax value of this game tree?"
- Provide the alternative minimax value.

### Analysis Instructions
- Analyze the tree from the bottom up, determining the MAX and MIN values at each level.
- Apply the minimax algorithm accordingly, switching between maximization and minimization at each level transition.

This visual representation serves to understand the intricacies of decision-making in competitive environments and illustrates basic principles of AI strategy formulation.

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