Monty Hall Simulator

CIS220 Sample code that implements a Monty Hall simulator to demonstrate probability theory and statistical analysis.

🎯 The Problem

The Monty Hall problem is a famous probability puzzle based on the game show "Let's Make a Deal." Here's how it works:

Given three doors where a random door contains a prize and the other doors do not:

1. The player selects a door at random
2. Another non-winning door is exposed (revealing no prize)
3. The player has the choice to change their mind or stick with their original choice

The Question: Does changing your mind affect the probability of winning?

🧮 Probability Theory

The Counterintuitive Answer

• Sticking with original choice: 1/3 probability of winning (33.33%)
• Changing your choice: 2/3 probability of winning (66.67%)

This result often surprises people because it seems like there should be a 50-50 chance after one door is revealed. However, the key insight is that the host's action of revealing a door provides additional information that changes the probability distribution.

Mathematical Explanation

When you first choose a door:

• Probability of choosing the correct door: 1/3
• Probability of choosing an incorrect door: 2/3

If you initially chose incorrectly (2/3 probability), the host must reveal the other incorrect door, leaving only the correct door. Therefore, switching gives you a 2/3 chance of winning.

🚀 Features

• Statistical Simulation: Run thousands of game rounds to verify theoretical probabilities
• Two Strategies: Compare "stick" vs "switch" strategies
• Detailed Analysis: Track win rates, loss rates, and statistical significance
• Educational Value: Demonstrate probability concepts through practical simulation
• Gradle Build System: Modern Java project structure with dependency management

🛠️ Installation and Setup

Prerequisites

• Java JDK 8 or higher
• Gradle (latest version recommended)

Building the Project

1. Clone the repository:

   git clone https://github.com/vramdhanie/montyhall.git
   cd montyhall
   

2. Build the project:

   gradle build
   

3. Run the simulator:

   gradle run
   

🏗️ Project Architecture

Technology Stack

• Java: Core programming language for the simulation engine
• Gradle: Build system and dependency management
• JUnit: Testing framework for validation
• Statistics: Mathematical calculations and probability analysis

Project Structure

montyhall/
├── src/
│   └── com/vincentramdhanie/montyhall/
│       ├── MontyHall.java          # Main simulation logic
│       ├── Game.java               # Individual game implementation
│       ├── Player.java             # Player strategy implementation
│       └── Statistics.java         # Statistical analysis utilities
├── test/
│   └── com/vincentramdhanie/montyhall/
│       └── MontyHallTest.java      # Unit tests
├── build.gradle                    # Gradle build configuration
├── gradle.properties               # Gradle settings
└── README.md                       # Project documentation

🎮 How the Simulation Works

Game Flow

1. Initialization: Three doors are set up, one randomly contains a prize
2. Player Choice: Player selects one door at random
3. Host Action: Host reveals one of the remaining doors (always a non-prize door)
4. Player Decision: Player chooses to stick with original choice or switch
5. Result: Outcome is recorded and statistics are updated

Strategy Comparison

The simulator runs two parallel strategies:

• Strategy A: Always stick with the original choice
• Strategy B: Always switch to the remaining unopened door

Statistical Analysis

• Sample Size: Configurable number of game rounds
• Win Rates: Calculate success percentages for each strategy
• Confidence Intervals: Statistical significance of results
• Variance Analysis: Measure consistency of outcomes

📊 Expected Results

Theoretical Probabilities

• Stick Strategy: 33.33% win rate
• Switch Strategy: 66.67% win rate

Simulation Validation

Running the simulator with a large number of rounds (e.g., 100,000) should produce results very close to these theoretical values, demonstrating the power of statistical simulation in validating mathematical concepts.

🔧 Development Features

Code Quality

• Object-Oriented Design: Clean separation of concerns
• Unit Testing: Comprehensive test coverage with JUnit
• Documentation: Clear code comments and documentation
• Error Handling: Robust error handling and validation

Build System

• Gradle Integration: Modern Java build system
• Dependency Management: Automated dependency resolution
• Testing Integration: Automated test execution
• Build Automation: Consistent build process across environments

🎓 Educational Value

Learning Objectives

• Probability Theory: Understanding conditional probability
• Statistical Simulation: Using computers to validate mathematical concepts
• Critical Thinking: Questioning intuitive assumptions
• Mathematical Proof: Connecting theory to practical results

Classroom Applications

• Statistics Courses: Demonstrate probability concepts
• Computer Science: Show simulation and testing techniques
• Mathematics: Connect theoretical and applied probability
• Psychology: Explore cognitive biases and intuition

🚀 Future Enhancements

Potential Improvements

• Web Interface: Interactive web-based simulation
• Visualization: Charts and graphs of results
• Multiple Strategies: Additional player strategies
• Advanced Statistics: More sophisticated statistical analysis
• Real-time Simulation: Live demonstration of games
• Mobile App: Android/iOS application

Extensions

• Different Door Counts: Explore with 4, 5, or more doors
• Host Behavior: Vary host's door selection strategy
• Player Psychology: Model different decision-making patterns
• Historical Analysis: Track performance over time

🤝 Contributing

Contributions are welcome! This project serves as both an educational tool and a demonstration of good Java programming practices.

1. Fork the repository
2. Create your feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add some amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

📝 License

This project is licensed under the MIT License - see the LICENSE file for details.

👤 Author

Vincent Ramdhanie

• GitHub: @vramdhanie
• Website: vincentramdhanie.com

📊 Project Status

This project was originally created for CIS220 coursework and has been updated with modern build tools. It serves as both an educational resource and a demonstration of Java programming skills.

About

CIS220 Sample code that implements a Monty Hall simulator to demonstrate probability theory and statistical analysis.