Interactive Monty Hall Problem Explorer

Educational game demonstrating conditional probability through interactive MATLAB app

Overview

Project Repository Video Demo

An interactive MATLAB application that teaches conditional probability through the famous Monty Hall problem, transforming a counterintuitive mathematical concept into an engaging, hands-on learning experience.

Educational Focus: Conditional Probability, Game Theory, Interactive Learning

How It Works

The game provides:

  • Three-door interface: Classic Monty Hall setup with interactive gameplay
  • Real-time statistics: Track win/loss ratios for “stay” vs. “switch” strategies
  • Immediate feedback: See results after each round
  • Multiple rounds: Build statistical evidence through repeated trials

Why Interactive Demos Matter

The Monty Hall problem is famously counterintuitive—most people incorrectly assume 50/50 odds after a door is revealed. Mathematical proofs alone rarely convince. This game lets you play repeatedly and see the empirical evidence: switching wins ~67% of the time, staying wins ~33%.

Using the Game

  1. Choose a door where you think the prize is hidden
  2. Host reveals a non-winning door
  3. Decide whether to switch or stay with your original choice
  4. See the result and watch statistics accumulate
  5. Play multiple rounds until the pattern becomes clear

The Mathematics

When you first choose, you have 1/3 chance of being correct. The host, knowing where the prize is, reveals a non-winning door from the remaining two. Now:

  • If you stay: still 1/3 chance of winning
  • If you switch: 2/3 chance of winning

Switching is optimal because the host’s action provides information that updates the probabilities.

Educational Value

Students gain:

  • Conditional probability understanding through hands-on experience
  • Statistical evidence appreciation via large sample sizes
  • Cognitive bias awareness by confronting counterintuitive results
  • Computational thinking: Monte Carlo simulation for probability demonstration

This experiential approach transforms abstract probability theory into memorable, visceral understanding.

Repository & Resources

All source code, documentation, and educational materials are available in the GitHub repository, enabling educators to adapt and extend the tool for their specific teaching needs.