Monty Hall Simulation

A Python simulation of the Monty Hall problem to empirically prove the winning probability with and without switching doors.

What is the Monty Hall Problem?

In the Monty Hall problem, a contestant picks one of three doors. Behind one door is a car; behind the others are goats. The host opens a different door revealing a goat, then asks if the contestant wants to switch.

Math result: switching raises your win probability from $\frac{1}{3}$ to $\frac{2}{3}$.

Installation

pip install streamlit

Usage

python main.py 

Sample Output

Winning percentage without switching doors: 33.20%
Winning percentage with    switching doors: 66.50%

Launch the dashboard

streamlit run app.py

Then open http://localhost:8501 in your browser.

Functions

• montyhaal(switch) — simulates a single game. If switch=True, the player switches doors.
• counter(num) — runs num games and returns the win count for each strategy.

Requirements

• Python 3.x — no external libraries needed.
• streamlit