Pick a door!
Behind one door is a car. The other two have goats. Click a door to choose!
Wins: 0Losses: 0Switched: 0Stayed: 0
Monty Hall Problem
Experience the famous Monty Hall probability puzzle interactively. Pick one of three doors, watch the host reveal a goat, and decide whether to switch or stay. The game tracks your wins, losses, and switch/stay ratio so you can see the counter-intuitive 2/3 probability advantage of switching play out over time.
Frequently Asked Questions
- What is the Monty Hall problem?
- The Monty Hall problem is a famous probability puzzle based on the TV game show 'Let's Make a Deal.' You pick one of three doors. The host, who knows what's behind each door, opens another door to reveal a goat. You then choose whether to stick with your original pick or switch to the remaining door. Statistically, switching gives you a 2/3 chance of winning the car.
- Should I switch or stay?
- You should switch! When you first pick a door, you have a 1/3 chance of picking the car. The host always reveals a goat, so switching gives you a 2/3 chance of winning. Play many rounds and check your stats to see this probability in action.
- Why does switching work?
- When you first choose, there's a 1/3 chance your door has the car and a 2/3 chance the car is behind one of the other two doors. When the host reveals a goat behind one of those two doors, the entire 2/3 probability transfers to the remaining unopened door. So switching doubles your odds.
- Is the Monty Hall simulation fair?
- Yes! The car is placed randomly behind one of the three doors using a uniform random generator. The host always reveals a door with a goat that you didn't pick, exactly like the original problem.
- Does the game track my statistics?
- Yes, the game tracks your total wins, losses, how many times you switched vs. stayed, and your overall win rate. Stats are saved in your browser so they persist between visits.