No. 01
🚪Monty Hall
Why switching doors wins twice as often
The setup
- 1Behind one of three doors is a car; behind the other two, goats.
- 2You pick a door. The host — who knows where the car is — opens a different door to reveal a goat.
- 3Now the big question: do you stay with your door, or switch to the other unopened one?
🤔 Intuition says: Two doors left, so it feels like a 50/50 coin flip. Why bother switching?
🎮 Play a round
Pick a door to begin.
📊 Simulate thousands of games
Hand-playing is slow. Let the server play both strategies across many games and compare the win rates.
Why it's a paradox
Your first pick had a 1/3 chance of being right — and a 2/3 chance of being wrong.
The host is constrained: he can never open your door or the car. When your pick is wrong (2/3 of the time), he is forced to leave the car behind the other door.
So switching is really a bet that your original guess was wrong — and that bet pays off 2/3 of the time.
💡 Key insight: The host's knowledge leaks information. Switching converts your likely-wrong first guess into a 2/3 win.
Further reading on Wikipedia →