Monty Hall Problem

= −

Tap a term to see what it means, or .

Calculate

Example: on a TV show, there is a car behind one of 3 doors. You pick one; the host, who knows where the car is, opens another door, an empty one, and offers you the switch. Should you switch? Change the number of doors and games, or draw again.

Doors d Simulated games Simulation seed

Step by step

What each term means

Chance of Winning by Switching: The probability of getting the car by switching to the door the host left closed. With 3 doors, 2/3.
Complement (1 −): Switching wins exactly when staying loses: if the first pick was wrong, the only other door left closed is the car's.
First-Pick Hit (1/d): The chance that the first pick is already the car, among d doors. Opening empty doors afterwards doesn't change that chance, because the host can always open an empty door.