Pick a door. The host, who knows what's behind every door, opens a different one to show you a goat. Then you decide: keep your door, or switch to the one still closed?
Setting up the game engine (loading Python in your browser)…
Pick a door to begin.
Click your original door to stay. Click the other closed door to switch.
Your results
Games played0
Stay wins0 / 0 (N/A)
Switch wins0 / 0 (N/A)
Decision Tree
Top row: which door hides the car. Your most recent round is highlighted below.
Simulation results
Games simulated0
Stay wins0 / 0 (N/A)
Switch wins0 / 0 (N/A)
StayN/A
SwitchN/A
The Monty Hall Problem
There are three doors. One hides a car, the other two hide goats. You pick a door. Then the host, who knows what's behind each one, opens a different door to show you a goat.
Now you get to decide: keep your original door, or switch to the other one still closed?
Your first pick has a 1-in-3 chance of hiding the car, and that never changes. But the host's reveal doesn't spread that remaining 2-in-3 chance evenly. It collapses entirely onto the one door you didn't pick and the host didn't open. That's why switching wins about two-thirds of the time, while staying wins only about one-third.