Pick a door. The host, who knows what's behind every door, reveals a goat one at a time, and you get a stay-or-switch decision after each reveal, right up until only two doors remain.
Setting up the game engine (loading Python in your browser)…
Pick a door to begin.
Click a closed door to hold it. After each reveal, click your current door to stay or another closed door to switch.
Your results
Games played0
Stay → Stay0 / 0 (N/A)
Stay → Switch0 / 0 (N/A)
Switch → Stay0 / 0 (N/A)
Switch → Switch0 / 0 (N/A)
Decision Tree
Top row: which door hides the car. Your most recent round is highlighted below.
Simulation results
Trials per strategy0
Stay → Stay0 / 0 (N/A)
Stay → Switch0 / 0 (N/A)
Switch → Stay0 / 0 (N/A)
Switch → Switch0 / 0 (N/A)
Stay → StayN/A
Stay → SwitchN/A
Switch → StayN/A
Switch → SwitchN/A
The Monty Hall Problem (Four Doors)
There are four doors. One hides a car, the other three hide goats. You pick a door, and the host, who knows what's behind each one, reveals a goat. You decide: stay, or switch to one of the two other closed doors.
The host then reveals one more goat, leaving only two doors closed: whichever you're holding, and one other. You make a final choice, and that one is revealed.
If you hold your original door the whole way through and switch only at that final choice, you win about three-quarters of the time. That's because your first pick keeps its 1-in-4 chance the entire game, no matter how many goats get revealed, and switching at the end hands you the other 3-in-4 all at once. Switching earlier can still win, but it no longer guarantees that same 3-in-4 edge.
This is a variant of the classic three-door version. Read more about the original on Wikipedia.