Behind one door is a car. Behind the other two are goats. Pick a door, watch the host reveal a goat, then decide: stick or switch?
Want to see the law of large numbers in action? Run the simulation automatically:
When you first pick a door, there's a 1/3 chance you've picked the car and a 2/3 chance the car is behind one of the other two doors.
The host then must open a door with a goat — this is the crucial constraint. He can never reveal the car, and he can never open your door. So that entire 2/3 probability that was split across two doors now collapses onto the single remaining door.
Staying gives you your original 1/3 odds. Switching gives you 2/3. Play enough rounds above, and you'll see the numbers converge on exactly this.