monty hall

You're on a game show. Three doors — behind one is a car, behind the other two are goats. You pick a door. The host, who knows what's behind each door, opens another door to reveal a goat. Should you switch to the remaining door?

P(win | switch) = 2/3   P(win | stay) = 1/3

Counterintuitively, switching doubles your odds. Your initial pick had a 1/3 chance of being right — the host's reveal doesn't change that. The remaining door absorbs the full 2/3 probability. Play the game below, then run the simulation to watch the numbers converge.

references

Selvin. "A problem in probability." The American Statistician, 1975.

Rosenhouse. "The Monty Hall Problem." Oxford University Press, 2009.