The Monty Hall Problem
Steve Selvin, popularised by Marilyn vos Savant · 1975 / 1990
The puzzle
Three doors. A car behind one, goats behind the others. You pick a door. The host, who knows where the car is, opens one of the other two and reveals a goat. Should you switch?
Note
Yes. Switching wins two-thirds of the time, sticking one-third. Most people refuse to believe this until they see it simulated. The intuition fails because the host’s choice carries information: he was constrained to open a goat door, and that constraint concentrates probability on the door you didn’t pick. Vos Savant published the answer in Parade magazine in 1990 and received thousands of angry letters, including dozens from PhDs in mathematics, before everyone agreed she was right. The paradox isn’t in probability theory but in human reasoning about it. We under-count the role of conditioning on what other agents knew. The same shape lurks in courtroom evidence, medical screening results, and most newspaper graphs about base rates.