In 1990, a Parade magazine reader sent Marilyn vos Savant a simple game show puzzle: three doors, one car, two goats. Her answer, that you should always switch and double your odds to two thirds, drew roughly 10,000 angry letters, including nearly a thousand from PhDs, and made the front page of the New York Times. Even Paul Erdős refused to accept it until a computer simulation proved it.

This episode explains why the host’s deliberate, knowledge-driven choice concentrates probability in the remaining door, using vos Savant’s million-door analogy and a lottery-ticket comparison. It then digs into the psychology that makes people stick anyway: the endowment effect, status quo bias, and the sharper regret of errors of commission over omission. It also examines the standard assumptions the math depends on, and the variants known as Monty from Hell and Ignorant Monty that flip the answer entirely.

• Why two closed doors are not a 50-50 coin flip when the host knows where the car is
• What a veridical paradox is and why experts fell for the independence assumption
• How pigeons learned to switch faster than human subjects
• The three host constraints required for the two-thirds answer to hold
• What the puzzle suggests about algorithms that curate which doors we see