Door.

After one door opens, should you switch?

One door hides the crumb. Pick a door. One of the others will open, and it will always be empty. Then you can stay, or switch.

STAYED

SWITCHED

Filled dots found the crumb. Hollow ones didn’t.

THE BREADCRUMB

Who else got stuck here

Joseph Bertrand1889Posed a puzzle about three boxes and gold coins that trips up the same instinct: new information changes the odds in ways that feel wrong.

Steve Selvin1975A statistician who wrote the door puzzle up in a letter to The American Statistician, naming it after Monty Hall, the host of the game show Let’s Make a Deal.

Marilyn vos Savant1990Answered it in her magazine column: switch. Thousands of readers wrote in to say she was wrong, many of them with doctorates. She wasn’t.

Paul ErdősAround 1990One of the great mathematicians of the century, who reportedly stayed unconvinced until he watched a computer play it out many times.

STILL OPEN

The maths is simple. So why does nearly everyone’s instinct say it doesn’t matter, even after seeing the answer?