# The Monty Hall Problem

A simple brain teaser that stumped one of history’s most prolific mathematicians.

The Monty Hall problem is a probability puzzle based on the American television show *Let’s Make a Deal*. The problem was created and solved by Steve Selvin in 1975 in a letter he wrote to the scientific journal *American Statistician*.

Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, and goats are behind the other two. You pick a door, say the first door, and the host, who knows what’s behind the doors, opens another door, say the third door, which has a goat. He then says to you, “Do you want to pick the second door instead?” Is it to your advantage to switch your choice?

Counter intuitively, the answer is yes. You double your odds of winning by switching to the other door.

Paul Erdős, a Hungarian mathematician, was known for being a genius and for being a bit of an oddball. His contributions to mathematics are enormous, and to this day he is so adored by mathematicians that they keep track of their Erdős number, the number of “hops” needed to connect the author of a paper to him (An author’s Erdős number is 1 if he has co-authored a paper with Erdős, 2 if he has co-authored a paper with someone who has co-authored a paper with Erdős).