Monty has a problem

A faux tweet mentioned that mathematical conundrum known as the Monty Hall Problem. As the New York Times once intoned in its deepest, most conventionally wise voice:

[The Monty Hall Problem] has been debated in the halls of the Central Intelligence Agency and the barracks of fighter pilots in the Persian Gulf. It has been analyzed by mathematicians at the Massachusetts Institute of Technology and computer programmers at Los Alamos National Laboratory in New Mexico. It has been tested in classes from second grade to graduate level at more than 1,000 schools across the country.

The famous issue is whether to switch doors once Monty has revealed a zonk behind one of the doors you didn't select.

The famous answer is that you gain a real advantage by switching. This website, naturally named montyhallproblem.com, makes the counterintuitive answer obvious by creating a wildly exaggerated version of the problem:

Imagine that there were a million doors. Also, after you have chosen your door; Monty opens all but one of the remaining doors, showing you that they are "losers." It’s obvious that your first choice is wildly unlikely to have been right. And isn’t it obvious that of the other 999,999 doors that you didn’t choose, the one that he didn’t open is wildly likely to be the one with the prize?

Well, now that you put it that way...

I once saw a fellow actuary try to explain the problem to a disbelieving audience of non-actuaries. Let me tell you, it's hard to convince people. And it's not every game show that creates a math problem all its own.