Monty Hall

I've never watched the show but he did give rise to the epic "Monty Hall" problem in mathematics (probability theory really but it also has implications in the field of game theory and information theory.)

Here's the problem:

There are three doors labelled 1, 2, 3. Behind one of them is a car, the other two are empty. Pick a door. Now the host shows you a door different than the one you picked and opens it and shows you that it is empty. Should you switch doors or keep the one that you picked?

It's entirely non-obvious. Even when shown the solution mathematicians frequently react with horror.

Let me give you two re-phrasings of the problem:

Two couples go to the baseball game. Within each couple group, one of them likes spicy burritos and the other one non-spicy. They are seated far apart unfortunately and the burrito shop hasn't labelled the four burritos so they each just grab one at random. What is the chance that they all end up happy?

Perhaps the most perfect re-statement is the following:

I have two black socks and two white socks in a drawer. It's dark outside and I grab two socks without looking. What is the chance that they match?

I'll let you work out all three of them. (They're basically the same problem in disguise.)

My favorite part is that the statement "Isn't this just Monty Hall in disguise?" has entered mathematical folklore.

(The restatements do have implications on the implied subjects of game theory and information theory though. They are still the same basic problem though.)

Amazing.

May we all be so lucky.

R.I.P.