That god damn Monty Hall problem. God damn that thing. God damn it straight to Hell!
I hadn’t never heard of the Monty Hall problem until I saw a Sam Harris lecture in DC a few years ago (got my copy of The Moral Landscape signed, what-what!), and he used it to illustrate how our intuitions can be faulty. I did not at all understand what he was talking about, but I mostly let it go. But as the years went on, I always had that little niggling thought in my head, everyone else in that room knew what he was talking about, and you still don’t.
(I’m not going to explain the entire problem here, go look it up.)
It came up again recently in this BBC piece I stumbled on who-knows-how. And after reading it, I still didn’t get it. And I began to feel very stupid.
So I told Twitter, which I sometimes do because I think maybe I’ll get sympathy or something. Instead, I got a barrage of well-meaning smartypants trying to help me understand it. This only made me defensive and embarrassed, which made it even harder for me to get why “It doesn’t matter if you switch” is wrong. I moved from feeling stupid to feeling like a Grade-A dumbass.
But somehow, through a melding and processing of all that I had by that point digested, I think — I say I think — I finally got it. Here’s why you should always switch:
Chances are, you probably picked a goat the first time, and the odds that you did don’t magically reset when Monty opens a door to reveal another goat. It remains that you still probably picked a goat.
So you should switch. You see? Because you probably picked a goat.
Is that it? Did I get it? I’m still not sure. But I think so.
I should say, there were some good alternate explanations proffered on Twitter:
The solution: punch Monty Hall out, because what kind of sadistic ass gives that choice to another human being?
the point is, no one knows who Monty Hall is any more 😦
Monty Hall’s biggest problem: death.
Marc: If you don’t understand the 1st of 3 explanations, you’re better off switching the next explanation you were planning to read.
Me: I SEE WHAT YOU DID THERE
Marc: Actually your odds of seeing what I did there just went from 33.3% to 50%.
Me: ok stop.
Marc: We have a goat!