You are not as smart as you think

2 Apr

I could be the last numbers geek on earth to have heard of the “Monty Hall Problem,” but it was mentioned on Joe Posnanski’s blog this week and it effectively broke my brain in half for the better part of a day. And since I enjoyed thinking myself a halfwit so goddamn much, I’m going to generously pass that feeling on to you. You’re welcome.

Here’s the question, in Joe’s words:

OK, so, there are three curtains. Behind one is a a great prize – let’s say a season baseball pass for every stadium in the big leagues. And behind the other two are lousy prizes – let’s say a four-hour mandatory lunch with Bud Selig and Gene Orza.

OK, you choose your curtain – for simplicity, we’ll say that you choose what’s behind Curtain No. 1. And Monty goes: Well, before we see what’s behind your curtain, let’s show you what’s behind Curtain No. 3! And they pull back the curtain and there are Selig and Orza, and Bud is yapping about how he wanted mandatory drug testing but the player union would not allow it, and Orza is blabbing about players rights and the irresponsibility of owners and so on.

Now, Monty gives you an option. He says that you can stay with Curtain No. 1 or switch to Curtain No. 2.

So what do you do?

A: Stick with Curtain No. 1.
B: Switch to Curtain No. 2
C: It doesn’t matter because there is an equal chance the prize is behind either curtain.

The answer, somehow, is option B. You always switch. I know it’s completely counterintuitive to your kneejerk reasoning skills, but it’s true. This is insane to me, and I’m sure I’m not the only one. In fact, I’m sensing that my phD-having scientist friend is going to have an honest-to-god mental breakdown while trying to rationalize this answer. I may never see him again. He could very well go Bobby Fisher on us. 

To help defend against that very real possibility, I’ll provide the best reasoning I’ve read so far, featured in the comments section of a following Joe Poz post:

If the prize is behind A:
If you pick A, Monty shows B or C, switch and lose.
If you pick B, Monty shows C, switch and win.
If you pick C, Monty shows B, switch and win.

If the prize is behind B:
If you pick A, Monty shows C, switch and win.
If you pick B, Monty shows A or C, switch and lose.
If you pick C, Monty shows A, switch and win.

If the prize is behind C:
If you pick A, Monty shows B, switch and win.
If you pick B, Monty shows A, switch and win.
If you pick C, Monty shows A or B, switch and lose.

6 out of 9 times, if you switch you win.
3 out of 9 times, if you switch you lose.

There. Does that help rationalize this maddening brainteaser? No? Join the club.

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