Stole this from the 21 script
We're gonna call this the game show host problem, all right? Ben, suppose you're on a game show. And you are given a chance to choose
from three different doors, all right?
Now, behind one of the doors is a new car. Behind the other two, goats.Which door would you choose, Ben? Door number one?
Door number one.
Ben chooses door number one. All right, now, the game show host,who, by the way, knows what's behind all the other doors, decides to open another door.
Let's say he chooses door number three.
Behind which sits a goat. Now...
Ben, game show host comes up to you. He says, "Ben, do you want to stay
with door number one "or go with door number two?"
Now, is it in your interest to switch your choice?
- Yeah.
- Well, wait.
Remember, the host knows where the car is so how do you know he's not playing a trick on you? Trying to use reverse psychology to get you to pick a goat?
Well, I wouldn't really care.
I mean, my answer's based on statistics.
Based on variable change.
Variable change? But he just asked you a simple question.
Yeah, which changed everything.
Enlighten us.
Well, when I was originally asked to choose a door, I had a 33.3% chance of choosing right. But after he opens one of the doors and then re-offers me the choice, it's now 66.7% if I choose to switch. So, yeah, I'll take door number two, and thank you for that extra 33.3%.