Do the math or get the goat!

I originally got this story from the wonderful WWW trilogy by Robert J. Sawyer, second book, which is WWW:Watch.  The idea is that you are on “Let’s Make A Deal” and you can pick from one of three doors.  Behind one door is a brand new car.  Behind each of the other two doors is a goat.  You make your choice (door No. 1, 2 or 3) and Monty Hall opens one of the other two doors to reveal – a goat.  Then he says you can change your mind or you can stay with your original choice.  What do you do?

Cancerninja posted this on her tumblr and I see that the scenario was discussed in another book, one I have not read, called The Curious Case of the Dog In The Night, by Mark Haddon.

The point is that every fiber of my being says it doesn’t matter if you change your mind about the remaining two doors.  But Marilyn vos Savant proved that your chances of getting the car go WAY up if you simply change your mind when confronted with the 50/50 proposition.

In WWW:Watch, Sawyer reasoned that the natural selection had not favored the trait of accurately evaluating probability because of the following scenario:  If proto man see a rustling in the bush and there is a 1 in 10 chance the rustling is a hungry tiger, and proto-man plays the odds, 1 in 10 times he will get eaten.  But if proto-man always thinks its a tiger, he will be wrong 9 out of ten times, but he will still be alive.

Anyway, here is vos Saavant’s proof, as reprinted in the Cancerninja post:

I have no idea what any of that means, but it looks awfully cool.  Would you have thought that changing your mind would have improved your odds of getting the car?

And remember, all of this starts with the basic assumption that you don’t want a goat.