The other day while browsing through the archives of Dean’s

World I came across a fascinating little nugget of a post called *The
Brainteaser That Changed My World*. I love brain teasers,

and this one was especially intriguing:

You find yourself on a game show called "Let’s

Make A Deal." The

game is very simple. There are three doors: door #1, door #2, and door #3.

Behind

one door is a million dollars. The other two doors contain worthless joke

prizes. All you have to do is pick which door you want to open, and you get

whatever

is behind it. But you only get to open one door. By simple math, then, you

obviously have a 1 in 3 chance of picking the correct door and becoming an

instant millionaire.You

pick a door. As soon as you tell Monty (the gameshow host) what door you

want to open, he stops and says, "Okay, you’ve made your choice. Now, I’m

going to do what we always do here on this game. I’m going to open one of the

other two doors for you that I know has a booby prize." And he does so.

Then he asks, "Okay, now, would you like to stay with your original

guess, or would you like to switch to the other door that’s still closed?

You only

get one shot, so do you want to stay with your original choice, or switch?"Here’s

the question: is there any compelling reason to switch doors?

Of course not,

I thought. Why would you switch doors? They both have a one in three chance

of being correct, or maybe even a one in two chance, but neither

has a clear advantage over the other.

But then I had an epiphany and thought, “Yes,

by all means switch doors.” Given

that you initially choose one door out of three, the door you choose clearly

has a one in three chance of being correct. The removed door has a zero in

three chance of being correct, which means the third door (the only other door

remaining)

must have a two in three chance of being correct. Nothing could be more obvious,

right?

I explained the problem to a few coworkers, and they all thought I was

insane for insisting that it’s best to switch answers. Dance with the

one that brung ya, they said, especially when there’s no reason to switch

partners, which there’s definitely not. When faced with my irrefutable

logic, they said I was arguing semantics, which doesn’t apply to mathematical

problems.

I don’t remember the last time so many people told me I was

wrong.

So

I came home and shared the story with my wife. She too came to the conclusion

that switching has no advantage over sticking with your first answer, but nevertheless

agreed to help me do a practical test. Before we could perform an experiment,

I was able to pick the brain of my father-in-law, a computer programmer who

has a degree in math. I thought surely he would agree with my conclusion. But

he

said the same thing everyone else did: “I see what you’re saying,

but I still think you’re wrong.” I should note, however, that my

mother-in-law agreed with me. I love her.

Anyway, Mrs. Happy and I set up the

experiment. I took three playing cards (taking the place of the three doors,

which we don’t have), one of which was the

ace of spades (taking the place of the million dollars, which we also don’t

have), and placed them face down. She chose one. I removed one of the other

two that was definitely not the ace of spades. She then changed her choice,

turned

over the remaining card, and marked down whether her first choice or second

choice was correct. We did that 100 times. The first choice turned up the ace

35 times,

and the second choice turned up the ace 65 times. Basically, the first choice

has a one in three chance of being correct while switching will win you the

money two out of every three times. So basically, I was right and everyone

but my mother-in-law

was wrong.

Here’s my point: My wife supported me and didn’t try

to make me feel stupid even when she thought I was dead wrong. She always left

open the

possibility

that I had come to the right conclusion and even took time out of her busy

day to help me perform a tedious test of an inconsequential problem, because

it was

important to me. That, my friends, is a good wife.