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Old 12-16-08, 09:04 PM   #1
carbonlife
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Oooh, your favorite puzzle question

Siu's mind fart thread reminded me of my favorite puzzle question.

You go on a game show where you have three doors in front of you, and you simply have to pick a door to win a prize. Behind one of the doors is a pot of gold, behind the other two doors are bad prizes, say a couple of jsharr's delicious basses that passed their sell-by date.

You pick Door #1, and the host says "Before we open Door #1, we're going to give you a choice. First, let's open up a door that you did not choose." So they open up Door #3, knowing that a bad prize is definitely behind it (i.e., they will always open a door with a bad prize behind it).

The host says "OK, now you know that the pot of gold is behind Door #1 or Door #2. You can stick with your original choice of Door #1, or you can now switch your choice to Door #2. What do you want to do?"

Should you:

A. Stick with Door #1.
B. It doesn't matter, the odd are 50-50 between Door #1 and Door #2.
C. Switch to Door #2.
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Old 12-16-08, 09:22 PM   #2
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Punch Regis in his big, fat face, and take the money and the bass, of course.
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Old 12-16-08, 09:26 PM   #3
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My answer is B...and I will furiously pummel any logic chopper who tries to convince me that eliminating door 3 affects the odds of door 1 vs door 2.
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Old 12-16-08, 09:40 PM   #4
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Gotta stick with gut instinct. choice A.
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Old 12-16-08, 09:50 PM   #5
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Switch to door number 2. Because they didn't open THAT one for a reason.
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Old 12-16-08, 09:56 PM   #6
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I've been through this fight before, and despite other peoples' insistence that c. gives the best chance of getting the good prize, I disagree and would act as though b is the answer.
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Old 12-16-08, 10:13 PM   #7
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C.
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Old 12-16-08, 10:35 PM   #8
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Yes, of course the answer is "C. Switch to Door #2," but some people will never be convinced.
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Old 12-16-08, 10:42 PM   #9
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But if the gold were indeed behind door #1, they could reveal door #3 (or #2) in the same manner, could they not?

Unless you're taking into account the player paying very close attention to the reaction of Regis and Vanna.
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Old 12-16-08, 10:48 PM   #10
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Yes, of course the answer is "C. Switch to Door #2," but some people will never be convinced.
Why is this the correct answer?
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Old 12-16-08, 11:07 PM   #11
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Why is this the correct answer?
When you choose Door #1, you know you have a 1/3 chance of being right. There is a 2/3 chance of the prize being behind one of the other two doors (i.e., if you could open both doors). When one of those doors (#2 or #3) is opened, your odds don't change, they simply reveal which of those two doors doesn't have the prize. If they open Door #3, and you then switch to Door #2, you have both Door #2 and Door #3 open, and there is a 2/3 chance of the prize being revealed.

It is easy enough to demonstrate. Play the game three times (assume that's enough iterations to give each door a 1/3 chance):

Game 1: Prize is behind Door #1
Choose Door #1. Door #2 or #3 opened, you switch and Lose.

Game 2: Prize is behind Door #2
Choose Door #1. Door #3 opened, you switch and Win.

Game 3: Prize is behind Door #3
Choose Door #1. Door #2 opened, you switch and Win.



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I think your puzzle was originally referred to as the monty hall problem
Ah, I think you're right.

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i remember reading someone using the theory of cognitive dissonance and a study involving monkeys and three colors of m & m's to prove it was to switch doors....

Last edited by carbonlife; 12-17-08 at 02:55 AM. Reason: typo
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Old 12-16-08, 11:58 PM   #12
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.....I came across it a few months ago......I just found it again....the first article
Fantastic! I didn't actually realize it was that famous a problem. Great article, thanks for the link!
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Old 12-17-08, 01:11 AM   #13
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When you choose Door #1, you know you have a 1/3 chance of being right.....
Heh. So I'm not so stupid AFTER all..
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Please dont outsmart the censor. That is a very expensive censor and every time one of you guys outsmart it it makes someone at the home office feel bad. We dont wanna do that. So dont cleverly disguise bad words.
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Old 12-17-08, 02:48 AM   #14
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Yes, of course the answer is "C. Switch to Door #2," but some people will never be convinced.
You're right about switching, and you're probably right about people never being convinced.

Another way to look at it:

When you made your choice, you had a probability of 1/3 of being correct, and the odds of the prize being behind one of the other doors is thus 2/3. That doesn't change...even after one of the other doors is opened. You still have a probability of 1/3 that your original choice was correct. But...now you know a door that isn't correct, so the probability of the other, unopened one, being correct is 2/3.
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Old 12-17-08, 02:54 AM   #15
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Switch to door number 2. Because they didn't open THAT one for a reason.
No, stick with door number 1, because they opened another door to get you off the trail of door number 1, that's the one with the pot of gold.
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Old 12-17-08, 08:42 AM   #16
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I like this problem. The answer is, of course C and was explained well by a couple of posters.

What makes this problem fascinating is how different some brains work. I am not suggesting that some are better than others but people are just wired differently.

The key to this problem is that the host knew the second door he opened did not contain the big prize. If the host had no idea, then the odds do remain the same. Of course, the contest would not be run this way as there would be a chance he opened the wrong door and the game is over.

More reading here http://www.marilynvossavant.com/articles/gameshow.html
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Old 12-17-08, 10:14 AM   #17
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D) The backstage crew is going to roll the pedastal with a rotten fish on it behind whichever door you choose, regardless of your logic.

Why do you think the host of the show makes sure there's a nice long pause before the reveal?
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Old 12-17-08, 10:15 AM   #18
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My bass are full of gold, just so you know.
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Phobias are for irrational fears. Fear of junk ripping badgers is perfectly rational. Those things are nasty.
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Old 12-17-08, 10:18 AM   #19
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Doesn't matter. The pot of gold is on casters, and the bathing suit chics will move it to whichever door I don't choose.

edit: Crap...I see Clifton was ahead of me on this one.
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