Monty Hall Problem has struck again

Discussion in 'Science and Technology' started by midcan5, Apr 10, 2008.

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midcan5liberal / progressive

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I have always been fascinated by game theory and rational choice theories. How is it we make decisions particularly ones that involve choice or doubt. Thought this worth sharing.

Monty Hall Problem has struck again

"Here&#8217;s how Monty&#8217;s deal works, in the math problem, anyway. (On the real show it was a bit messier.) He shows you three closed doors, with a car behind one and a goat behind each of the others. If you open the one with the car, you win it. You start by picking a door, but before it&#8217;s opened Monty will always open another door to reveal a goat. Then he&#8217;ll let you open either remaining door.

Suppose you start by picking Door 1, and Monty opens Door 3 to reveal a goat. Now what should you do? Stick with Door 1 or switch to Door 2?"

http://www.nytimes.com/2008/04/08/science/08tier.html

http://www.nytimes.com/2008/04/08/science/08monty.html

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GunnyGold Member

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I'd stick with the one I originally chose. You can second-guess all you want, but all it ever comes up as is a guess. Second-guessing, in my opinion and based on my personal experience, usually leads to a wrong choice with the original choice being correct.

There really is no rational choice in such a game. It's random choice as no pattern is established. At least as far as I recall from the show, there was no real pattern estblished to which door the booby prize was behind.

The odds on the show were different though. IIRC, there were two good prizes and one boooby prize, not one good one and two bad ones. It's just that one of the good ones would be like a car while the other would be more like consolation furniture.

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RetiredGySgtDiamond Member

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Yup a total guess, no reason at all to change your choice.

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midcan5liberal / progressive

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interesting as you're both wrong.

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GunnyGold Member

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I was kind enough to answer your question. Would be nice if you could explain why it is you believe I am wrong.

If their was something to the show that made the choice not random, I don't recall. Not that I have even SEEN it in 40 years.

Oh, and I cannot be wrong insofar as my opinion concerning second-guessing and my personal experience goes. If you hump a rifle for a living, that can get you dead REAL quick.

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jillianPrincessSupporting Member

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I changed my choice each time. That netted me about a 70% or so win rate.

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FoxfyreEternal optimistGold Supporting MemberSupporting Member

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I changed my choice each time which netted me about 33% or win rate. I don't really understand that if a goat is revealed behind a door you didn't pick how there isn't a 50%-50% chance that you picked the right door. Seems like if there is a truly random distribution, over time you would wind up right approximately 50% of the time.

Maybe you guys who are math whizzes can show me the logic of my reasoning here.

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jillianPrincessSupporting Member

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I'm not a math whiz by any stretch of the imagination. But I kind of like statistics (as opposed to, say, geometry or algebra). The way it supposedly works is that on your first choice, you have a 1 in 3 chance of being correct. Once one choice is eliminated, the odds are reduced to a 1 in 2 chance of you being correct, so you go from a 33% chance of being correct if you don't change your choice to a 50% chance. So without changing your choice, you would generally be right 33% of the time. I'm probably not explaining it very well.... but that's the best I can figure

• Thank You! x 1
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GunnyGold Member

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I don't get that reasoning. If you have a 33% chance of being right with 3 choices, and one choice is eliminated, leaving two choices and one of them is yours, it stands to reason you then have a 50% chance of being right whether you change your choice or not. You still have chosen between what is now two options.

Nor do I see where mathematics and/or science come into play unless there is a pattern established as to which door the goats are usually behind/which door the prize is behind.

Perhaps Midcan will come along and enlighten us.

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LarkinnSenior Member

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Its not that hard to explain, or understand. Intuitively it makes no fucking sense, it just happens to be right thats all.

Ok. Imagine you are picking between 3 doors. Now there is a 33% chance of picking the right door. So, you choose one and there is a 33% chance of it being there and a 66% chance of it being in the other 2. But, one of the other 2 is then eliminated and shown there is nothing in it. Remember that *nothing has changed from your original probability of your guess*. It makes no sense that showing that another door is wrong somehow increases the probability of your original guess being right.

Take, for example, the game Deal or No Deal. Lets assume there are 50 different suitcases (no idea how many are actually there). If you pick a random suitcase hoping that the \$1 mil will be in there, you have a 2% chance of getting the right one. Now, assume you pick #1 as the right suitcase. Remember there is a 2% chance of it having 1 mil. Now, the person who runs the game shows you that the \$1mil is NOT in boxes 3-50. So, it can only be in box 1 or box 2. The action of opening up boxes known to not contain the \$1 mil cannot raise the probability of you picking the 1 mil when you first picked it.

Its not intuitive and takes a while to grasp, but its definitely the case that you should switch if Monty asks you if you want to switch. Probability theory is sort of a bitch.

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