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Author Topic:   Three Curtains
rstrats
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Posts: 119
Joined: 04-08-2004

 Message 1 of 48 (729241) 06-07-2014 9:16 AM

You are a contestant on a game show. There are three curtains. Behind one of the curtains is a new car. You are asked to choose one of the curtains. Lets say that you choose curtain #1. The host of the show - who knows where the car is so as not to end the game prematurely - opens curtain #3 and of course there is no car behind it. The host now gives you a choice. You can stay with curtain #1 or you can change your choice to curtain #2. The question now is: would it be to your advantage to stay with curtain #1, or would it be to your advantage to change to curtain #2 or would there be no advantage either way?
 Replies to this message: Message 2 by kjsimons, posted 06-07-2014 9:30 AM rstrats has responded Message 5 by ringo, posted 06-07-2014 12:49 PM rstrats has not yet responded Message 9 by faceman, posted 06-07-2014 2:09 PM rstrats has not yet responded

kjsimons
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Posts: 661
From: Orlando,FL
Joined: 06-17-2003

 Message 2 of 48 (729243) 06-07-2014 9:30 AM Reply to: Message 1 by rstrats06-07-2014 9:16 AM

Rstrats, this is simply the Monty Hall problem and your odds of winning increase from 1 in 3 to 1 in 2 if you switch, so the answer is it's to your advantage to switch.
 This message is a reply to: Message 1 by rstrats, posted 06-07-2014 9:16 AM rstrats has responded

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rstrats
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Posts: 119
Joined: 04-08-2004

 Message 3 of 48 (729247) 06-07-2014 10:20 AM Reply to: Message 2 by kjsimons06-07-2014 9:30 AM

Anyone disagree with kjsimons?
 This message is a reply to: Message 2 by kjsimons, posted 06-07-2014 9:30 AM kjsimons has not yet responded

 Replies to this message: Message 4 by Larni, posted 06-07-2014 11:06 AM rstrats has not yet responded Message 6 by Modulous, posted 06-07-2014 1:56 PM rstrats has not yet responded Message 7 by Phat, posted 06-07-2014 2:02 PM rstrats has not yet responded

Larni
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Posts: 3975
From: Liverpool
Joined: 09-16-2005
Member Rating: 7.0

 Message 4 of 48 (729250) 06-07-2014 11:06 AM Reply to: Message 3 by rstrats06-07-2014 10:20 AM

I never really got this when I heard about it.

Once the 3rd option is removed and you have the chance to change it becomes 1 in 2 regardless of whether you change your decision because you are making a decision not to change in the same way the you would need to make a decision to change.

It's just one more way for God to limit our free will

The above ontological example models the zero premise to BB theory. It does so by applying the relative uniformity assumption that the alleged zero event eventually ontologically progressed from the compressed alleged sub-microscopic chaos to bloom/expand into all of the present observable order, more than it models the Biblical record evidence for the existence of Jehovah, the maximal Biblical god designer.
-Attributed to Buzsaw Message 53

The explain to them any scientific investigation that explains the existence of things qualifies as science and as an explanation
-Attributed to Dawn Bertot Message 286

Does a query (thats a question Stile) that uses this physical reality, to look for an answer to its existence and properties become theoretical, considering its deductive conclusions are based against objective verifiable realities.
-Attributed to Dawn Bertot Message 134

 This message is a reply to: Message 3 by rstrats, posted 06-07-2014 10:20 AM rstrats has not yet responded

ringo
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Posts: 15971
From: frozen wasteland
Joined: 03-23-2005
Member Rating: 2.4

 (1)
 Message 5 of 48 (729262) 06-07-2014 12:49 PM Reply to: Message 1 by rstrats06-07-2014 9:16 AM

That car ain't gonna move. My original wild guess is as good as any.
 This message is a reply to: Message 1 by rstrats, posted 06-07-2014 9:16 AM rstrats has not yet responded

Modulous
Member (Idle past 116 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005

 Message 6 of 48 (729271) 06-07-2014 1:56 PM Reply to: Message 3 by rstrats06-07-2014 10:20 AM

There is a 1/3 chance you picked the right answer.

There is a 2/3 chance you picked the wrong answer. Therefore there is a 2/3 chance the car is behind #2 OR #3

Once you are given the additional information it is not behind #3 the state of affairs remains

There is a 1/3 chance you picked the right answer and 2/3 chance you picked the wrong answer. It is not #3, therefore there is a 2/3 probability it is behind #2 and a 1/3 probability of being behind #1.

Therefore, switching doubles your chances of winning a car to 2 in 3.

It is functionally equivalent to being given the choice:

You can either open one curtain or two, which do you choose?

 This message is a reply to: Message 3 by rstrats, posted 06-07-2014 10:20 AM rstrats has not yet responded

 Replies to this message: Message 8 by Phat, posted 06-07-2014 2:05 PM Modulous has responded Message 40 by Larni, posted 06-10-2014 9:18 AM Modulous has acknowledged this reply

Phat
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Posts: 11871
From: Denver,Colorado USA
Joined: 12-30-2003
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 Message 7 of 48 (729272) 06-07-2014 2:02 PM Reply to: Message 3 by rstrats06-07-2014 10:20 AM

Full Monty
I agree that it does not matter if one changes their mind. The host is always gonna eliminate the third option.

“When I use a word,” Humpty Dumpty said, in a rather scornful tone, “it means just what I choose it to mean—nothing more nor less.”

 This message is a reply to: Message 3 by rstrats, posted 06-07-2014 10:20 AM rstrats has not yet responded

Phat
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Posts: 11871
From: Denver,Colorado USA
Joined: 12-30-2003
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 Message 8 of 48 (729275) 06-07-2014 2:05 PM Reply to: Message 6 by Modulous06-07-2014 1:56 PM

Probability Changes Based on Data
 There is a 1/3 chance you picked the right answer and 2/3 chance you picked the wrong answer. It is not #3, therefore there is a 2/3 probability it is behind #2 and a 1/3 probability of being behind #1.
I don't see the math. Once 3 is eliminated, you have a 1 in 2 chance period. The original math no longer applies to the current reality.

“When I use a word,” Humpty Dumpty said, in a rather scornful tone, “it means just what I choose it to mean—nothing more nor less.”

 This message is a reply to: Message 6 by Modulous, posted 06-07-2014 1:56 PM Modulous has responded

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faceman
Member (Idle past 1397 days)
Posts: 149
From: MN, USA
Joined: 04-25-2014

 Message 9 of 48 (729276) 06-07-2014 2:09 PM Reply to: Message 1 by rstrats06-07-2014 9:16 AM

Press Your Luck
I'm not sure, but I bet Michael Larson could have figured it out.
 This message is a reply to: Message 1 by rstrats, posted 06-07-2014 9:16 AM rstrats has not yet responded

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Modulous
Member (Idle past 116 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005

 Message 10 of 48 (729279) 06-07-2014 2:36 PM Reply to: Message 8 by Phat06-07-2014 2:05 PM

Re: Probability Changes Based on Data
 I don't see the math. Once 3 is eliminated, you have a 1 in 2 chance period. The original math no longer applies to the current reality.

I'll show you. We'll do every combo possible, which all occur with equal frequency. You pick 1 every time and you stick.

`1 2 3C1 2 CYou win! 1-0 for sticking1 2 3  C1 2  CYou lose! 1-1 for sticking1 2 3    C1 3  CYou lose 2-1`

Alternatively, always switching

`1 2 3C1 2CYou lose! 1-0 to sticking1 2 3  C1 2  CYou win! 1-1 to sticking1 2 3    C1 3  CYou win! 2-1 to switching!`

As I said, you are essentially being given the choice of picking 1 OR picking 2 AND 3. The puzzle is just given window dressing designed to bamboozle the way the human mind naturally estimates probability. Basically you think that because there are two possibilities that means they must be equiprobable, but this assumption is not always true, such as in this case where the host knows which curtain the car is behind and simply reveals the one option you didn't pick that is a loser. In the case where the host always reveals 3 when you always pick 1, then of course you should only switch 1/3 of the time, otherwise it doesn't matter.

This is the illustration I like to use to demonstrate how professional poker players are able to make a living - and how the people they make money off are just as confident in their estimations of probability as their sharks. You've probably seen people who think the probability of God existing is 50% because he either does or he doesn't. But then, the chances of winning the lottery are the same by the same reasoning.

Edited by Modulous, : No reason given.

 This message is a reply to: Message 8 by Phat, posted 06-07-2014 2:05 PM Phat has acknowledged this reply

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Dr Adequate
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Joined: 07-20-2006
Member Rating: 6.3

 (1)
 Message 11 of 48 (729283) 06-07-2014 2:58 PM Reply to: Message 8 by Phat06-07-2014 2:05 PM

Re: Probability Changes Based on Data
 I don't see the math. Once 3 is eliminated, you have a 1 in 2 chance period. The original math no longer applies to the current reality.

You had a one in three chance of picking the right curtain. Once one curtain has been drawn aside, the chance that you originally picked the right curtain is still one in three.

Here's an argument many people find convincing. Suppose there were a hundred curtains. You pick one, and then the game show host draws back 98 of them. Which is more likely, that you picked the right curtain first off, or that you picked the wrong one, and that therefore the one remaining curtain, the one that the host chose not to draw back, conceals the prize?

With three curtains, the reasoning is just the same, only with fewer curtains.

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 Replies to this message: Message 14 by Capt Stormfield, posted 06-08-2014 2:28 PM Dr Adequate has responded

Capt Stormfield
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Posts: 402
From: Vancouver Island
Joined: 01-17-2009
Member Rating: 4.9

 Message 12 of 48 (729300) 06-08-2014 1:54 PM Reply to: Message 10 by Modulous06-07-2014 2:36 PM

Re: Probability Changes Based on Data
It doesn't seem like this is a probability question so much as it is about the rules that govern the game show host. If he knows where the car is, and also gets to choose which curtain to open, then there is the potential that he is communicating with you. So, interesting question about game show tactics, but not about probability.
 This message is a reply to: Message 10 by Modulous, posted 06-07-2014 2:36 PM Modulous has responded

 Replies to this message: Message 13 by ringo, posted 06-08-2014 2:27 PM Capt Stormfield has not yet responded Message 15 by Modulous, posted 06-08-2014 2:34 PM Capt Stormfield has responded Message 18 by PaulK, posted 06-08-2014 2:57 PM Capt Stormfield has not yet responded

ringo
Member
Posts: 15971
From: frozen wasteland
Joined: 03-23-2005
Member Rating: 2.4

 Message 13 of 48 (729303) 06-08-2014 2:27 PM Reply to: Message 12 by Capt Stormfield06-08-2014 1:54 PM

Re: Probability Changes Based on Data
 Capt Stormfield writes:So, interesting question about game show tactics, but not about probability.

Indeed, the host doesn't care whether you win or not. He's just interested in showing off the car for the dealer who sponsors the show. If he doesn't give it to you, he'll give it to somebody else tomorrow. His goal is to keep the audience watching by keeping up the suspense. He has to have winners to keep the suckers coming in.
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Capt Stormfield
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Posts: 402
From: Vancouver Island
Joined: 01-17-2009
Member Rating: 4.9

 Message 14 of 48 (729304) 06-08-2014 2:28 PM Reply to: Message 11 by Dr Adequate06-07-2014 2:58 PM

Re: Probability Changes Based on Data
 With three curtains, the reasoning is just the same...

And equally flawed. The original question is meaningless unless we know the structure of the game. If the host has knowledge, and gets to use it in the choice of which unchosen curtains are opened, then the question is just about Monte Hall's likely behavior, not about probability.

 This message is a reply to: Message 11 by Dr Adequate, posted 06-07-2014 2:58 PM Dr Adequate has responded

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Modulous
Member (Idle past 116 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005

 Message 15 of 48 (729305) 06-08-2014 2:34 PM Reply to: Message 12 by Capt Stormfield06-08-2014 1:54 PM

Re: Probability Changes Based on Data
 It doesn't seem like this is a probability question so much as it is about the rules that govern the game show host.

Well its the rules that govern the game show host are what determines the probabilities. If it helps, replace the host with a computer program that always picks curtain which does not have a car behind it and was not the one you picked.

 If he knows where the car is, and also gets to choose which curtain to open, then there is the potential that he is communicating with you.

The OP describes the scenario as you hypothetically perceive it. If you detect some communication, tell me - which curtain is the car behind?

Edited by Modulous, : No reason given.

 This message is a reply to: Message 12 by Capt Stormfield, posted 06-08-2014 1:54 PM Capt Stormfield has responded

 Replies to this message: Message 19 by Capt Stormfield, posted 06-08-2014 2:58 PM Modulous has acknowledged this reply

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