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  #1  
Old 09-03-2009, 12:23 AM
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Default Twist on an old favorite

Usually this is told within the context of a gameshow, but.. still. It's pretty controversial, and I'd like to see what you guys have to say about it:

Quote:

Three condemned prisoners share a cell. A guard arrives and tells them that one has been pardoned.

"Which is it?" they ask.

"I can't tell you that," says the guard. "I can't tell a prisoner his own fate."

Prisoner A takes the guard aside. "Look," he says. "Of the three of us, only one has been pardoned. That means that one of my cellmates is still sure to die. Give me his name. That way you're not telling me my own fate, and you're not identifying the pardoned man."

The guard thinks about this and says, "Prisoner B is sure to die."

Prisoner A rejoices that his own chance of survival has improved from 1/3 to 1/2. But how is this possible? The guard has given him no new information. Has he?
Discuss.
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  #2  
Old 09-03-2009, 12:26 AM
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Hey Prof. Snow! Talk to Prisoner A about the law of averages!!!
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  #3  
Old 09-03-2009, 08:18 AM
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What is really happening is that they are all really going to die and the guard is just messing with them for a couple of laughs.
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  #4  
Old 09-03-2009, 08:34 AM
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I don't get the question, I guess.

1 chance to survive/3 prisoners (A,B,C).

Take 1 prisoner (B) out of the equation, because you know he isn't on the list of people who will survive anymore, given the guards answer. Which leaves

1 cts/2 prisoners (A,C)

I kind of read it like figuring odds on a horse race...maybe that was the wrong way to look at it.

If prisoner A shanks prisoner C and makes it look like prisoner B did it, he might be able to seal the deal and get the pardon. Either that or everyone dies, so no one gets special treatment, which is really the correct way to deal with things in the long run.
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  #5  
Old 09-03-2009, 08:59 AM
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All right, let's extend the story a bit.

Prisoner B takes the guard aside, and the guard tells him the name of a prisoner who is going to die too. Same with prisoner C.

So now, according to the claimed logic, every prisoner only has a chance of one out of two to die, yet still two of the three prisoners are going to be executed.

Continue with the discussion.
  #6  
Old 09-03-2009, 09:40 AM
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But he didn't say executed, he said "is sure to die". Well, of course, we all will surely die. So he didn't tell him anything of value at all.

I'm with Zanguini on this one.
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  #7  
Old 09-03-2009, 09:50 AM
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I think we need to know more about prisoner A first. If he's rich and white while the others are black and poor, I know where I'd put my money.
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  #8  
Old 09-03-2009, 11:42 AM
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Quote:
Originally Posted by Jokeslayer
I think we need to know more about prisoner A first. If he's rich and white while the others are black and poor, I know where I'd put my money.
LOL! Touche.
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  #9  
Old 09-03-2009, 11:44 AM
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Quote:
Originally Posted by Jokeslayer
I think we need to know more about prisoner A first. If he's rich and white while the others are black and poor, I know where I'd put my money.
Yeah, but if he were rich and white, what's he doing in prison?
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  #10  
Old 09-03-2009, 11:50 AM
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Quote:
Originally Posted by Davian93
Yeah, but if he were rich and white, what's he doing in prison?
He's Conrad Black.
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  #11  
Old 09-03-2009, 11:59 AM
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Quote:
Originally Posted by Brita
He's Conrad Black.
I just had to look him up on Wikipedia (sad, I know). Sounds like a real winner.
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  #12  
Old 09-03-2009, 12:01 PM
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Quote:
Originally Posted by Frenzy
Hey Prof. Snow! Talk to Prisoner A about the law of averages!!!
or the Law of Large Numbers, eh?
(or was that Numbnuts?)
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  #13  
Old 09-03-2009, 03:24 PM
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OK, here are the two arguments:

1) One camp claims that the information given has no effect on the outcome -- he's still got a 1/3 chance of being pardoned.

2) Another camp claims that the information given has increased his odds for a pardon from 1/3 to 1/2.

The reasoning is as follows:

You've got two prisoners who will die and one prisoner who will be pardoned. Since Prisoner A is asking, the guard can't reveal Prisoner A's fate.

Which prisoner is going to die is irrelevant -- the fact is that the guard says that another prisoner will die. The fact that Prisoner B will die means that there are only two choices left: Prisoner A will be pardoned or Prisoner C will be pardoned.

Thus, there is a 50/50 chance that Prisoner A will be released.
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  #14  
Old 09-03-2009, 03:41 PM
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Camel, I already answered that with a scenario where every one of the prisoners asks the question, and is told that one of the other prisoners will be executed. So, if you are correct, that means that all three of the prisoners have 50% chance of being released. Thus, either your reasoning is incorrect, or 1.5 prisoners will be released, and the other 1.5 prisoners will be executed. Naturally, the fairest way of doing that would be chop each of the prisoners in two, and then pardon their right (or left) sides. But that contradicts the "one will be pardoned thing".
  #15  
Old 09-03-2009, 03:52 PM
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Quote:
Originally Posted by GonzoTheGreat
Camel, I already answered that with a scenario where every one of the prisoners asks the question, and is told that one of the other prisoners will be executed. So, if you are correct, that means that all three of the prisoners have 50% chance of being released. Thus, either your reasoning is incorrect, or 1.5 prisoners will be released, and the other 1.5 prisoners will be executed. Naturally, the fairest way of doing that would be chop each of the prisoners in two, and then pardon their right (or left) sides. But that contradicts the "one will be pardoned thing".
Well, the thing is that Prisoner B has a 100% chance of dying (1/1) whereas the others have a 50% chance, so your logic fails. The only way your scenario would be true is if, when asked by each prisoner, the guard picks a different prisoner (i.e. when A asks, he says B will die, when B asks, he says C will die, and when C asks, he says A will die). Only in that case does the 50% logic fail.. but it wouldn't happen (assuming the guard is telling the truth) because ONE of those prisoners will be pardoned.
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  #16  
Old 09-03-2009, 03:57 PM
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Quote:
Originally Posted by JSUCamel
Which prisoner is going to die is irrelevant -- the fact is that the guard says that another prisoner will die. The fact that Prisoner B will die means that there are only two choices left: Prisoner A will be pardoned or Prisoner C will be pardoned.
No, the problem with this is the wording the guard used about the fate of Prisoner B. He said, "Prisoner B is sure to die." Like Brita said, we're all going to die. A is going to die, B is going to die, C is going to die. Two of them will be executed, and one will die from other means. But, they all will die at some point. Whether or not they are pardoned is completely independent of the fact that they will die. So, no new info here.

It's kinda like the brainteaser: how many months have 28 days? They all do. Not just February.
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  #17  
Old 09-03-2009, 04:04 PM
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I agree with Bowlwoman. The guard gave no new information.
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  #18  
Old 09-03-2009, 04:07 PM
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Quote:
Originally Posted by JSUCamel
Well, the thing is that Prisoner B has a 100% chance of dying (1/1) whereas the others have a 50% chance, so your logic fails. The only way your scenario would be true is if, when asked by each prisoner, the guard picks a different prisoner (i.e. when A asks, he says B will die, when B asks, he says C will die, and when C asks, he says A will die). Only in that case does the 50% logic fail.. but it wouldn't happen (assuming the guard is telling the truth) because ONE of those prisoners will be pardoned.
Nope, the problem is that you are looking at it from the outside, but you are asking what the prisoners can know.

Suppose, just for the sake of argument, that prisoner C has been pardoned.

Prisoner A asks the question, and is told that B will be executed.
Prisoner B asks, and is told A will die.
Prisoner C asks, and is told that A will die.

Now, would it really be correct for every one of those three to conclude that they have 50% survival chance?
We know that, after they've gotten the (truthful) answer to their question, two out of three prisoners will die. So given those actual odds, how do you defend the one out of two odds you are claiming?

Of course, in my scenario, if the three prisoners compare their answers, they can figure out which of them will survive.
  #19  
Old 09-03-2009, 04:23 PM
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Quote:
Originally Posted by JSUCamel
OK, here are the two arguments:

1) One camp claims that the information given has no effect on the outcome -- he's still got a 1/3 chance of being pardoned.

2) Another camp claims that the information given has increased his odds for a pardon from 1/3 to 1/2.

The reasoning is as follows:

You've got two prisoners who will die and one prisoner who will be pardoned. Since Prisoner A is asking, the guard can't reveal Prisoner A's fate.

Which prisoner is going to die is irrelevant -- the fact is that the guard says that another prisoner will die. The fact that Prisoner B will die means that there are only two choices left: Prisoner A will be pardoned or Prisoner C will be pardoned.

Thus, there is a 50/50 chance that Prisoner A will be released.
So I got it right! Wooohooo!
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  #20  
Old 09-03-2009, 04:33 PM
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Quote:
Originally Posted by GonzoTheGreat
Nope, the problem is that you are looking at it from the outside, but you are asking what the prisoners can know.

Suppose, just for the sake of argument, that prisoner C has been pardoned.

Prisoner A asks the question, and is told that B will be executed.
Prisoner B asks, and is told A will die.
Prisoner C asks, and is told that A will die.

Now, would it really be correct for every one of those three to conclude that they have 50% survival chance?
We know that, after they've gotten the (truthful) answer to their question, two out of three prisoners will die. So given those actual odds, how do you defend the one out of two odds you are claiming?

Of course, in my scenario, if the three prisoners compare their answers, they can figure out which of them will survive.

Hmmm...
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