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Old 02-05-2015, 10:12 AM
  # 41 (permalink)  
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That's how it seems to me. That probability function for B and C, totalling 2/3, collapses as soon as you know that it's not C. And it collapses to B, with a 2/3 probability. So 1/2 if he stays, 2/3 if he moves.
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Old 02-05-2015, 10:45 AM
  # 42 (permalink)  
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Originally Posted by anattaboy View Post
Yes, and the probability of two inmates tunneling to each other's cell under the guise of escaping is uh...stupid or a plot to a gay prison porn.
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Old 02-05-2015, 10:55 AM
  # 43 (permalink)  
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I still stick to the "it doesn't matter answer" and a 50-50 odds unless he figures out a way to tip the odds in his favor (which is doable)
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Old 02-05-2015, 10:56 AM
  # 44 (permalink)  
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The suspense is killing me.
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Old 02-05-2015, 10:58 AM
  # 45 (permalink)  
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I'm in the 50/50 camp, with props to the Princess Bride meme.
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Old 02-05-2015, 10:58 AM
  # 46 (permalink)  
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All adjoining rooms I've ever been in had doors---so the tunnel was mox-nix.
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Old 02-05-2015, 11:07 AM
  # 47 (permalink)  
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I'm assuming the king already made a choice of A, B or C and told the warden, so that's done and the choice is already made, no need to talk about 1/3 probabilities. The warden won't tell A who the choice was, but he tells him it's not C. That leaves A or B as the person pardoned. It's one or the other, 50/50 chance, so it doesn't matter if A and B switch places unless you add more to the storyline (C rats on B and tells king about the tunnel, king changes his mind, etc.). Furthermore, A and B are identical so there is no way to tell them apart. Doesn't matter if they switch places or not.
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Old 02-05-2015, 11:39 AM
  # 48 (permalink)  
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Great responses, on many different levels. I'm most interested in the reasoning behind the answers. I think it's best I keep my mouth shut at this point.

A little less than 8 and 1/12 hours to go.
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Old 02-05-2015, 11:40 AM
  # 49 (permalink)  
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It's simple. When you don't switch, you limit yourself to 1/3 probability. When you switch, you increase it by another third. No need for any other math.
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Old 02-05-2015, 11:59 AM
  # 50 (permalink)  
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If the king has applied no logic or reason to any of his decision making, logic and reason are not useful To resolve the issue.

Seems random.

So "no difference "
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Old 02-05-2015, 12:00 PM
  # 51 (permalink)  
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Originally Posted by Purpleknight View Post
In the beginning every prisoner had the same 1/3 chance of a pardon:

-A - 1/3
-B - 1/3
-C - 1/3

Once we know C will not be pardoned, the probability doesn't become 1/2 or 50%:

-Prisoner A staying where he is will remain at the original 1/3 chance
-Swapping with Prisoner B increases the chance to 2/3 - So Swapping is the way forward!!

In probability terms if it was 100 boxes with 1 box having a $1 million cheque, if you chose 1 box at the beginning, then 98 boxes containing nothing were removed, would you swap? yes because there was more probability in the beginning, 99 out of 100 boxes that you chose a box with no cheque in it, this makes it more statistical, using people in the problem blinds the numbers I think!!

In the same way the probability surely increases with the info that 1 prisoner won't get a pardon if he switches!!

That's my best shot, but I could be wrong!!

Just can't wrap my brain around it.......
So, if you started with a 1 in a 100 or 1% chance and took out 98 empty boxes, I just cannot see that the probability now isn't 1 in 2 or 50% and switching doesn't matter?!?!? How can then switching based on events that have already transpired affect the outcome of the draw????

Why is it any different than simply saying I have two boxes and one has money in it. Isn't the probability at that point 1 out of 2 regardless of switching ones choice or not???

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Old 02-05-2015, 12:01 PM
  # 52 (permalink)  
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I was close but forgot how to add. The correct answer is 1/3 chance of surviving if he stays, and 2/3 chance of surviving if he changes. P + Q = 1.

Final answer.

We all agree that he has a 1/3 chance at the beginning, if he stays in A. That doesn't change. And a 2/3 chance for the other two cells. When the warden breaks the news about his buddy in B, this stuff doesn't change. It does mean however that this 2/3 chance now resides only in B.
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Old 02-05-2015, 12:03 PM
  # 53 (permalink)  
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Freshstart, you're saying the same as me.
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Old 02-05-2015, 12:04 PM
  # 54 (permalink)  
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Originally Posted by awuh1 View Post
Great responses, on many different levels.
It's kind of telling though that I seem to be the only one obsessed with formulating strategies to rescue poor a or at least punish b even with the "no adding to the story rule" more than with cold probabilities.
I m surprised that you guys have not sent me back to the F&F forum LOL
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Old 02-05-2015, 12:05 PM
  # 55 (permalink)  
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And so is PK.
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Old 02-05-2015, 12:08 PM
  # 56 (permalink)  
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Yes, and PurpleKnight too, Jennie. Kudos to both of you!
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Old 02-05-2015, 12:19 PM
  # 57 (permalink)  
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Originally Posted by Carlotta View Post
It's kind of telling though that I seem to be the only one obsessed with formulating strategies to rescue poor a or at least punish b even with the "no adding to the story rule" more than with cold probabilities.
I m surprised that you guys have not sent me back to the F&F forum LOL
Carlotta says rescue the guy

If the king has changed the rules once, probability suggests he will do it again.

The outcome is indefinite.
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Old 02-05-2015, 12:21 PM
  # 58 (permalink)  
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Let the bodies hit the floor
Let the bodies hit the floor
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Old 02-05-2015, 12:34 PM
  # 59 (permalink)  
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Originally Posted by Flynbuy View Post
Just can't wrap my brain around it.......
So, if you started with a 1 in a 100 or 1% chance and took out 98 empty boxes, I just cannot see that the probability now isn't 1 in 2 or 50% and switching doesn't matter?!?!? How can then switching based on events that have already transpired affect the outcome of the draw????

Why is it any different than simply saying I have two boxes and one has money in it. Isn't the probability at that point 1 out of 2 regardless of switching ones choice or not???
The other way of looking at it is that your chances have improved because many of the empty boxes have now been taken away, or 1 prisoner not being pardoned has now been taken away.

-100 boxes - 1 in 100 chance
-50 boxes - 1 in 50 chance
-2 boxes - 1 in 2 chance

That improvement in chance has to be factored into the equation when mathematicians do their fancy calculations.

Starting with only 2 boxes can't be the same as starting with 100 boxes and then switching your first choice with 1 of the final 2 boxes, it can't both be 50% because at the start there was a 1 in 100 chance rather than a 1 in 2 chance!!

So start with a 1/100, take out 98 boxes can't equal the same as simply starting with 2 boxes to begin with, which is a 1/2.

Probability surely needs to reflect the increase in probability, or the change in probability somehow with numbers, even though the options, number of boxes, number of prisoners remains the same!!
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Old 02-05-2015, 01:06 PM
  # 60 (permalink)  
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Originally Posted by Purpleknight View Post
The other way of looking at it is that your chances have improved because many of the empty boxes have now been taken away, or 1 prisoner not being pardoned has now been taken away.

-100 boxes - 1 in 100 chance
-50 boxes - 1 in 50 chance
-2 boxes - 1 in 2 chance

That improvement in chance has to be factored into the equation when mathematicians do their fancy calculations.

Starting with only 2 boxes can't be the same as starting with 100 boxes and then switching your first choice with 1 of the final 2 boxes, it can't both be 50% because at the start there was a 1 in 100 chance rather than a 1 in 2 chance!!

So start with a 1/100, take out 98 boxes can't equal the same as simply starting with 2 boxes to begin with, which is a 1/2.

Probability surely needs to reflect the increase in probability, or the change in probability somehow with numbers, even though the options, number of boxes, number of prisoners remains the same!!
I am leaning towards this which is a nod to a changing set of variables..right. Variable variability. A football team's chances change with each shift of the line of scrimmage…it opens up a new set of combinations. Think about it, during the Superbowl the field of final scores shifted with each score added, narrowing the possibilities, but also altering the possibilities.

Oh, I don't know. Mind…blown as my 10 year old would say.
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