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Earlier quoted context omitted.
But, did he discovered new information? What if the guard had said "Prisioner C is sure to die"?
He did discover new information. The probabilities of survival switched from: A: 1/3, B: 1/3, C:1/3 to A: 1/3, B:0, C: 2/3 He just didn't discover any information to change the probability of his own survival.
Earlier quoted context omitted.
Yeah, except it's pretty obvious why there is a switch to 1/2 from 1/3 in Prisoner's Paradox and it's not obvious in MH. What I understand happened in Prisoner's Paradox is that the very field of probabilistic distribution of pardons has shrinked from 3 to 2. It's like binary search. You cheated your way by knowing where _not to look_. Another simple analogy: you can increase the value of rational number both by incr…
You mean it's pretty obvious why there is no switch to 1/2 from 1/3? As the Wikipedia article you linked points out: "The answer is he didn't gain information about his own fate, but he should switch with C if he can." This isn't the same as Monty Hall. Monty Hall only increases the odds after switching doors. This actually seems like a trick meant to fool people who know about the Monty Hall problem but don't really…
I re-read all three problems after you replied and this is what I understood. Talking about Three Prisoners' problem since the article's wording doesn't include the very crucial ingredient for easier understanding: coin flip on warden's side.
For A, it doesn't really matter if B or C were executed. In fact, he knew that either B or C are going to be executed for sure. He knew that at least one person who is not him will be executed.
Warden just named the sure-to-be-executed-guy. Didn't change what he previously knew about his chances, since he still doesn't know for sure whether the-other-not-named-guy is going to be executed.
However, the distribution changed for C. Now A still knows that there 1/3 chance of him living but since we know for sure that the-guy-who-warden-named (B or C) will be killed the-guy-who-warden-didn't-name-and-who-isn't-A (C or B) will have 1 - 1/3 = 2/3 probability of living.
Prisoner B could just as well be Prisoner A since A was defined by the narrator, and Prisoner B by the guard. I know we're descending into the theoretical stuff, probabilities and so on, but might there not even be enough information to go down any path at all given this dilemma?
Forgive me, but doesn't it seem odd that the problem defines Prisoner A from one perspective, and Prisoner B from another? Prisoner B could just as well be Prisoner A since A was defined by the narrator, and Prisoner B by the guard. I know we're descending into the theoretical stuff, probabilities and so on, but might there not even be enough information to go down any path at all given this dilemma?
Earlier quoted context omitted.
You mean it's pretty obvious why there is no switch to 1/2 from 1/3? As the Wikipedia article you linked points out: "The answer is he didn't gain information about his own fate, but he should switch with C if he can." This isn't the same as Monty Hall. Monty Hall only increases the odds after switching doors. This actually seems like a trick meant to fool people who know about the Monty Hall problem but don't really…
It's strange why my blatantly stupid post was upvoted. I re-read all three problems after you replied and this is what I understood. Talking about Three Prisoners' problem since the article's wording doesn't include the very crucial ingredient for easier understanding: coin flip on warden's side. For A, it doesn't really matter if B or C were executed. In fact, he knew that either B or C are going to be executed for…
Forgive me, but doesn't it seem odd that the problem defines Prisoner A from one perspective, and Prisoner B from another? Prisoner B could just as well be Prisoner A since A was defined by the narrator, and Prisoner B by the guard. I know we're descending into the theoretical stuff, probabilities and so on, but might there not even be enough information to go down any path at all given this dilemma?
Prisoner A is the one that asks. That sets the one an only perspective for the guards answer.