Quote:
Originally Posted by magicmcq
I don't usually like outing villains in these threads, but since it's been mentioned already and there's so much confusion, I'll say villain was ZZ.
Regarding Paul's answer to the brain teaser, I'll give everyone the problem / paradox since I legitimately think it's interesting and cannot solve it at current.
The Envelope Problem:
Part 1) two envelopes are placed in front of you and you are told one contains twice As much money as the other, but the absolute quantities are unknown. So u pick one and open it and see $10. You are then asked if you wish to switch (this isn't the Monty hall problem I promise). The trivial calculation here is that the other envelope will contain half the money ($5) half the time and twice ($20) half the time. This means EV of switch is 12.5, or 5/4x. It would be, based on this reasoning, 5/4x regardless of the amount u open.
Part 2 / the paradox) You and another person each take one of these envelopes (same rules). In theory, from each of your perspectives, switching envelopes is a +EV proposition, but this is clearly a zero sum game. How is this possible?
I'm sorry but you're kind of messing up the description here. The paradox doesn't need a second person to switch with, and this not a zero sum game. The paradox is more basic and involves just one person: as soon as you've chosen one envelope and even before you open it, you could perform the EV calculation and decide that you should switch, and soon as you've done that you are forced to switch again etc.
The resolution of this paradox is instructive, it involves a careful consideration of what the expected value calculation looks like. Basically you can't just say there are two cases, and in one the value is 2A and the other is A, because A is a random variable whose expectation changes conditioned on which situation you're in. You should read the wikipedia article on it (two envelopes paradox), it has a lot of information and variants of the problem.
If you have trouble understanding the wikipedia explanation, then you should read the resolution of the necktie paradox first, that is much clearer and essentially the same thing.
Last edited by thesilverbail; 03-18-2016 at 01:51 AM.