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the two box paradox
there are two closed boxes. you are told one box has 3 times more than the other. you pick a box and open it. you see that is has 9 dollars in it. would it be in your benefit to switch? obviously the answer is yes, as you stand to gain more than you lose. now imagine after picking a box, you are not allowed to open it. would it still be in your benefit to switch?
argument for:
since you either still gain 3 times more or lose 1/3, the answer should be yes. for example, lets say there are three boxes, you pick the middle box, but don't know how much is inside, you are told that in one of the boxes you didn't pick holds 1/3 the amount and the other 3 times the amount of the box you picked. clearly its beneficial to switch to one of the two boxes.
argument against:
since you don't know how much is in each box, you have 50/50 chances of getting what you want. to demonstrate, it would be equally beneficial to switch back to the original box.
anyone see a clear way to prove which is better?
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