rsl12

This paradox bothered me for a long time, but I think I've figured it out. Would be interested in hearing other people argue their point.

Two cups are presented to you. You are told that one cup contains twice as much money as the other cup. Without knowing which cup contains what, you can choose to keep the contents of one of the cups. Which do you choose?

Let's suppose that you are allowed to look in one of the cups before choosing. You find that Cup A contains X amount of dollars. Therefore, you can reason that there is a 50% chance that cup B contains half that amount, and a 50% chance that it contains double the amount. Therefore, the expected value of the amount of money you will get, if you choose cup B is

(0.5*X)+(2X) divided by 2, or 1.25X.

Therefore, if you choose cup A, you will definitely get X dollars, but odds are that choosing cup B gives you the better deal.

So it seems that if you choose to look under cup A, it would be better to choose cup B. But if you had instead chose to look under cup B, it would have been better to choose cup A! How is that possible?? Why bother looking at the money in one cup in the first place? Let's suppose you weren't allowed to look in the cups, but followed the same logic as above. You would say, "Let's assume that cup A has X dollars. Therefore, the expected amount in cup B is 1.25*X dollars, and it's better for me to choose cup B." Or else you would say, "Let's assume that cup B has Y dollars. Therefore, the expected amount in cup A is 1.25*Y dollars, and it's better for me to choose cup A." Something is wrong.

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