Comment by antognini

There is a related puzzle which I've also heard called the Two Envelopes Problem. The premise is that you are handed two envelopes. Inside each envelope is a piece of paper with a number written on it. I have written down these numbers by sampling from some probability distribution, but you don't know what it is. All you know is that the two numbers are different. You get to pick one envelope and then look at the paper inside. You then need to guess whether or not the number in the other envelope is larger or smaller than the one you are looking at. Can you guess with better than 50% chance?