Suppose you're on a gameshow where you can choose either of two sealed envelopes, A or B, both containing money. The host doesn't say how much money is in each, but he does let you know that one envelope contains twice as much as the other. You pick envelope A, open it and see that it contains $100. The host then makes the following offer: you can either keep the $100, or you can trade it for whatever is in envelope B. You might reason as follows: since one envelope has twice what the other one has, envelope B either has 200 dollars or 50 dollars, with equal probability. If you switch, then, you stand to either win $100 or to lose $50. Since you stand to win more than you stand to lose, you should switch. But just before you tell the host you would like to switch, another thought might occur to you. If you had picked envelope B, you would have come to exactly the same conclusion. So if the above argument is valid, you should switch no matter which envelope you choose. But that can't be right. What's wrong with your reasoning?