Again credit goes to my former teacher Ulrich Berger:
Suppose you face a choice among two boxes, both of which contain a certain amount of money. You are told that one box contains double the amount of the other box. The position of the higher prize has been determined by a coin flip.
Based on your gut instinct you think about grabbing box A. Then, however, you think back to your high school introduction into probability. Evaluating whether you should take the other box you realize that box B contains either X/2 or 2*X if X is the amount in box A. Since both cases are to occur with equal probability you conclude that box B contains 1/2*(X/2)+1/2*(2*X)=5/4*X. Based on the fact that that 5/4*X exceeds X should you take the other box?