Check out this math problem I found on the xkcd blog:
Alice secretly picks two different real numbers by an unknown process and puts them in two (abstract) envelopes. Bob chooses one of the two envelopes randomly (with a fair coin toss), and shows you the number in that envelope. You must now guess whether the number in the other, closed envelope is larger or smaller than the one you’ve seen. Is there a strategy which gives you a better than 50% chance of guessing correctly, no matter what procedure Alice used to pick her numbers?
HINT: I’ll give a slight hint in that if you consider the range of the real numbers, it should make the answer clearer. Hopefully that didn’t give it away.