Suppose I have two envelopes. All you know is that
they contain different numbers. I randomly hand you
one of them. You open it, look at it, then hand it
back. You now have sufficient information to, with
guaranteed better than even odds, correctly tell me
whether I gave you the envelope with the larger
number. How?

No, that question actually is:
If I give you a number from a set of two
diffrent numbers tell me if you got the small
or large number?

My odds of doing that is exactly 50%.

If you sit down and do the algebra, you
will find that your probability of being right turns out
to be exactly 50% plus 1/2 the probability that you pick
a number between my two.

Hmm. If I choose to guess myNumber + epsilon(where epsilon is
small enough) I have 50% chance of being between your two numbers
and hence have 75% chance of being correct, which is silly:-)