Two Numbers

So, about a year ago, I posted a puzzle based on the two envelope paradox. I had intended to finish that one off with another puzzle, but then I guess I forgot to. Now I have learned about a follow up to that puzzle, but I can't exactly post i until I have posted the original. Anyway, here we go:

Alice writes down two distinct real numbers and puts them into two separate envelopes. Bob then selects one of the envelopes to open randomly (50-50 chance) and looks at the number. Bob must then guess whether the number he is looking at is the larger of the two or the smaller of the two. Find a strategy for Bob that is guaranteed to succeed more than 50% of the time, no matter what numbers Alice chooses.

Its very similar to the final problem I posted a year ago, so I'll give the solution out in the next few days so we can move on to the real problem. Its trivial for Bob to do 50% simply by flipping a coin to decide his answer, but doing better just seems crazy. If you need, feel free to assume Alice is choosing her numbers from an unknown but well defined distribution over the reals.