I think this works, but put a big disclaimer on it:
The number is revealed; call it Q. Calculate . Now, flip your own coin, with weighted probability P of heads. If heads is revealed, then you guess that Q is the larger of the two numbers (i.e. call "heads"). It should work out that your probability of guessing right is:
, but since the term associated with Y is strictly larger than the one associated with X (because Y is bigger), you will win with a probability greater than 1/2.
EDIT: LOL, this doesn't work for negative numbers, but maybe you can tweak it using a similar method. I think the main step to take in solving this is to have a switching probability based on the number revealed, and devise a way for it to make you switch away from the smaller one more frequently than the larger one.