A friend of mine told me a similar problem that he got at D.E. Shaw interview. Person A writes random real numbers in two envelopes. Then person B randomly 50/

A friend of mine told me a similar problem that he got at D.E. Shaw interview. Person A writes random real numbers in two envelopes. Then person B randomly 50/50 picks one envelope and sees the number X written there. Then, B has to guess whether X is the bigger of the two numbers or not. Show that B has a strategy, that even if A knows it, B can guess correctly in more than 50% of the cases. The mathematical beauty of this problem is that you can derive what are the non-trivial steps towards the solution.