Prophet vs Gambler, Two Prizes

Two prizes arrive in sequence, each an independent Uniform(0,1) value, revealed one at a time; you must accept one immediately when shown (no recall, and if you reject the first you must take the second). A prophet who sees both in advance collects E[max(X1,X2)]. Compute the prophet's expected reward, the best the online gambler can guarantee in expectation, and the ratio of gambler to prophet.