Guess the biggest

Question

Two different numbers between 0 and 1 are chosen at random. You see only one of them. Then, without knowing the other one, you must decide if the hidden number is greater or less than the one you have seen. At first glance, it seems impossible to do better than random. Is there a strategy that gives you a greater probability of success than simple chance? And if it exists, what is that probability?

Riddle of the Day · Accepted Answer

Yes. The optimal strategy is to compare the seen number with 1/2: if it is less than 1/2, it should be said that the hidden number is greater; If it is greater than 1/2, it should be said that the hidden one is less. The maximum probability of success is 3/4.