This puzzle is tricky. Mary writes two real numbers on the opposite side (A and B) of a paper. The numbers must be different. Then she gives the paper to John who can select one side of the paper. Say he selects A-side. He sees the number on A-side and, without having a look to B-side, he must bet if the number on A-side is greater of the number of B-side. They continue this game forever. Questions:
1. What is the probability to win for John?
2. Is there any strategy better than break-even?