[22c]

> But the win probability will always be >0.5 so long as the "prior" probability distribution has a nonzero probability of being between Alice's two numbers.

I'm not sure if that always holds true. Let's say Alice flips a coin and picks 3 or 4 for num1, then Alice flips another coin and picks either num1 - 2 or num1 + 2 for num2.

You come along and pick a number between 1 and 6. You have a non-zero chance of having picked a number between Alice's two numbers, but your chances of winning are not > 0.5.

If you picked a number between 2 and 5 though, your chances of winning are now > 0.5. Like jstanley said, you'd have to know how Alice picks numbers in order to win in the long run.