[mundo]

> You can guarantee there is > 50% chance you win on the first guess.

You mean "greater than" and not "greater than or equal to"?

The latter is easy; lots of naive strategies accomplish that. But the former implies that you can declare a strategy and the puzzle offerer cannot then pick a distribution that defeats it. It's hard to imagine how you could get >50% for example if the puzzler's strategy is to pick N and N+1 for very large N.