Heuristics are also what make games fun and learnable. "I am thinking of a number between 1 and 10e256" has no learnable heuristics, for example.

Sure it has. For example, 42 is more likely than 48884566544542789. People play rock-paper-scissors competitively and good players win more often than a pure chance would imply.

17?

Darn it! You got me :-)

What's most interesting to me is that if the human is picking the random number, there are heuristics you could use to guess it. A birthday, for example. A favorite number perhaps. But perfect play is easy and requires brute force search.

One of my favorite numbers is 355/113 but it's still hard to guess.