Considering heuristics is the only tool humans have, such a game is inherently unplayable.

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.

Some games were designed to be difficult for computers, primarily by having a large branching factor. Aarimaa [1] seems to be holding up so far. Octi [2] is perhaps too obscure to get much attention and Havannah [3] has been defeated in the years since the author invited computer challengers to try.

[1] https://en.wikipedia.org/wiki/Arimaa#World_Computer_Champion...

[2] https://boardgamegeek.com/boardgame/450/octi

[3] https://en.wikipedia.org/wiki/Havannah#Computer_Havannah

> Aarimaa seems to be holding up so far.

Not anymore it looks like:

In 2015, the challenge was won decisively by the computer (Sharp by David Wu), with top players agreeing that computers had become better at the game than humans.

Snakes and ladders? https://xkcd.com/1002/