Maybe some randomness will help, but might not be enough.
My ideea is that bots can't win in the real world economy, no fund driven solely by algorithms can win more than funds driven by humans.
So if we can find a game modeled like the economy, where nothing is random but many things are uncertain, then it might be harder for the software to win.
But yes, I think you're right that you'd need a game where crunching a lot of numbers really fast doesn't give you an advantage. For instance, if the state space of the game is so big that number crunching is useless, and other approaches like AI style pattern matching (used IIRC by Alpha-Go?) don't work either.
Though ultimately, what is the uniquely human trait that would allow a human to beat an AI? Can you make a game that depends on that? Is there even such a thing?
I guess all the slot machine players tend to differ in opinion there :)
Sure, slot machine operators adjust winning chances so players keep on playing, but to a player, it's not influenced by anything they do, other than "just one more time and I'll win".
But in the extreme case of a random game (like rolling the highest number on a die) they are equal (obviously).
We can ask any successful CEO. Fortune 500 companies would use bots if that was possible.
Uncertainty doesn't equal randomness. Randomness is flipping a coin and asking you the result. Uncertainty is hiding the coin behind my back and asking you in which hand is it.