Uh, zero?

Probably, but is it that obvious? Having an opponent that is not even trying to win is much harder to predict.

I've heard several poker players saying that it's hard to play against novices, because they do nonsense.

Surly there is some game theory that says something about this. Anyone?

I wouldn't have thought so, because there isn't the same element of unknown information that there is in poker (i.e. I don't know your hand in Poker), but I know the board and if you're just playing random moves, then I can probably use some variation of Scholars mate to end the game early. (some beginners keep playing it until they finally reach a level that their opponents know how to defend against it)