[Brainwalter]

Yeah, I guess it doesn't matter that "A selects a number and B tries to guess it." Their selections are independent and for all practical purposes simultaneous.

If A selects his numbers randomly B cannot increase his EV above 0. So I think what you're really asking is whether A's optimal strategy is to select randomly (0 EV) or whether there is a strategy where B has forced -EV. This is different from your original question, and each player has the same (limited or long-run nonexistant) opportunity to outwit the other.