math question regarding headsup situation

[Wynton]

I posed this question in the probability forum, but no replies yet. I pose it here because I think the situaton arises frequently at six-max tables.

Say you're headsup on the flop (without a pocket pair), and fail to flop a pair. And say the flop itself does not contain a pair. What would the odds be that our opponent neither has a pocket pair nor has flopped a pair himself?

And what would those odds be if you still fail to make a pair on the turn?

Ultimately, I'm trying to get a mathematical basis for dealing with headsup situations when it's impossible to make assumptions about our opponents' holdings, e.g., the opponent is loose and open-completes from sb or defends his bb from a open-raise from the button (or sb) with virtually anything.