It's not that he's seeking truth out of her for truth's sake. He doesn't want to bring up something painful in seeking an honest talk out of her. All he really wants is to get a better sense of who she is and where he stands with her. That's all. Via a bet seemed like a way to do that without making her feel like she was just giving up her closely valued secrets to him.

Was that a proposition?

"You'll have to forgive me, Natasha." He says tilting his head to regard her more thoughtfully. "I'm not familiar with all of your earth customs yet, but I think you're implying your reward for winning this bet is something I would indulge you with anytime."

And gladly so. To the point where he'd consider losing on purpose.