"It's like he's a little bit on edge and about to blow any second," Giamatti tells TimeOut. "Or maybe punch somebody, or bite somebody. So I like that about it."
Rhoades is revealed to be from a prominent New York family whose name casts a long shadow - his upper class background informs how he contrasts with his much richer prey.
"With my character, there's lots of interesting issues of wealth and privilege. In certain realms of wealth and privilege, the idea comes along with it that one must serve, too, that service is an obligation if you have that privilege. And he's serving [as a government prosecutor] out of that kind of thing, so I think he's turned off by the notion of somebody whose success doesn't seem to serve something.
"My relationship to his success is interesting. There's jealousy things that go on that are interesting."
Although the global financial crisis was indeed global, Billions taps into how loaded the concept of wealth is in America.
"It's interesting," says Lewis. "My understanding of America and Americans is that great wealth is not resented, it's to be aspired to. And that people of great wealth are admired, respected, sometimes even sort of feted.
"And they become a sort of aristocracy here, which doesn't have its own aristocracy. Where I come from - which is Great Britain by the way, if it's not clear - I still have the sense that wealth might be resented a little bit. And it's going to be interesting, I think for people watching: Will people like Bobby for his wealth and respect and admire him for the fact that he made this enormous amount of money? Or is there now in the US a creeping resentment towards these people because of the inequities of social life here and what's happening financially?"
"That's true," adds Giamatti. "But I think it's one of the interesting master strokes of how they've characterised both guys. Because on the other hand, my guy's sort of background is also resented in America. Which is one of wealth and privilege that's gained and passed on, and that seems sort of inauthentic somehow. So both of them have an incredibly fraught relationship to money.
"I mean, everybody does in the world. But Americans in particular have this incredible sort of anxiety and conflict about how you gain it, how you use it."
That anxiety and conflict will drive much of the drama in Billions, along with ongoing questions regarding the morality of the two main characters, both power-mongers. As Lewis explains, both men will be tested:
"I certainly have never met anyone in positions of great power or great influence, who has to run something, whether it be a country, a company, an attorney's office, that wasn't compromised on a daily basis by the running of that institution, whatever it happens to be. You start as ideologues, 21-year-old idealistic, impassioned students. But by the time you're running a country or an attorney's office, a major multi-national company, your day-to-day life is fraught with compromise."
Although Billions stops short of Wolf of Wall Street-level insanity, it's not without some degree of kinky edge as well, as declared by an early S&M moment involving Giamatti, an actor not known for his bedroom scenes.
"The sex stuff gives it a little bit of a heated feeling," says Giamatti. "It's got, in the best possible way, a bit of a pot boiler-ish feeling to it. It's a little bit sweaty."
Lewis is best known for playing the moderately traitorous Brody on Homeland, a show he was originally supposed to be on for just one season. The success of his character led to Lewis sticking around for three seasons before Brody finally left via a noose.
Lewis assures TimeOut there is no such exit strategy for Axe in Billions: "I don't think they hang people for insider trading, so I should be safe. I'm assuming I'm going to be here for a while. If you know anything different, would you tell me? That would be good."
Lowdown
What: Billions
When: Premieres on Tuesday, 8.30pm
Where: Sky SoHo
