I seem to have annoyed Paul Giamatti. I have asked him about being typecast. People have in their head a specific idea of a Paul Giamatti character, and he wants to analyse exactly what that is.

“You can say that to me, and I’m, like, ‘Typecast as what?’ As complicated people? As dark, complicated guys . . ? I played Hamlet, too, and it’s on stage, and I guess that was typecasting, but nobody would ever have thought of me to play Hamlet before . . . I do tend to play these kinds of dark, weird guys, but what are they? They’re different things all the time.”

He's right – but there's often something of the neurotic oddball in the people he plays. We have the relatable Everyman of Barney's Version, Cinderella Man and Saving Mr Banks and the self-loathing grump of American Splendour and Sideways. Then there are recent performances as evil music men in Love & Mercy and Straight Outta Compton. He laughs. "I did two of those guys, so I guess that makes me typecast as egotistical band managers."

Ultimately, he’s pragmatic. “I guess my other response is, if I’m typecast, great – because I work. So it’s fine by me if I am . . . It’s better than the alternative.”

Giamatti thinks the typecasting question is a polite way of asking how his looks affect his career. He was nominated for an Emmy for his part in Inside Amy Schumer's parody of 12 Angry Men, in which a roomful of men debate whether Schumer is hot enough to be on television. ("Her ass makes me furious!" Giamatti's character roars.)

He relates to some extent to the way women are scrutinised by Hollywood. “It’s all about looks, being an actor,” he says. “Seventy-five per cent of it is what you look like, so for sure I’ve been made well aware by critics and people over the years how I’m not a traditionally handsome person, to put it mildly.” Some of those people have referred to him in print as Mr Potato Head and “puddin’ face”.

“Funny-looking, not-handsome people”

“But I even think the typecasting thing is a weird way of asking the same question,” Giamatti says. “Like, ‘You have to play these types of funny-looking, not-handsome people.’ And it’s, like, ‘Well, yeah, I do, because I don’t look like Brad Pitt.’ I’m not going to play those things, guys: I just don’t look like that. I can only play a certain spectrum of things, because I don’t look like a superhero.

“So I do feel a weird sympathy,” he says. “I’m sure women will pile all over me, tell me to go f*** myself for saying that. But I’ve said ‘sympathy’; I don’t feel empathy. I don’t identify myself with a woman who’s being attacked, but I do see it, and I go, ‘Yeah, I know that.’ That can suck a lot of times.”

I tell him I feel bad for asking the typecasting question. “No, don’t. You’re the first person I’ve actually honestly answered the question for – which feels good, actually.”

Giamatti's most recent role is as a ruthless US attorney, Chuck Rhoades, in Billions, the new Sky Atlantic melodrama. Hunting for evidence of insider trading, Rhoades is determined to take down a cocky hedge-fund billionaire, Bobby Axelrod, who's played by Damian Lewis. "The stuff is really juicy that he and I are doing. We sit there and f***ing snarl at each other, so, like, it's fun."

His character, Giamatti says, is “a pretty powerful person, and I don’t usually play powerful people. He’s a person that actually tells people what to do and they do it, and that’s different. I’ve never done anything like that. And the thing with the wife, I’ve never done anything like that.”

“The thing with the wife” is revealed early on. The show opens with a dominatrix standing astride a hog-tied Rhoades, putting a cigarette out on his chest. We learn that they’re married and that this is simply what they get up to when the mood takes them.

It’s not new to give a powerful man a kinky sex life that’s centred on dominance and submission, but here it’s portrayed in a novel way. “I appreciated the fact that they were presenting it as just part of these people’s relationship. It’s nonjudgmental, which I really liked. The show is all about power and dominance and restraint, so I thought it was an interesting subtext of the entire show.”

Billions toys with the audience's ideas of morality – and as you might for Walter White or Don Draper, you often find yourself rooting for Lewis's billionaire antihero.

“I don’t have kind feelings about hedge-fund guys who break the law,” Giamatti says, although he accepts that “there’s a lot of people don’t see any reason to go after those guys”.

These are pertinent considerations in the age of Donald Trump: the zenith of the American idea that wealth equals greatness. "It's become relevant in a way I don't think anyone could've imagined," says Giamatti. "Billions posits two opposing camps that are tied up with each other in a weird way – political power and financial power – but now there's one guy who will potentially embody both at the same time.

“That’s one of the interesting things about the show: inherited money versus working-class money. The money Axelrod made as a working-class guy is interesting, because for Americans inherited money is just vile. So a guy who is making money, what’s wrong with that? How can that be bad?”

When it comes to making money himself, Giamatti has said he’s not motivated by a pay cheque. When I mention this he’s taken aback. “Did I say that? Where did I say that? I doubt I ever said that. What I imagine I said was, I’ve never done anything solely for the pay cheque. Believe me, I’m perfectly well motivated by a pay cheque. But I’ve never done something only for the money. I’m going to be part of a story, so the story has to be good.”

Despite those exacting standards, Giamatti has made satisfying progression towards centre stage. “I don’t know whether I’m a leading man or a character actor or what. I know that the parts got bigger. I have more responsibility.”

This move brings a new challenge. “It’s more like a surgical strike in the supporting roles. You know you have to come in and compactly nail something that kind of colours the scene. And with the leading guy you really have to have an incredible level of relaxed control over this thing that I find trickier. I tend to be somebody who likes to come in and hit something hard and then slip out. It’s like a sprinter and a distance runner.”

Billions is on Sky Atlantic on Thursdays