In retrospect, we should have seen that Natasha Lyonne had a Lt. Columbo waiting to burst out of her all along.

Like Peter Falk, she has one of TV’s most distinctive presences, with an old-soul rasp and a hipster-next-door bearing that’s simultaneously down-to-earth and cosmic. She put that quality to use in “Russian Doll,” an existential mystery about a woman who is continually reliving her death, set in a contemporary New York City that felt haunted by its past. (The follow-up second season involved actual time travel.)

With the appealing, shabby-slick “Poker Face,” Rian Johnson has put her in a time-travel story of a different kind: a contemporary revisiting of the underdog-detective crime stories of network TV a half-century ago. The logo may say Peacock — the streaming service that premieres the series on Thursday — but the vibe says NBC weeknights in the 1970s.

Like “Russian Doll” or Johnson’s “Knives Out” mystery flicks, “Poker Face” starts with a simple premise that the show then twists and retwists: Charlie Cale (Lyonne) always knows when people are lying.

As any reasonable person would, she applied her gift to gambling, but after some unfortunate turns she has ended up waitressing at a casino. The murder of a friend makes her realize that she can also use her intuition to solve crimes — and after she implicates a dangerous suspect, she ends up on the run down the back roads of an America that turns out to be full of wacky killings.

You would think that Charlie’s superpower would make the solution to the cases less than suspenseful. You would be correct. Johnson (who also writes and directs multiple episodes) shows you up front who did it and how, as “Columbo” did. The real mystery is whether and how Charlie can assemble enough proof to make the case stick. Along the way, the series makes some sly points about who, in our society, cases do and don’t stick to.

“Poker Face” draws you in first with its retro style. The camera tracks the baroque carpet pattern of a slightly dated casino hallway; the yellowed screen credits could be lifted straight from a “Columbo” episode of the early ’70s. The atmosphere is so immersive that when a contemporary reference comes up — to MAGA, say, or “Euphoria” — it feels anachronistic.

But the vintage echoes are also deeply thematic. The ’70s loved a beautiful loser, like James Garner’s Jim Rockford, the ex-con private eye whom the world gave the bum’s rush no matter how many cases he cracked.

Charlie has a similar working-class panache. “I’ve been rich,” she tells a casino boss (Adrien Brody) in the pilot. “Easier than being broke, harder than doing just fine.” But her Zen has limits; she has a deep-seated sense of justice and fairness, which at the outset of the series she channels into angry replies on Twitter.

Her first case, involving a casino housekeeper (Dascha Polanco, Lyonne’s castmate from “Orange Is the New Black”), awakens that rage. It also suggests a darker, “Chinatown”-like direction, with its themes of exploitation, violence against women and the rich getting away with unspeakable acts.

But as Charlie hits the highway in her rattletrap Plymouth Barracuda, “Poker Face” takes a lighter turn, one you might recognize from the guest-star-laden procedurals of the ’70s and ’80s. Judith Light plays a former radical in a retirement home; Ellen Barkin and Tim Meadows spar as former TV co-stars; Chloë Sevigny and John Darnielle of the Mountain Goats play washed-up rockers in a caper with the metal satire cranked up to 11.

“Poker Face” quickly settles into a pattern. Act 1, you see the deed done. Act 2 rewinds to put Charlie at the scene. After a few applications of her B.S. detector, the real game begins: how to find more than circumstantial proof. (As one baddie sneers to Charlie, “Encyclopedia Brown”-type sleuthing doesn’t hold up well in court.) Then it’s next town, next corpse.

As its mysteries unfold, it becomes clear that Charlie’s other superpower is her common touch. She’s a friend to truckers, stagehands and strays, and more often than not, her connection to the people ignored or put upon by the powerful is what gets her the goods.

Lyonne’s performance, simultaneously laid-back and wired, makes “Poker Face” worth the buy-in. Charlie’s apparent flightiness manifests in the whirring of her hyperactive mind, agitated by the ceaseless “birds chirping” of people’s constant everyday lies. It’s a delight to watch her feel her way down the dark corridors of a run-on sentence, landing in odd semantic corners, as when she repeatedly struggles to remember the word “locker” or stops halfway through a deduction to marvel at the verb “figure”: “God, there’s a weird word you say it over and over.”

It’s all light fun, but not 100 percent weightless. “Poker Face” shares with Johnson’s most recent detective film, “Glass Onion,” the awareness that having the facts does not equal getting justice, and that justice is harder to come by the higher the culprit is on the economic ladder.

The cases of the week involving two-bit schemers and has-beens are easy enough to make stick. Against the more powerful, as she discovers in the series’s continuing story line, you sometimes need to take justice into your own hands, and the consequences upon your own head.

In the six episodes (out of 10) screened for critics, however, that story line mostly takes a back seat to the self-contained mysteries. This makes “Poker Face” an outlier in a streaming-drama environment that is usually friendly to seriality. And that’s both its strength and weakness.

“Poker Face” benefits from the freedom of streaming (Charlie reflexively uses a familiar expletive for lying that would not have gotten past network standards and practices in Columbo’s day). And in theory you could binge it: Peacock drops the first four episodes at once, one per week thereafter. But it almost begs to be portioned out weekly. “Poker Face” makes a great diversion if you’re in the mood for a crime-y treat, but when you watch episodes back-to-back-to-back, the repetitiveness of the formula becomes glaring.

Of course, formulas become formulas because they work. So does “Poker Face,” in all its unapologetic quaintness. This is a low-stakes table, but it’s a fun one to hang out at.