Now here’s a mystery worth solving: Why doesn’t Hollywood give us more ridiculously complicated, gratuitously eccentric whodunits? You know, the kind of all-star affairs where a colorful assortment of highly suspicious characters gather in a remote manor, or at an old castle, or on the Orient Express, in order to be confronted by a corpse and the prospect that a murderer lurks among them. It’s not that audiences have lost their appetite for such tales. Au contraire, ’twas television that killed the old-fashioned detective story. Over the years, “Murder She Wrote” and “Masterpiece Mystery!” have rendered such movies redundant — on the big screen at least — by solving procedurals on the small screen each week.

With “Knives Out,” writer-director Rian Johnson shows that there’s life left in the genre, paying crowd-pleasing tribute to the likes of Arthur Conan Doyle, Agatha Christie and Ruth Rendell with a wondrously convoluted case recounted in the most roundabout way possible. Taking a break between “Star Wars” sequels to knock off something a little less far, far away from his heart (which is not to say that he hasn’t put himself into George Lucas’ galaxy), Johnson returns to the genre that started it all for him — as the director who translated hard-boiled detective novels to a high school setting in his 2005 debut, “Brick.” The director has learned a few tricks since, and here he gets to show them off in service of a suitably squirrelly plot.

When a best-selling mystery novelist is found dead by what appears to be his own hand, it seems only natural to assume that the “suicide” is in fact the first clue in an elaborate game of some kind. Harlan Thrombey (Christopher Plummer) is the only mastermind living in the family mansion. His three ostensible heirs — elegant Linda (Jamie Lee Curtis), earnest Walt (Michael Shannon) and widowed Joni (Toni Collette) — and their various offspring have gathered for the patriarch’s 85th birthday, which is festive enough until the following morning, when Harlan is discovered with his throat slit.

He always knew how to deliver an ending. Now, it’s up to the police (Lakeith Stanfield and Noah Segan), plus a celebrity detective (Daniel Craig), to figure out who’s responsible. While the principal suspects — Linda’s husband Richard (Don Johnson) plus the aforementioned three make four — each share their version of events, Johnson begins to feature flashbacks to the night in question. In other crime movies, such reenactments have been known to be unreliable, bent to reflect the testimony as it’s heard — a kind of “Rashomon”-like trick to keep the viewer guessing. Here, the vignettes depict the truth, amusingly revealing the omissions and lies in each speaker’s story.

Twists abound in “Knives Out,” but by far the most unexpected is Johnson’s decision to treat this brain teaser as a comedy. Apart from the zany screwball headache that was “The Brothers Bloom,” the director’s films have been undeniably clever but distressingly serious. Here, he manages to blend the two, populating the Thrombey household with one-of-a-kind weirdoes. The only remotely normal individual among them is Harlan’s nurse Marta (Ana de Armas), the immigrant outsider with the innocent eyes and lie-detector stomach (like a dyspeptic Pinocchio, she pukes at the first sign of falsehood).

It all serves to remind what a pleasure is to be had untangling elaborate cases when the mystery is twistery and the ensemble, like that creaky “dark and stormy night” cliché, is sufficiently over-cast. By enlisting stars to play each of the characters who plausibly coulda done it, Johnson recalls movies such as “Murder by Death” and “Clue,” which walked a fine line between homage and self-parody. The setting may be American, but there’s a decidedly British flavor to the proceedings — which makes Craig’s chicken-fried accent all the more peculiar. Taking a breather between James Bond movies, the actor seems determined to amuse himself, going overboard with the character, much as he did in “Logan Lucky” (although there, at least, it played to more amusing effect).

Craig is perhaps the only one whose performance seems to have spiraled out of Johnson’s control. The others are each encouraged to make an impression without leaving quite so many teeth marks on the scenery. And what scenery it is! The Thrombey estate is an art director’s dream, as production designer David Crank imagines a mansion that only a mystery novelist could fashion for himself, full of secret panels, back hallways and overt references to the genre (as in the macabre circle of daggers and swords decorating the library). It’s like Guillermo del Toro’s “Bleak House,” the building next door to the horror director’s actual home, which he’s stuffed to the gills with all the things that inspire him.

Thrombey’s best-sellers may have bought that mansion, but his kids, their kids and the various ungrateful in-laws seem willing to do just about anything to get their slice of his publishing empire — whores d’oeuvre, if you will. By contrast, “the help” — as Marta and the maid, Fran (Edi Patterson), are called — respected the old man, and cooperate to solve the case. America may not have the same rigid class system that features in so many British mysteries of this sort, but Johnson engineers a way to make a statement about wealth and entitlement in his own country. The rich-folks jabs provide the film’s cheapest laughs, although the choice to tell the story largely through Marta’s perspective makes a statement, and helps to exaggerate how awful the family members are. The only one who seems remotely decent is Harlan’s black-sheep grandson Ransom (Chris Evans), who shows up late and whisks Marta away from the jackals.

If only Harlan could see how disgracefully his successors conduct themselves when he’s gone. Or maybe he knew them well enough to anticipate exactly how they’d behave. That’s a beguiling possibility as well — and one with which Johnson repeatedly entices us as his intricate narrative skips between various characters’ points of view. “Knives Out” recalls a time when audiences could still be surprised by such mysteries, before the genre devolved into a corny parody of itself. Johnson keeps us guessing, which is good, but the thing that makes this a better mousetrap than most isn’t the complexity, but the fact he’s managed to rig it without the usual cheese.

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