The decades-old game show, TV comfort food for many, has been rocked by drama over who would replace the late Alex Trebek.When Ken Jennings arrived at the “Jeopardy!” studios in November for the first day of his audition to become the new host of the long-running quiz show, he found a gift waiting for him: a pair of Alex Trebek’s cuff links, along with a handwritten note from his widow, Jean.Mr. Trebek, the “Jeopardy!” galaxy’s central star, had died of pancreatic cancer three weeks before, setting off a frenzy in Hollywood: one of the greatest jobs in television was available for the first time in 37 years.For some members of the “Jeopardy!” crew, the cuff links validated their assumption that Mr. Jennings, a genial Utahn who rose to fame in 2004 after winning a record 74 consecutive games, had been Mr. Trebek’s preferred successor. (“Jeopardy!” producers had arranged for a phone call between Mr. Jennings and Mr. Trebek two days before he died.) But “Jeopardy!,” while a beloved cultural icon, is also a lucrative asset of Sony Pictures Entertainment, and in the television industry, sentiment only goes so far.“Jeopardy!,” whose first iteration began in 1964, is one of TV’s last bastions of comfort food, a place where politics don’t matter and the real world is easily digested in just-the-facts bites. Then its succession drama got messy. After a cattle call of guest hosts, including Anderson Cooper, Robin Roberts, Aaron Rodgers, LeVar Burton and even Dr. Mehmet Oz, the announcement of the winner sent fans into a tailspin. The new weekday host would be Mike Richards, the show’s obscure executive producer and the man initially charged with finding Mr. Trebek’s replacement.Mr. Richards, it seemed, did not have to look very far.Critics accused Mr. Richards of rigging the contest à la Dick Cheney, who led the vice-presidential search for George W. Bush. Old lawsuits surfaced from Mr. Richards’s previous job, at “The Price Is Right,” involving his treatment of female staff members. (He denies wrongdoing.) After Sony said the “Big Bang Theory” actress Mayim Bialik would host the show’s prime-time spinoffs, her past skepticism about vaccines recirculated. (Her team said “she is not at all an anti-vaxxer.”)Mike Richards, the show’s executive producer, was named Mr. Trebek’s weekday replacement.Carol Kaelson, via ReutersUnder the retro, feel-good surface of “Jeopardy!,” the succession battle is a story of television’s dwindling real estate in American life and the strenuous efforts to occupy one of its remaining desirable plots.“It is a little like choosing a pope,” Mr. Jennings said, in his first interview since the new hosts were announced. “If you don’t watch ‘Jeopardy!,’ you don’t understand, but people take this very seriously.”In an age of atomized audiences, “Jeopardy!” still averages 8.8 million viewers a week, according to Nielsen — not quite “NCIS” territory, but roughly comparable to a network evening newscast. Its audience skews older: Last year, about four viewers out of five were over age 55.And the job itself is, as any Hollywood agent would tell you, a pretty sweet gig.When the “Jeopardy!” cast and crew gather on the Sony Pictures stage in Culver City, Calif., they film five 30-minute shows in a single day, the equivalent of one week of syndicated television. The host works roughly two days a week, two weeks a month — and toward the end of his tenure, Mr. Trebek’s salary was estimated at $16.5 million. Sony would not disclose Mr. Richards’s compensation, but several people familiar with internal discussions said it was significantly less.There are other perks to being the face of a show that is still watched by a broad audience on local network affiliates, a rarity as the nation divides into ever-more-partisan extremes and as traditional TV is supplanted by niche streaming services.“It’s appointment television, which is rare,” said George Stephanopoulos, the ABC News anchor, who guest hosted for a week. “It’s the kind of thing you can watch with your whole family.”Plus there is the reflected glow of always having the right answers.“It’s absolutely iconic,” said Rick Rosen, the TV superagent at Endeavor. “Everybody knows the show and has played along with it. And it’s not the type of show where you’re just a genial host — there’s a perception of intelligence that goes along with it.”Unlike his rivals, Mr. Richards, 46, had a deep background in game shows. Born in Burbank, Calif., he started his career as a stand-up comedian and went on to host game shows like the mid-2000s concoction “Beauty and the Geek.” He hosted and produced numerous series on the Game Show Network before auditioning to replace Bob Barker on “The Price Is Right.” Drew Carey got the job, but Mr. Richards was brought on as executive producer; his successful 11-year tenure revived the wilting franchise into a hit.By “Jeopardy!” standards, though, he was a newcomer.He started as executive producer at both “Jeopardy!” and “Wheel of Fortune” in May 2020, replacing Harry Friedman, who oversaw both shows for 25 years. Mr. Richards overlapped with Mr. Trebek on set for only 15 shoot days before the host stepped aside, 10 days before he died.Sony said that while Mr. Richards initially led the hunt for Mr. Trebek’s replacement, he moved aside after he emerged as a candidate.But as executive producer, Mr. Richards retained a key role in selecting which appearances by each prospective host would be screened for focus groups, whose reactions weighed heavily in Sony’s decision-making, according to three people familiar with the show’s internal deliberations. The other supervising “Jeopardy!” producers were excluded from that process, the people said.Asked about Mr. Richards’s role, Sony referred to a memo from its TV chairman, Ravi Ahuja, who told staff that after the company began considering Mr. Richards as a potential host, “he was not part of” the selection process. The ultimate decision was made by Tony Vinciquerra, the chairman of Sony Pictures Entertainment.As questions mounted, Mr. Richards sent a memo to “Jeopardy!” staff that was distributed by Sony’s publicists.“The choice on this is not my decision and never has been,” Mr. Richards wrote. He said the “Price Is Right” litigation — which included an allegation that he made insensitive comments to a pregnant employee — “does not reflect the reality of who I am.” (Sony said it had “spoken with Mike about the issues raised in these cases and our commitment to maintaining a workplace environment where our employees are respected and supported.”)Mayim Bialik was announced as a co-host.Carol Kaelson, via ReutersOn Thursday, Sony announced Mr. Richards and Ms. Bialik as co-hosts, although for now, only one prime-time special featuring Ms. Bialik is scheduled. “What started out with my 15-year-old repeating a rumor from Instagram that I should guest host the show has turned into one of the most exciting and surreal opportunities of my life!” Ms. Bialik said in a statement.Mr. Jennings, who remains a consulting producer at “Jeopardy!,” praised Mr. Richards’s performance. “Mike was the only person up there with any game show hosting chops, and it showed,” he said.Some fans argue that a relatively bland, little-known host was always a better outcome than a celebrity. “The game is the star, and the contestants are the stars,” said John Podhoretz, the editor of Commentary magazine and a 1987 quarterfinalist in the “Jeopardy!” Tournament of Champions. “The host should be a secondary figure.”For his part, Mr. Jennings agreed. “What was great about Alex was we didn’t know anything about him: He came into our homes every night and he hosted ‘Jeopardy!,’” Mr. Jennings said. “Today, it’s very hard to find a broadcaster whose priors and opinions you know nothing about.”Mr. Jennings, who guest hosted six weeks’ worth of shows, said he harbored no hard feelings about the outcome.“I knew ‘Jeopardy!’ was in a spot this year, and I mostly wanted them to have a smooth transition,” Mr. Jennings said. “I was not going to lobby for that job in the media, ever. I was not going to plant stories about what a promising young candidate I was. I wasn’t interested in doing any of that. I am a company man.”Marc Tracy More