Mr. Zuckerberg started training on a lark mostly in his garage in 2021, where he built what he called a “mini academy” with a circle of friends who spar with him. He has said he appreciated that Brazilian jujitsu required “100 percent focus” and strategic thinking to defeat an opponent, rather than brute strength.

Mr. Zuckerberg has sought out martial arts experts, including Dave Camarillo, James Terry and Khai Wu. In May, he competed in his first public martial arts tournament in Redwood City, Calif., which he attended undercover — up until the moment he took off his hat and sunglasses to fight. He won gold and silver medals in the challenge.

Last year, Meta also announced it had partnered with the U.F.C. to bring mixed martial arts fights to Horizon Worlds, its virtual reality app.

Mr. White said Mr. Zuckerberg was truly dedicated to the sport.

“I’ve been talking to Zuckerberg now for maybe close to two years now,” he said. “And there’s never like banter or we’re joking and laughing.” He said the Meta chief executive was “dead serious all the time.”

Mr. Zuckerberg is likely in fighting shape. He has been on a strict workout regimen, going for runs and challenging friends and colleagues to beat his times, two people close to him said. This month, he posted a personal record for completing the “Murph” challenge, which requires completing a series of pull-ups, push-ups, running multiple miles and doing hundreds of squats, all while wearing weighted, military-grade body armor.

“Doing sports that basically require your full attention, I think, is really important to my mental health and the way to stay focused on everything I’m doing,” he said in a recent podcast episode.

Mr. Musk, on the other hand, has tweeted that he “almost never” works out and once suffered a back injury that required surgery after participating in an exhibition with a sumo wrestler. This month, he said he had trained in “judo, Kyokushin (full contact)” — two Japanese martial arts — and “no rules streetfighting.”