Around noon on Nov. 17, Sam Altman, the chief executive of OpenAI, logged into a video call from a luxury hotel in Las Vegas. He was in the city for its inaugural Formula 1 race, which had drawn 315,000 visitors including Rihanna and Kylie Minogue. Mr. Altman, who had parlayed the success of OpenAI’s ChatGPT chatbot into personal stardom beyond the tech world, had a meeting lined up that day with Ilya Sutskever, the chief scientist of the artificial intelligence start-up. But when the call started, Mr. Altman saw that Dr. Sutskever was not alone — he was virtually flanked by OpenAI’s three independent board members. Instantly, Mr. Altman knew something was wrong. Unbeknownst to Mr. Altman, Dr. Sutskever and the three board members believed Mr. Altman had been dishonest and should no longer lead a company that was driving the A.I. race. On a hush-hush 15-minute video call the previous afternoon, the board members had voted one by one to push Mr. Altman out of OpenAI.