“Why don’t you pass the time by playing a little solitaire?” Nothing is as it seems in John Frankenheimer’s quintessential Cold War thriller, as even this banal directive can trigger world-scale pandemonium. George Axelrod adapts Richard Condon’s account of a decorated Korean War hero (Laurence Harvey) whose inscrutable behavior and ties to a Joseph McCarthy–like demagogue alarm his former commander (Sinatra). Frankenheimer’s taut direction captures the paranoid charge of the Kennedy era, with Angela Lansbury’s turn as Harvey’s manipulative, quasi-incestuous mother landing the coup de grâce. Realizing the urgency and importance of the subject matter, Sinatra gave his all to the production, including the use of his private plane. J. Hoberman contextualized the film’s legacy by calling it “a chunk of America’s psycho-history—as much oracle as movie.”