On a layover in Hawaii two conniving Navy seamen borrow money to lay down bets that their ship will win the upcoming gunnery practice trophy, having found out that the current gunnery champ has just transferred aboard their ship. What they haven't learned, however, is that the marksman's enlistment is up before the contest is supposed to take place.
It's the week before Christmas and Jack drops by Edgar Bergen's house to go over the upcoming show's script with his guest star. When Edgar is detained rehearsing his radio show, his wife Frances entertains Jack. Jack is amazed when Charlie McCarthy and Mortimer Snerd walk into the room and are introduced. Jack always assumed they were merely ventriloquist's dummies. Edgar finally returns and is ready to present his ideas for a sketch to Jack, but insists on Jack sitting on his knee to hear them.
Milton Haskins, a math genius known for his infallibility with numbers, quits his job with an insurance company when he discovers he made a mistake, and hooks up with a traveling carnival. His knowledge of mathematics makes him a natural as an assistant at the wheel of fortune. His fiancée begs him to return to his job but he refuses, so she joins the carnival and becomes a striptease artist. When Milton attempts to drag her off the stage, a brawling mêlée breaks out and the entire troupe is arrested by the local police. The carnival is sold but Milton reveals that the new owner has conspired to defraud the insurance company. The insurance company has to accept the carnival in lieu of the money owed, and they allow Milton and his fiancée, Vivian, to stay with and help run the carnival.
