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At the Nutmeg Insurance Company in Hartford, Connecticut, Havard-educated actuary Milton Haskins is awarded a quick promotion for his unerring rate tables.  His secretary, Vivian Reilly, thrills to the news, since the promotion will speed up Milton's life plan and allow them to marry earlier.  Soon after, however, boss Mr. Bixby and company president Mr. Mapleton point out that Milton has made his first mistake, which cost the company thousands of dollars, and he decides he must quit.

While walking dejectedly in the park that day, he meets carnival pitchman John "Goldie" McGoldrick, who quickly realizes that Milton's genius at predicting mathematical progressions can serve them well with carnival chance games.  Goldie gets Milton drunk and brings him to the carnival, where he finagles a job for Milton from owner Jason "Pop" Carter, who is struggling to keep an investor, Mrs. Minerva Henkle, from buying the failing carnival out from under him.  Goldie puts Milton to work as a fake customer on the Wheel of Fortune game of chance, but Milton cleans out the game by successfully predicting the outcome of every spin of the wheel.  Goldie then urges him to work in the carnival follies, where Milton blooms as a dancer and singer.

Soon, Vivian arrives and jealously watches Milton dancing with beautiful women.  After the show, someone tries to break into Milton's suitcase and throws a knife at him, but he insists to a fellow performer that he has never felt so alive.

Later that day, the carnival's accountant, Herman Bogel, who suspects Milton might be a spy from the insurance company, urges dancer Sally to seduce information out of Milton.  When Vivian stands at Milton's door and hears them together, she mistakenly assumes they are having an affair, and lets Goldie's girlfriend, dancer Bunny LaFleur, talk her into joining the carnival show to make Milton jealous.  In the middle of the show, Milton attempts to drag her offstage, resulting in an audience mêlée which lands all the carnies in jail.  Though Bixby bails out Milton and Vivian and coaxes them back to work, they refuse to leave until he promises to release their friends, in exchange for Milton's salary for the next two years.

Milton returns to the office, but leaves immediately when Vivian finds an insurance file on Mrs. Henkle which incriminates her and Bogel.  Though Pop has just sold the carnival to Mrs. Henkle, Milton, Vivian, Bunny and Goldie run to the arena and entertain the crowd to keep the carnival alive until Bogel, Henkle, Bixby and Mr. Mapleton can be assembled.  Milton then reveals that, years before, Mrs. Henkle collected on an insurance policy on her dead husband, and if Bogel has a tattoo of a heart on his chest, it will prove he is her husband and they have committed fraud.  Though at first Bogel displays a tattoo of a boat, Vivian's accusation that she is having Bogel's baby makes Mrs. Henkle attack Bogel until he pulls off the fake tattoo and reveals the real one underneath.  After they are arrested, and Pop regains control of the carnival, Milton and Vivian agree to do Nutmeg's accounting as long as they can continue to work at the carnival with their friends.