Superstitious New York gambler Joe Baldwin, Onslow Stevens, owner of the thoroughbred racing horse Sarcasm, believes luck can be bought with charitable deeds. To test this theory, he finances an expensive trip to Europe for his supposed "good luck charm," the gold-digger Jean Jason, Maxine Jennings, not realizing she is bringing along her lover, the gigolo and sometime artist Paul Vinette, Vinton Hayworth. He also hands cash to his old friend Frank Bent, Paul Guilfoyle, to rescue his cab business, and then visits an orphanage in Louisville with his sister, where he meets Betty McKay, Helen Mack, a practical teacher who scoffs at his philosophy.
Betty McKay's skepticism is tested when Joe hopes for rain on Derby day to muddy the track in Sarcasm's favor. It rains as he wishes, but the race ends with a defeat for his horse, and Joe becomes convinced that it was the orphans at the orphanage who were somehow pulling against him. The setback only deepens his belief that luck is something one can engineer through acts of generosity, even as the crowd rituals around the race unfold.
To repair the image before the Preakness, Joe throws a lavish party for the orphans, filling the night with clowns and entertainment. Betty is surprised by his sudden warmth and generosity, and a genuine connection grows between them. In the aftermath, Sarcasm takes the win at the Preakness, affirming Joe's stubborn faith in luck, and he heads back to New York a more hopeful, if still improbable, believer.
Back in New York, Jean is back from Europe, and Joe tells her he will not be seeing her again because he is planning to marry Betty. Jean, however, pressures him for money and squeezes out a $50,000 "luck insurance" payment before a final parting. Before Joe can present the check, Paul arrives at Jean's apartment. They argue when he learns that she plans to run away with the money, and in the heat of the moment Jean threatens him with a gun; during a scuffle, she kills him.
Joe reaches Jean's building shortly after, and Paul, posing as Joe, calls the police and reports a murder. Joe is tried for Jean's murder and convicted on circumstantial evidence, but he escapes before his final lockup. With the help of Frank's cab, and Betty's patient questioning of the many suspects, Joe traces the evidence to Paul, using the passenger lists of Jean's voyage. The plan collapses when Paul discovers the setup, and he is ultimately implicated in the murder and forced to confess.
In the end, the lesson lands with quiet conviction: luck cannot be bought. Joe, now free to choose honesty over illusion, embraces Betty as their future together begins, a tempered man who has learned to see beyond a man-made creed of luck.
