Crystal Shackleford [Geraldine Fitzgerald] lures two strangers, solicitor Jerome K. Arbutny [Sydney Greenstreet] and Johnny West [Peter Lorre], to her London flat on Chinese New Year in 1938, convinced that the goddess Kwan Yin will grant a shared wish if three strangers conjure the same desire. The plan hinges on pooling strength to buy a sweepstakes ticket for the Grand National, with a strict agreement: they will not sell the ticket if it’s drawn, and they will hold on to it until the race is run. Crystal hopes the prize will help her win back her estranged husband, Arbutny seeks a smoother path to admission in the prestigious Barrister’s Club, and Johnny dreams of buying a bar and making a life of his own.
The stories of the three strangers unfold in parallel, each marked by longing and deception. Crystal Shackleford’s husband, David Shackleford [Alan Napier], has moved to Canada and fallen in love with Janet Elliott [Marjorie Riordan]. He returns just after Johnny and Arbutny depart, demanding a divorce, but Crystal refuses. She engineers a cruel ruse, telling Janet that David still loves her and that she is pregnant, a lie that convinces the trusting Janet to go back to Canada.
Meanwhile, Johnny West’s past catches up with him. With the aid of Icey Crane [Joan Lorring], he’s been hiding after a drunken botched bank robbery that ended in a policeman’s death. Icey testifies falsely to provide an alibi for the ringleader, Bertram Fallon [Robert Shayne]. When a second witness is undermined, Fallon confesses to the robbery but shifts blame for the murder to Johnny and to Timothy "Gabby" Delaney [Peter Whitney]. Johnny is condemned to die, yet Gabby tracks Fallon down on the way to prison and stabs him. Fallon dies in a railway carriage, and his dying act serves to clear Johnny.
Arbutny’s fortunes swing on the edge of risk as well. He has been gambling with funds from the trust of Lady Rhea Beladon [Rosalind Ivan], and when a stock fall and a margin call loom, he proposes to Lady Beladon. After consulting with her late husband, she refuses, even hinting that Lord Beladon wants the books checked. On the brink of despair, Arbutny contemplates suicide, but a glance at the newspaper reveals that their sweepstakes ticket has been drawn for the Grand National.
The trio converges again at Crystal’s flat. Arbutny wants to sell his share of the ticket immediately to replace the funds he stole, while Johnny prefers to honor their original agreement. Crystal’s death interrupts the plan when Arbutny, in a fit of rage, kills her with a statue of Kwan Yin. Ironically, the radio announces that their horse has won. Johnny points out that the winning ticket must be destroyed to erase the motive for Crystal’s murder, and the group departs. In his guilt, Arbutny rushes into the busy street, stopping traffic and confessing to the murder in front of a gathering crowd and a police officer. David Shackleford arrives with the intent to shoot Crystal, only to be shocked to learn she is already dead.
In the end, Johnny returns to the pub, where Icey finds him, and, content with the life she’s helped him secure, he sets the winning ticket on fire.
