Both the mother and the father of this family have small incomes that are not quite enough to support the lifestyle they desire or purport to have, and all of their attempts to better themselves fail. One day Paul, the only son among the three children, questions his mother as to why they don't have a car of their own. His emotionally distant mother answers that they are the poor members of the family and it is because they have no luck. Paul tells his mother that he has luck and he knows it's so because God told him.
Determined to prove it, Paul spends hours furiously rocking himself into a trance on his rocking horse, a too-expensive toy he received for Christmas one year, trying to divine the names of winning horses for upcoming horse races. He partners with the family's gardener, who bets on horses and begins to invest and win. Paul's uncle finds out about the partnership and is at first merely amused by the boy's interest in horse racing, but then joins in the betting once he sees that Paul has a gift for choosing winners.
After amassing a tidy sum, with his uncle's help Paul implements a plan to anonymously gift his mother a portion of his winnings in hopes of making her happy and quieting the whispering voices in the house. Using the family lawyer, Paul bequeaths an amount of 5,000 pounds to his mother to be allotted at 1,000 each year for five years. Upon receiving notice of the annuity, with cold determination the mother visits the lawyer to request the whole 5,000 at once. After consulting with his uncle, Paul accedes and his mother receives the full amount. With the arrival of this large sum, the whisper in the house becomes a deafening roar for even more money.
The voices frighten Paul terribly, and after a couple of losses at the races, he becomes determined to the point of madness to satisfy the house's demand for money. Noticing Paul's anxiety, his mother tries to send him to the seaside for healing and rest, but he begs her to let him stay until after the Derby. She allows him, but two days before the Derby, on a premonition of disaster, she comes home early from a party to check on him. She finds him in his room, rocking furiously on his toy horse in the dark. She flicks on the light, and in a strange voice Paul cries out the name of the winning horse and then collapses to the ground.
Paul lingers bedridden for a couple of days until the Derby, neither asleep nor conscious. His uncle and the gardener place his bets for him, having learned of the name he cried out before falling stricken. He is right once again, and the winnings are enough to make the family rich. Upon being told of the results, Paul awakens from his stupor and tells his mom that he is lucky, just as he told her before. He dies later that night.