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Each year, rancher Chuck Rodwell returns to the Sands Hotel and Casino in Las Vegas, Nevada where he hopes to make a fortune using that year’s profits to gamble, despite years of losses at the casino’s tables.  One day in the casino, as temperamental prima ballerina Maria Corvier storms out of her rehearsal in the Copa Room, Chuck grabs her hand for good luck during his game of roulette and consequently wins.  Insulted that she is forced to perform her "high art" in a chaotic hotel, Maria haughtily refuses her share of Chuck’s profits, but later apologizes for her behavior.  When Chuck once again wins a slot machine jackpot as he takes Maria’s hand, he attributes his winning streak to her.

Returning to her room, Maria calls her manager, Pierre, to break the Las Vegas engagement, but learns she must fulfill it.  Meanwhile Maria’s chaperone, Seri Hatvany, having seen Chuck, tells Maria that romantic love motivated her during her dancing career, but Maria insists that her only love is dancing.

Later, after hours of losing at the gambling tables, Chuck goes to Maria’s room, where he shares his belief that she is his good luck charm and begs her to test his theory on a slot machine.  Maria is bewildered when they win the jackpot two times in row and agrees to a game at a casino roulette table, where they win repeatedly.  When Chuck, in his excitement, kisses Maria, she is immediately smitten with the rancher.  Despite being anxious to earn more winnings, Chuck agrees to accompany Maria to dinner, after she pleads to spend time alone with him.

While watching the evening stage performance, Maria bemoans that she has missed out on life, having been sheltered by the ballet.  After spending hours successfully gambling at various casinos, Chuck and Maria arrive at the New Frontier and within minutes have won a considerable sum.  On express orders from the casino’s owner, dancer Kelly Donavan, one of Chuck’s old girlfriends, flirtatiously lures the rancher away from the table to prevent him from bankrupting the house.  She then invites Chuck and Maria to the Silver Slipper where she performs a sultry stage number.  A drunken Maria, jealous of Kelly’s sexy routine, stumbles onto the stage and joins the chorus girls in high kicks and lewd hip movements while a photographer catches a snapshot.

Later in her hotel room, Maria complains to Seri that she has no skills to seduce Chuck, and then refuses to take Chuck’s call.  Fearing he will gamble the night’s profits away, Chuck gives the money to friend and blackjack dealer Lotzi for safekeeping.

When the next morning’s paper features a picture of the drunken ballerina’s escapade, Sands manager Tom Culdane, fearing bad press, cancels Maria’s contract.  However, the Sands’ owners later insist that the publicity will pack the house and order Culdane to book additional performances.  Fearing the temperamental dancer will not accept his apology, Culdane asks Chuck for help, but Chuck refuses, saying he wants only to split the profits and leave Maria alone.  Determined to have her own way, Maria approaches Culdane to demand that her contract be upheld, thus solving Culdane’s dilemma.

That night, Chuck is entranced by Maria’s performance during rehearsal and compliments her.  Maria at first rebuffs him but, seeing Kelly waiting to compete for Chuck’s affections, Maria agrees to go out with him, thus defeating Kelly’s efforts.  As Maria prepares to leave, Chuck, sensing young Japanese singer Mitsuko Sawamura’s stage fright during an audition, encourages her to join him in a crowd-pleasing duet.

Touched by his gentle nature, Maria asks to know more about him, prompting Chuck to take her to his ranch.  As they tour the property, Chuck and Maria’s luck extends to the hens, who suddenly deliver dozens of eggs; to a pregnant cow, who suddenly delivers a healthy calf; and to a derelict oil rig which suddenly spouts the "liquid gold" as they pass it.

Later, when his mother, Miss Hattie, declares Maria is the perfect wife, Chuck complains that he has only known her one day and the romance of the ranch will wear off if she was forced to stay there.  However, after Maria joins them wearing Chuck’s grandmother’s western dress, Chuck is so entranced he invites her to stay for dinner.  That night, when Miss Hattie asks if Maria has plans for Chuck, the dancer laments that they do not have much in common, but Miss Hattie retorts that they will have living together in common.  When Chuck and the ranch hands serenade Maria and then entice her into country western dancing, the versatile dancer enthralls the crowd with her quick steps.

Later, as they leave for Las Vegas, Maria ponders life on the ranch and her growing love for Chuck, who then proposes to her.  Upon reaching the hotel, Maria announces her engagement to the newly arrived Pierre, explaining that she will spend six months at the ranch and six months performing.  Although he congratulates her on the decision, Pierre secretly hopes to dissuade Maria from the marriage by cunningly suggesting the couple prove their luck in the casino.  Dozens of people crowd around the now famously lucky couple to witness the winning streak, but the roulette dice repeatedly fall on losing numbers.  When a dejected Maria returns to her room, Pierre happily reports to Seri that "whatever luck they had, they lost."

Pierre finds Chuck at the bar and, after the rancher admits that the love spell has "broken," Pierre advises him to allow Maria to concentrate on her work the following day.  The next morning, Maria and Chuck, disappointed by the change in luck at the tables, agree that that their romance has also come to an end.  That night, Maria performs an elaborate modern dance stage rendition of "Frankie and Johnny" with co-star Kelly, while Chuck looks on, still enchanted by the ballerina.  When a young bride and groom at Lotzi’s table tell him that they have had no gambling luck, but realize their fortune in having found each other, Chuck rushes to Maria’s dressing room, where the couple renew their vows and agree to quit gambling.