On the French Riviera, Theo Wilkins reunites with his old friend Paul Mason, who has spent the last three years in an American penitentiary. When the wary Paul wonders why Theo suddenly sent him a plane ticket to fly to France, Theo takes him to a sidewalk café, where Pancho and Melanie, seated at a rear table, size him up. Pancho and Melanie are two of Theo's five accomplices in an elaborate caper he is planning, and Theo begs Paul to join them and be the "one friendly face among strangers." Theo, who was once a prominent science professor before turning to crime and being unceremoniously "cast out into the gutter," has devised his revenge in the form of what he terms an elaborate experiment that will make the world gasp--the $4,000,000 robbery of the Monte Carlo casino. Reluctant to commit himself, the cautious Paul agrees only to meet Theo's five accomplices at a tawdry club, where Melanie performs seductive dances while Pancho plays saxophone. In addition to Melanie and Pancho, Paul is introduced to Raymond Le May, who works as the secretary to the casino director and is in Melanie's thrall; Louis, a seasoned safecracker; and Hugo Baumer, an expert mechanic and get-away driver. Paul suggests continuing the discussion at Pancho's hotel room, and there they examine a blueprint of the casino that depicts a private elevator leading from the director's office to the vault two floors below. The next day, everyone except Raymond and Theo regroup in Pancho's room, and Paul agrees to throw his lot in with them on the condition that he be given total authority. Paul then asserts that they must move up the heist to the evening of the Governor's Ball, the night the casino will be the most crowded, and to draw the timid Raymond deeper into their web, insists that he issue them invitations to the ball. After Hugo purchases a limousine, an ambulance and a swift get-away car, the group holds a dress rehearsal of the theft. Posing as a wheelchair-ridden baron, Pancho, accompanied by Theo, the baron's "personal physician," drives to the casino in a limousine chauffeured by Hugo. Meanwhile, Paul and Louis check out access to the governor's apartment and the elevator leading to the vault. On the night of the ball, they reconvene at Pancho's, and Paul is surprised to discover that Melanie does not live there, but has her own place. When Theo shows Pancho a cyanide tablet that will make it appear that he has suffered a heart attack, thus creating a diversion at the casino, Pancho balks, fearful that the tablet may kill him. At the casino, Louis, Melanie and Paul present their invitations, and soon after, Pancho and Theo, as the baron and his physician, arrive. Paul and Louis then slip out the window and onto a narrow terrace to scale the casino façade up to the governor's apartment. Louis, terrified of heights, is prodded by Paul until they reach the elevator and descend to the vault. As Louis drills open the safe, upstairs in the casino, the Duc di Salins recognizes Melanie as an exotic dancer. When the Duc alerts the casino director about Melanie, Raymond begins to lose his nerve, but Melanie coolly instructs him to delay the police. Meanwhile, at the roulette table, Theo reminds Pancho to take his medicine and when Pancho places the tablet in his mouth but refuses to bite down on it, Theo injects him with a dose of cyanide, after which he collapses. After declaring that his patient has suffered a heart attack, Theo advises that the baron be taken to the director's office. Soon after, a concerned doctor knocks at the door to report that he detected the odor of cyanide, thus disputing Theo's diagnosis of a heart attack. Stating that he was simply being discreet, Theo explains that the baron committed suicide and then calls for an ambulance to pick up the body. After Theo and the others leave the room to wait for the ambulance, Paul and Louis, carrying a satchel of stolen bank notes, enter the office, stash the money in the seat of the wheelchair and then take the elevator up to the governor's apartment. As they slip onto the ledge to climb down to the casino, Melanie struggles to unlock a window so that they can sneak back inside. Soon after the window pops open, the police arrive to question Melanie about her escort. Just then, Louis and Paul appear and identify themselves as Melanie's escorts. As Louis and Melanie dance toward the exit and their waiting car, Paul nods to Theo that their mission is a success. Turning to the director, Theo suggests removing the baron in his wheelchair so as not to call attention to his condition. They then wheel the baron to the waiting ambulance, where Paul and Hugo, dressed as ambulance attendants, wheel him in. After the ambulance drives off, the exhilarated Theo anxiously anticipates hearing "the world gasp" about his crime, and then exhausted, drifts off to sleep. Soon after, Pancho regains consciousness and notices that Theo has died. Pulling off the road, Paul tearfully cradles Theo's lifeless body in his arms and insists on driving him back to his hotel. Melanie asks to go with them, and after putting Theo to bed, Melanie confides that she envies him because he died happy. When Paul bitterly muses about Theo's inauspicious fall from hero to social pariah, Melanie realizes that Paul is Theo's son. Deciding to renounce their share of the money, Paul and Melanie return to Pancho's, and after Paul scrutinizes the bank notes, he discerns that they have been newly minted and recorded and are therefore unspendable. Paul then reasons that if they return the money, the casino will forgo pressing charges to avoid a scandal. When the others disagree, Paul pulls his gun and they resentfully toss the bank notes into a suitcase. Returning to the casino, Paul and Melanie drop an envelope addressed to the director that contains the claim check for the suitcase. As the director retrieves the satchel, Paul places a bet at the roulette table and wins handsomely.