In 1978, con artists Irving Rosenfeld and Sydney Prosser have started a relationship, and are working together. Sydney has improved Rosenfeld’s scams, posing as English aristocrat “Lady Edith Greensly”. Irving loves Sydney, but is hesitant to leave his unstable and histrionic wife Rosalyn, fearing he will lose contact with his adopted son Danny. Rosalyn has also threatened to report Irving to the police if he leaves her. FBI agent Richie DiMaso catches Irving and Sydney in a loan scam, but offers to release them if Irving can line up four additional arrests. Richie believes Sydney is English, but has proof that her claim of aristocracy is fraudulent. Sydney tells Irving she will manipulate Richie, distancing herself from Irving.
Irving has a friend pretending to be a wealthy Arab sheikh looking for potential investments in America. An associate of Irving’s suggests the sheikh do business with Mayor Carmine Polito of Camden, New Jersey, who is campaigning to revitalize gambling in Atlantic City, but has struggled in fund-raising. Carmine seems to have a genuine desire to help the area’s economy and his constituents. Richie devises a plan to make Mayor Polito the target of a sting operation, despite the objections of Irving and of Richie’s boss, Stoddard Thorsen. Sydney helps Richie manipulate an FBI secretary into making an unauthorized wire transfer of $2,000,000. When Stoddard’s boss, Anthony Amado, hears of the operation, he praises Richie’s initiative, pressuring Stoddard to continue.
Carmine leaves their meeting when Richie presses him to accept a cash bribe. Irving convinces Carmine the sheikh is legitimate, expressing his dislike of Richie, and the two become friends. Richie arranges for Carmine to meet the sheikh, and without consulting the others, has Mexican-American FBI agent Paco Hernandez play the sheikh, which displeases Irving. Carmine brings the sheikh to a casino party, explaining that mobsters are there, and that it is a necessary part of doing business. Irving is surprised to hear that Mafia boss Victor Tellegio, right-hand man to Meyer Lansky, is present, and that he wants to meet the sheikh. Tellegio explains that the sheikh needs to become an American citizen, and that Carmine will need to expedite the process. Tellegio also requires a $10,000,000 wire transfer to prove the sheikh’s legitimacy.
Richie confesses his strong attraction to Sydney, but becomes confused and aggressive when she drops her English accent and admits to being from Albuquerque. Rosalyn starts an affair with mobster Pete Musane, whom she met at the party. She mentions her belief that Irving is working with the IRS, causing Pete to threaten Irving, who promises to prove the sheikh’s investment is real. Irving later confronts Rosalyn, who admits she told Pete and agrees to keep quiet, but wants a divorce. With Carmine’s help, Richie and Irving videotape members of Congress receiving bribes. Richie assaults Stoddard in a fight over the money, and later convinces Amado that he needs the $10,000,000 to get Tellegio, but gets only $2,000,000. A meeting is arranged at the offices of Tellegio’s lawyer, Alfonse Simone, but Tellegio does not appear.
Irving visits Carmine and admits to the scam, but says he has a plan to help him. Carmine throws Irving out, and the loss of their friendship deeply upsets Irving. The federal agents inform Irving that their $2,000,000 are missing, and that they have received an anonymous offer to return the money in exchange for Irving and Sydney’s immunity and a reduced sentence for Carmine. It is revealed that the Alfonse Simone, with whom Richie had arranged the wire transfer, was a con man working with Irving and Sydney. Amado accepts the deal, and Stoddard removes Richie from the case, which ends his career. The Congressmen are prosecuted, and so is Carmine, who is sentenced to 18 months in prison. Irving and Sydney move in together and open a legitimate art gallery, while Rosalyn lives with Pete and shares custody of Danny with Irving.