In the year 1978, two con artists, Irving Rosenfeld and Sydney Prosser, form a romantic relationship while pooling their deceptive talents together. Irving's primary scheme involves charging $5,000 to individuals desperate for credit, only to vanish after pocketing the cash. However, things take a turn when Sydney enhances Irving’s scams by masquerading as “Lady Edith Greensley,” a purported British aristocrat with ties to London banking. This ruse significantly boosts their operation, tripling their profits almost instantaneously.
Though they make an excellent team, Irving is hesitant to leave his adopted son in the care of his wife, Rosalyn, who refuses to divorce him. Their lives complicate further when FBI agent Richard "Richie" DiMaso discovers the duo's scheme. Instead of arresting them, Richie offers a deal: their freedom in exchange for enabling four additional arrests. Sydney is skeptical of the deal, and fearing their exposure, she informs Irving that she'll manipulate Richie, putting distance between them.
As part of their scheme, Irving enlists a friend to pretend to be a wealthy Arab Sheikh interested in U.S. investments. With this façade, they plan a corrupt deal involving Mayor Carmine Polito of Camden, who is struggling to find funds for his campaign to revive gambling in Atlantic City. The grand con involves the Sheikh obtaining building permits and casino licenses from Carmine in exchange for a bribe. Richie gets enthusiastic about arresting a mayor charged with corruption and persuades his boss, Stoddard Thorsen, to covertly transfer $2 million into a Chase account under the Sheikh’s name, creating a façade of legitimacy.
Despite Stoddard's reservations, Richie pushes forward with a plan to entrap Carmine, enlisting the help of Sydney to manipulate an FBI secretary into making an unauthorized transfer of funds. When Stoddard’s superior, Anthony Amado, learns of the operation, he commends Richie for his initiative, further pressuring Stoddard to proceed.
Richie’s eagerness drives Carmine to leave their initial meeting. To reassure the mayor of the Sheikh's legitimacy, Irving builds a rapport with Carmine, expressing his disdain for Richie, and thus forging a friendship. Tension spikes when Irving invites Rosalyn to dinner with Carmine and his wife, angering Sydney.
Richie's ambition leads him to organize a meeting between Carmine and the Sheikh at an airfield, incurring additional expenses without consulting anyone else. Irrespective of the chaos, the Sheikh's staged persona takes center stage at a casino party attended by mobsters, including the violent figure Victor Tellegio, right-hand man to Meyer Lansky. Tellegio informs them that in order to facilitate business, the Sheikh must become a U.S. citizen, involving bribery of officials, and demands a significant transfer of $10 million, hence proving the Sheikh's authenticity to the authorities.
As the operation spirals out of Irving’s control, Richie confesses his feelings for Sydney, only to feel betrayed when she drops her British accent and reveals her American roots. In a bid to protect Sydney, Irving attempts to sever their deals with Richie, but Richie insists on carrying through with threats of exposing their scam to Tellegio.
Meanwhile, Rosalyn embarks on an affair with mobster Pete Musane, leading to tensions at home when she expresses suspicions about Irving's involvement with the Internal Revenue Service. Confronted, she admits feeling unloved, prompting Irving to reassure her while also negotiating a divorce.
In a dramatic turn, they all conspire together to expose members of Congress, filming a bribery deal concerning the Sheikh's citizenship process. Although initially motivated by self-gain, Irving feels a moral pang as he realizes his role in Carmine’s downfall, ultimately confessing his desire to protect the mayor to Sydney. Richie, in a bid for more power, pressures Amado to greenlight a larger transfer for entrapment, only to face setbacks when Tellegio becomes inaccessible.
Realizing that their path is littered with moral compromises, Irving confronts Carmine, owning up to their con and witnessing the pain it inflicts. An anonymous benefactor offers a lifeline: returning the missing money in exchange for immunity for Irving and Sydney, while reducing Carmine’s sentence. In a twist of fate, Richie’s overzealousness costs him his position as Amado reclaims control, sidelining Richie from the investigation.
Eventually, Irving and Sydney embark on a legitimate future, opening an art gallery together, while Rosalyn moves on with Pete. The mob, realizing Irving has effectively shifted focus away from them, allows him to continue his new path without further issue.
