In 1973, sports handicapper and mafia associate Sam "Ace" Rothstein (Robert De Niro) is sent to Las Vegas to run the Teamsters Union-funded Tangiers Casino on behalf of the Chicago Outfit, which secretly controls the Teamsters, while Philip Green (Kevin Pollak) serves as the mob's frontman. Taking advantage of gaming laws that allow him to work in a casino while his gaming licence is pending, Sam doubles the casino's profits, which are skimmed by the mafia before they are reported to income tax agencies. Impressed with his work, mafia boss Remo Gaggi (Pasquale Cajano), sends Sam's childhood friend and mob enforcer Nicholas "Nicky" Santoro (Joe Pesci) and his associate Frank "Frankie" Marino (Frank Vincent) to protect Sam and the whole operation. Nicky's volatile temper soon gets him banned from every casino in Las Vegas, so he gathers his own crew and engages in independent shakedowns and burglaries instead.
Sam meets and falls in love with a hustler and former prostitute, Ginger McKenna (Sharon Stone). They conceive a daughter and marry, but their marriage is proven difficult by Ginger's strong independence and love for her former boyfriend, con artist-turned pimp Lester Diamond (James Woods), who is ordered beaten severely by Sam and Nicky after they catch him conning Ginger out of some money. Ginger subsequently turns to alcohol. Meanwhile, Sam makes an enemy in county commissioner Pat Webb (L. Q. Jones) for firing his brother-in-law Don Ward (John Bloom) for incompetence. When Sam refuses to reinstate him, Webb pulls Sam's licence from the backlog, forcing him to face a hearing for his gaming licence while secretly arranging for the board to deny Sam. Sam blames the incident on Nicky's recklessness and the two argue furiously in the desert after Sam attempts to tell Nicky to leave Las Vegas.
The casino counters begin stealing some money for themselves, prompting the Midwest mafia bosses to put Artie Piscano (Vinny Vella) of the Kansas City mafia in charge of overseeing the transactions. He rants about it in his grocery store, unaware that the FBI are listening on an old bug they had planted there long before. The FBI subsequently begin an investigation. Tired of his wife's alcoholism, Sam seeks a divorce from Ginger. She then kidnaps their daughter, Amy, taking her to Los Angeles, and plans to flee to Europe with Lester. Sam convinces her to come back with Amy, and then scolds her for stealing his money and kidnapping their daughter. After he overhears Ginger talking on the phone about killing him, he kicks her out of the house, but soon relents knowing if he gives Ginger money he would never see her again. Ginger then approaches Nicky for help in getting her valuables from their shared vault in the bank, and the two start an affair. Sam discovers this after finding Amy tied to her bed by Ginger, who is with Nicky at his restaurant. Sam disowns Ginger, and so does Nicky. A furious and drunk Ginger crashes her car into Sam's driveway, making a scene and retrieves the key to their deposit box after distracting the attending police. Though she succeeds in taking her share of the money from the bank, she is arrested by the FBI for aiding and abetting Sam.
The FBI move in and the casino empire crumbles. Green decides to cooperate with the authorities and Piscano dies of a heart attack, though Nicky flees Las Vegas before he can be caught. The FBI approach Sam for help, but he turns them down. The bosses are arrested and put on trial, but decide to eliminate anyone involved in the scheme to stop them from testifying and prolonging their coming sentences, among them three casino executives, Teamsters head Andy Stone (Alan King) and money courier John Nance. Ginger flees to Los Angeles and ultimately dies penniless of a drug overdose in a motel. Sam himself is almost killed in a car bomb, and suspects Nicky was behind it. Before Sam can take revenge, Nicky and his brother Dominick are ambushed by Frankie and their own crew and savagely beaten and buried alive in a cornfield, the bosses having had enough of Nicky's behaviour and offered his crew clemency in exchange for the murder.
With the mob now out of power, the old casinos are demolished and purchased by big corporations, who build new and gaudier attractions, which Sam laments are not the same as when the mafia was in control. Sam subsequently retires to San Diego and continues to live as a sports handicapper for the mob, in his own words, ending up "right back where I started". He closes the film with the words, "and that's that".

Question: Why does Sam want to divorce Ginger?
Answer: She is an alcoholic.
Alternative answer: Tired of her alcoholism.