Paul Montgomery, James Caan, and his heiress wife Jennifer Montgomery, Katharine Ross, are two wealthy but blasé Upper East Side socialites who fill their spacious townhouse with elegant parlor tricks and other upscale games, always seeking a new way to amuse themselves while flaunting their wealth.
Lisa Schindler, Simone Signoret, an older German woman with a calm, almost otherworldly presence, arrives at their door selling cosmetics. After she nearly faints and falls ill, Jennifer reluctantly lets her stay the night. The couple quickly take a liking to Lisa, who claims to possess psychic abilities, and Jennifer asks her to arrange a string of “games” for their entertainment. Lisa sets up several scenarios of simulated domestic discord designed to provoke reactions from the couple, including a staged affair between Jennifer and the grocery deliveryman, Norman, Don Stroud.
At first, Paul is furious when he discovers Norman in the couple’s bedroom, but that anger turns to bemusement as Lisa appears and reveals the whole thing as a sham. The next day, when Norman delivers groceries, Paul witnesses him making a romantic advance toward Jennifer. He warns him with a revolver, firing blanks, and Paul and Jennifer erupt in laughter, revealing that the whole scene was a ruse. Paul pretends to shoot again, but this time real bullets fly, and Norman falls dead. In a panic, Paul hides Norman’s bloodied corpse in a tiny elevator in the house, while Jennifer dispatches Lisa to the drugstore to buy a salve.
That night, Jennifer drugs Lisa so Paul can decide how to deal with Norman’s body. He ultimately decides to encase the corpse in plaster, turning it into a new statue for their collection. In the morning, Lisa reads Jennifer’s fortune with a tarot spread, drawing the Death card, which unsettles Jennifer. Late at night, Lisa confides that she senses a ghost moving through the house. In the parlor, Jennifer is horrified to glimpse an apparition of Norman with a bullet hole in his eye.
Lisa leaves the next morning after a confrontation with Paul, while Paul travels to Maine on business, leaving Jennifer alone in the townhouse. As she watches television, strange noises and a power outage accompany her; in the kitchen, she confronts a figure resembling Norman, then flees to the elevator and retreats upstairs to call for help, only to find the telephone dead. Norman enters the upper room with a bloodied eye, and Jennifer shoots him several times in fear. Paul soon arrives, calmly removing a prosthetic from Norman’s eye and then phones the police, claiming his wife has killed Norman. Jennifer realizes she has been manipulated by Paul, effectively groomed to kill someone so he could inherit her fortune; Norman, who agreed to participate, was an unwitting casualty.
After Jennifer’s arrest, Paul and Lisa share a celebratory drink as Paul awards her a ten-percent cut of Jennifer’s fortune. But the celebration is short-lived: Paul begins to feel ill, and it becomes clear that Lisa has poisoned his drink. He collapses and dies, and Lisa exits the townhouse with a briefcase full of money.
