Mr Shaitana hosts an unusual dinner party, with four sleuths and four he suspects have murder in their past as the guests. During the meal, Shaitana makes a veiled statement of accusation, listing the ways various people might commit murder based on their occupation. After the meal, he settles the latter four at one bridge table in the main room, and leads the four sleuths to a table in another room. He settles in a chair near the fireplace in the main room. When the sleuths end their game, two of them, Poirot and Colonel Race, in saying good night to their host, find the man dead in his chair, a fine weapon from his own collection in his chest. The two call Superintendent Battle to take over the situation.
Only Poirot knew Shaitana’s plan for the dinner party; he tells Battle, Race and Mrs Ariadne Oliver, the celebrated mystery author. The other four guests wait in a separate room while the police do their work, and remove the body. Battle questions each one by one. Dr Roberts, Mrs. Lorrimer, young Anne Meredith, and explorer Major Despard each deny the murder. Poirot rescues the score sheets kept for the four rubbers of the game, which he uses both to mark the passage of time and mark the character of each player as the evening passed.
The investigation proceeds openly on the connection of each of the four to Shaitana, and quietly in finding if there is a death that could have been murder in their past, seeking motives and psychology for Shaitana's murder. Each sleuth uncovers a death: Battle finds that one client of Dr. Roberts and her husband died separately, he of anthrax, she of a blood infection while in Egypt; Colonel Race learns that a botanist being guided through the Amazon by Despard died of fever, with rumors he was shot; Mrs. Oliver learns that a woman who employed Anne as a companion died of accidental poisoning; while Poirot learns at the end that Mrs. Lorrimer poisoned her husband. Colonel Race then leaves the country for his work in the Secret Service. During the investigation, tensions rise among the four guests, as they meet each other. Anne is skittish and afraid, even with offers of support from Mrs. Oliver and Mrs. Lorrimer, an older woman who wants the young woman to be free of accusation. Despard engages a solicitor for himself and for Anne. Dr. Roberts lives as before.
Mrs. Lorrimer tells Poirot that she killed her husband years ago, that she has a fatal health condition, and then not believably confesses to Shaitana’s murder, to save Anne. As Poirot leaves, Anne comes to visit Mrs. Lorrimer. The next morning, Mrs Lorrimer is found dead by Dr Roberts, who makes a dramatic entrance to her home, saying he received a note from Mrs. Lorrimer admitting to the murder as part of a suicide note she mailed to the other three guests. He says she is dead of a sleeping drug overdose. Poirot joins Battle at the scene, where Poirot sees the mark of hypodermic needle in Mrs. Lorrimer. The same morning, Anne takes her roommate Rhoda out in a punt in the nearby river, as they await a visit from Despard. Realizing another death is possible, Poirot and Battle race to Anne’s cottage, arriving just after Major Despard. Anne intentionally upsets the punt, and both girls fall in the water, neither able to swim. Despard first saves Rhoda then he and Battle bring in Anne. Rhoda survives, but Anne dies.
Gathered at Poirot’s apartment, the survivors of the dinner party plus Rhoda hear the final resolution. Poirot accuses Dr. Roberts of murder; he says there is no proof. Poirot introduces a window washer who saw Dr Roberts injecting Mrs Lorrimer. The police found her cause of death to be injected anesthesia. Roberts killed Shaitana as well. Roberts waited until he was “dummy” in the bridge game and the play of the game held the attention of the other three, as he wandered from the table to get a drink. Further, the doctor had killed Mr Craddock, husband of his patient, by infecting his shaving brush with anthrax during a house call. Then he injected Mrs Craddock during her required anti-typhoid injections prior to her trip to Egypt with the germ that led to her death by a blood infection. Roberts protests then confesses as Superintendent Battle makes clear the strength of the police cases against him. Later explaining the psychology, Poirot reveals that the window washer was an actor, used to elicit that confession.
Poirot learned from Mrs Luxmore, the wife of the dead botanist, and then from Despard, how the botanist had died. He did have fever but died from an accidental shooting. The Major is exonerated. The police investigation identified the woman Anne killed, out of anger at being found out for petty thievery. Anne meant to kill her roommate; instead, Despard courts Rhoda.