The novel begins at an exhibition of snuff boxes attended by the famous Belgian detective, Hercule Poirot. Whilst looking at the boxes Poirot encounters Mr Shaitana, a rich and exotic man of dubious character who is fascinated by the macabre and believes himself to be cleverer than most people. He tells Poirot that as well as collecting snuff boxes and other artefacts, he also collects myrdered who have literally gotten away with murder. Poirot finds him odious but fascinating and accepts his invitation to dinner on Friday the eighteenth. At the dinner, Poirot finds both familiar friends and complete strangers; Mr Shaitana has assembled three other sleuths; Superintendent Battle of Scotland Yard, Colonel Race, a retired secret service operative; and Ariadne Oliver, famous crime writer of many "whodunit" style murder mystery novels. The detectives quickly realize that the other four guests must be the murders about whom Me Shaitana spoke; Dr Roberts, a respected general doctor; Major Respard, a renowned adventurer and traveller; Mrs Lorrimer, a seemingly upstanding woman in her sixties; and Anne Meredith, a quiet young woman in her early twenties. Over a delicious dinner the guests discuss politics and theater before Mr Shaitana introduces the subject of murder, particularly by poisoning, a method used frequently in Ariadne Oliver's crime novels. He dramatically claims to feel a black angel passing over the dinner table.
After dinner, the guests play bridge, enjoying four rubbers of the game before tallying up the score and discovering the gentlemen have won. As they go to bid goodnight to their host, they discover him dead in his chair by the fire.
The detectives begin to question each of the bridge players but none seem to have observed anything out of the ordinary. Amongst themselves the sleuths discuss whom they believe to be the murderer and agree to investigate individually whilst of course reporting to Superintendent Battke as protocol dictates. Battle first visits Dr Roberts at his office and with his consent searches his office but finds nothing. A chat with the doctor's secretary is more revealing and she tells Battle about a handful of problem clients that the doctor has seen over the years, particularly the Craddocks, who passed away.
Meanwhile, Poirot visits Mrs Lorrimer, although he does not suspect her of the murder. She is a useful commentator on the bridge game but not particularly observant and Poirot does not learn much. Mrs Oliver visits Anne Meredith whose room-mate Rhoda Dawes is a big fan, although Anne seems unfriendly and withdrawn. As she leaves Mrs Oliver sees Desparf arriving and realizes he is attracted to Anne after meeting her at dinner.
Battle visits Anne to find out her background and collect personal references. The following day Poirot meets Desparf on a London bus in a carefully cultivated "coincidence" and learns that the adventurer knows Battle is having him followed.
In London for the day, Rhoda Dawes decides to visit Mrs Oliver and lets slip that Anne used to live in a house where the owner was poisoned which is why she has been so shaken by Mr Shaitana's murder. Meanwhile Anne runs into Mrs Lorrimer on Harley Street and accompanies her home for tea.
Sergeant O'Connor calls Poirot and summons him to Scotland Yard to meet Battle, and the Belgian finds Colonel Race and Mrs Oliver present too. They discuss the possibility that Dr Roberts poisoned Mr Craddock with anthrax but although they believe him to be a murderer, do not see any similarity between the manner of the Craddock and Shaitana murders and reluctantly dismiss him as a suspect for the time being.
Poirot visits a Mrs Luxmore in South Kensington and asks her about the death of her husband, an associate of Major Despard. Luxmore was said to have died from a fever but was actually shot by Despard, according to Mrs Luxmore, because he wanted to be with her. On his way to visit Despard, Poirot purchases seventeen pairs of silk stockings to set another trap later. The story he gets from Despard is different - Despard shot Luxmore on an attempt to save him from feverishly wandering into danger and his shot was diverted by an hysterical Mrs Luxmore - but Poirot believes him.
Battle goes to Combeacre in Devon to find our more about Mrs Benson, the elderly lady who had died whilst Anne Meredith was working for her. He learns that her death was an accident but has a strange feeling that it was murder.
Anne and Rhoda visit Pourot as he has requested. Anne is reticent about the murder but happy to help Poirot in selecting a gift for his niece who is her age. She selects the nicest of the stockings for the "niece" bit after the women leave Poirot realizes she fell into his trap And stole two pairs of the stockings. Poirot shares this with Battle and although they believe Anne killed Mrs Benson they do not see any similarities in that murder and that of Mr Shaitana.
Mrs Lorrimer sends for Poirot and stuns him by confessing to Shaitana's murder. Poirot does not believe her confession as he believes she would commit pre-meditated murder but not a murder of chance or opportunity. He realizes she is trying to protect Anne whom Mrs Lorromer tells him she saw stab Mr Shaitana. Mrs Lorromer is terminally ill and confesses to give Anne the opportunity for a fresh start.
in the early hours of the following day Mrs Lorrimer is found dead after committing suicide. She has written to her fellow suspects to confess and apologize for putting them in the position of also being suspects. Dr Roberts says he tried to resuscitate her but was too late. The parlor maid tells Poirot of the evening before's events; Poirot spots marks on Mrs Lorrimer's arm and realizes she was murdered and the letters forged.
Back in Wallingford, Anne and Rhoda wait for Despard whom they both like very much. AsRhoda tries to persuade Anne to be honest with the police about her time in Combeacre, Anne becomes irritated and realizes Rhoda is a threat to her secret and invites her for a punt at the river. Despard just misses them and follows them to the river. Believing Anne to be very dangerous, Poirot and Battle also go to Anne's house, also following after them towards the river. As the sleuths arrive at the water they see Rhoda go overboard, shoved hard by Anne who then also falls into the river when Rhoda's frantic thrashing overturns the punt. Despard dives in and rescues Rhoda first but Anne is caught in weeds and drowns before they can reach her.
Rhoda is extremely shocked that Anne deliberately pushed her into the water and devastated to hear that Anne had also murdered Mrs Benson years ago. The three drive to Poirot's apartment where Mrs Oliver and Doctor Roberts are waiting. On hearing about Anne's history of murder Mra Oliver observed that in life, as in books, the culprit is the least likely person. Poirot dramatically accuses Dr Roberts of Shaitana's murder as well as that of Mrs Lorrimer. Poirot states that there is a witness, a window-cleaner, who saw him inject something into Mrs Lorrimer. Dr Roberts had pretended to proclaim her dead when he arrived but actually killed her with poison whilst alone in her room. The window cleaner arrives to give his statement and Dr Roberts is arrested.
Poirot explains that his obsession with the bridge a ore cards led him to solve this murder. He realized that although the murders of the Craddocks seemed different to Mr Shaitana's mirder, they were actually similar in methodology as all were in a public situation requiring the disposition of a gambler. Rhoda observes how lucky they were to have a witness but the luck turns out to be Poirot's little grey cells as the "window cleaner" is an actor friend of his and the story of his witnessing the murder a bluff.