Quick recap
Stage star Sir Charles Cartwright throws a party at his Cornwall home. The Reverend Babbington sips a cocktail and dies, yet there's no poison in the glass. Months later, Sir Bartholomew Strange, a doctor, dies the same way at his own party, and this time it's nicotine. Cartwright, Mr Satterthwaite and young Egg Lytton Gore investigate as if staging a play, with Poirot watching closely. In the third act Poirot reveals the killer is Cartwright himself. The clergyman's death was a dress rehearsal to test the method. Strange knew Cartwright was married to a woman in an asylum, which barred him from marrying Egg.

