In the short story The Mystery of the Baghdad Chest, Major Jack Rich is a friend of Edward Clayton and his wife Marguerita. After the death of Edward, Rich was arrested he had opportunity and motive. The body had been found in a large "Baghdad" chest in Rich's house. Edward had come to see Rich (who was out) and had waited for him. Edward was not seen to leave. Rich was seen entering the room and was alone for some time. As for motive, it was believed (correctly) that he is in love with Marguerita Clayton.
Marguerita Clayton however did not believe that Rich is capable of murder and asks Poirot for help. How Poirot resolves the mystery of Edward's death forms the main plot of the story.
In the expanded story, The Mystery of the Spanish Chest, the character is renamed "Major Charles Rich" and plays the same role.
In ITV's 1991 adaptation of Spanish Chest, the character's name reverts to "Jack Rich". Here he has an expanded role. Poirot uses a ploy to smoke out the true killer who corners and threatens Poirot. However Poirot has anticipated this and Rich confronts the killer in a sword duel and captures him. The part of Major Rich is played by Pip Torrens.