Find the game
Improvisers and sketch writers use the word "game" for the single unusual pattern that makes a scene funny. Everything else in the sketch — the setting, the costumes, the polite customer — exists to make that pattern visible.
In Monty Python's "Dead Parrot" sketch, first broadcast in December 1969, the setting is a pet shop and the complaint is reasonable. The game is that the shopkeeper will invent any excuse rather than admit the bird is dead. Each new excuse is a fresh move in the same game, and the customer's growing list of synonyms for "deceased" becomes a second, parallel game.
The Two Ronnies' "Four Candles" (1976) runs on a different game: a hardware shop where every item on a list can be misheard as another item. The audience quickly learns the rule and starts guessing, which is half the fun. Abbott and Costello's "Who's on First?" is the same engine in a different body — a conversation that can never resolve because the words keep meaning two things at once.

