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running gag

n. An ongoing joke, one that is regularly repeated or continued.

Wikipedia
Running gag

A running gag, or running joke, is a literary device that takes the form of an amusing joke or a comical reference and appears repeatedly throughout a work of literature or other form of storytelling.

Running gags can begin with an instance of unintentional humor that is repeated in variations as the joke grows familiar and audiences anticipate reappearances of the gag. The humor in a running gag may derive entirely from how often it is repeated, the (in)appropriateness of the situation in which the gag occurs, or setting up the audience to expect another occurrence of the joke and then substituting something else (bait and switch). Running gags are found mostly in television shows, but also appear in other places, such as video games, films, books, and comic strips.

A running gag can be verbal or visual and may "convey social values by echoing belligerent speakers with a barrage of caricatured threats." For example, a character may present others with a proposition that is so ridiculous or outrageous it is likely to be self-mocking to the point where the original request has little or no chance of actually being carried out and results in a humorous effect. Occasionally, the characters themselves may be aware of the running gag and make humorous mention of it.