Sometimes called trebling, the Rule of Three is a pattern used in stories and jokes, where part of the story is told three times, with minor variations.The first two instances build tension, and the third releases it by incorporating a twist. The third of three brothers succeeds after his older siblings each failed.The protagonist is given three tests and receives the prize after the third.It's almost unusual to find a folktale that does incorporate the Rule of Three in some form.Another (geeky) variant is the engineer/physicist/mathematician series of jokes, however, these are virtually never considered offensive, largely because the stereotypes are often jokingly accepted by the members of those three groups. The engineer is overly practical, the physicist makes large assumptions, and the mathematician comes up with a correct, but useless answer; these are played up for humorous effect, but have some valid basis.) A more popular variation on the rule is to repeat the same joke or concept three times, but put a twist on the third one that makes it funny again. " (From .) Alternatively, the twist can come during the second iteration (such as Chekhov's Skill) failing the first time it's used only to return to its original form on the third pass; this version tends to accompany Chekhov's tropes.One version of this is The Triple, wherein a character lists three items - the first two logical and serious, and the third applying a twist or joke. The Overly Long Gag could be seen as a subversion of the Rule Of Three, because it fails to deliver the expected twist.This makes the story easier to remember than non-repeating tales of the same length, both for professionals who collect as many stories as possible, and for people that pass a story on pretty much because they happened to remember it.
This establishes that this is the standard way that things always happen.
The trope is also incredibly common in fairytales and ghost stories that are part of oral tradition.
The reason above is important, as audiences don't have a good idea of how this ghost/gnome/witch would typically behave, and it works well for building tension too. You get three times the story padding for only having to remember one short story and some minor variations.
In design, particularly three-dimensional design such as shop displays, groups of three objects, or objects arranged to form a triangle, are considered most attractive to the eye.
The Rule of Three may be a subtrope of a more general psychological phenomenon, as threes are well-noted in all forms of culture. They have a Three Act Structure, a Beginning, Middle and End.