On the number 3 in folk tales and jokes, I've always assumed that, apart from any mystical associations it has, it also happens to be the smallest number necessary to set up the common pattern of Event-Repetition-Variation. You need two to create an expectation in the reader/hearer, and the third to frustrate it. In the case of wishes, two might be wasted and the third used wisely, for example.
The structuralist in me would add...