No, not Chinese gangsters: sets of three.
Storytelling, at least in western culture, does love its sets of three. It’s something I’m currently up to my eyeballs in as a reader, thanks to Ciaran Carson’s excellent translation of selected Irish legends from the Tain (that Cu Chulainn, what a little tyke he was).
I like triads outside literature too, due to having a problem with binary choices. Give me two things to chose between, or a pair of facts to remember, and you’ll be out of luck; make it three and you might be OK.
In my writing, I seem to latch onto triads without thinking about it. Currently, in Bringer of Light, I’ve got two main plot threads. In one there are two sets of three, both variations on two parents plus a child, though in fact neither set consists entirely of blood relations. The other thread features a more unusual triad that was set up previously and should be with us for a while: the reckless crusader, the loveable fool and tortured mystic. At least that’s how I see them; readers are free to differ, of course.