It'd be nice if there was some understanding, even among the implementors, about what this particular aspect of the game entails.

I can think of three things off the top of my head that effect the luck stat in some way.

1. Certain pieces of gear.
2. The Deck of Fate
3. A certain power in a certain cabal that has a certain subsection that very very few people know about.

I think it probably effects gambling first and foremost, but I wonder about other things as well. These other things could be chalked up to coincidence and the RNG, but during my tinkering with the power in #3 I noticed my "victims" would do things like always flee in the direction of an aggro mob.