If you believe in \"fate\" as being predetermined by chaos, then luck must exist, since everything that happens is a random occurance. If you believe fate is created by some deity, then luck wouldn\'t exist in your envisioned universe...
In a free-will universe, luck would definatly still exist, since inanimate things that would determine if one is lucky or not obviously wouldn\'t have free-will. In a free-will universe, you\'ll have just as much luck in honest gambling as you would in a \"fated\" one.
Coincidence must exist in free will, since things are far more loosely connected in such a universe.
However, coincidence cannot exist in a fated universe, because everything is directly or indirectly related to each other thing.