I believe in luck as an "adjective" only. In other words, if someone stumbles onto an outstanding good fortune, then I would describe it as "good luck", or if someone ended up in the wrong place at the wrong time, I would describe it as "bad luck".
But as far as the belief in "luck" (ie: the noun) or a belief that luck is a phenomenon that some people have access to, then NO. I don't believe in luck at all. Luck is not a factor in anything other than as a way for us to explain either fortunate or unfortunate happenstances. Anything that CAN happen invariable WILL happen at some point, to somebody. It's just a matter of who and when. It's not luck, it's just statistics.
If you step on a crack, it's NOT going to break your mother's back and if you break a mirror you won't have 7 years of bad luck. I don't believe in superstition and LUCK is basically another form of superstition. There is no logical rationale for such a believe other than ignorance.
As far as "Karma" goes, in the strictest definition of the term, no I do NOT believe in Karma. In that, I don't belive in "cycles", "reincarnation", "predestination", "fate", or "destiny". However some of the principles of Karma (the logical ones) I do believe in (ie: cause and effect). If you constantly do BAD things, eventually it's going to catch up with you and bad things will inevitably happen to you. There is nothing "mystical" about that, it's just common sense. I believe in "The Golden Rule" as a philosophical principle (something everyone should do), but I do not believe there is a mystical, magical effect that certain actions have on your future.