What does the Bible teach/say about luck? Is there such a thing, do we have a measure of randomness and ability to shape our own destinies or ultimately are all things predestined.
I'll give you one perpective. According to the following verse:

Romans 8:28 (ESV)


  And we know that for those who love God all things work together for
  good,fn for those who are called according to his purpose.


In other words, to the Christian who has grown to love and trust God implicitly, God's hand is in everything in his life, in both good and "bad" events. Even the negative circumstances are taken as though from God, allowed by God to shape the believer's character, as it states in Romans 5:3-4,


  Not only that, but we rejoice in our sufferings, knowing that
  suffering produces endurance, and endurance produces character, and
  character produces hope,


You may be confusing luck and shaping our own destinies. They are not mutually exclusive. If I want to lose 10 lbs, I can trust to chance or make my own luck by eating fewer calories than I burn until I get the weight I want. But when I act on it, then, according to the dictionary of English words, the event is no longer luck, but a planned event. If you plan something to happen, then it is no longer luck. (This is not always correct though: you can intentionally make your way to a red-carpet gala to get a movie star's autograph (not luck) and either the star doesn't show up, or you're too far to get to him (bad luck.)