Trying to manipulate God to get good outcomes, or get “lucky,” is unbiblical and should be avoided (Amos 5:21-24; Isaiah 65:11-12). In Proverbs 16:31 it says, “The lot is cast into the lap, but its every decision is from the Lord.” Luck plays no role in our future; only God knows the future and has the power to directly influence future outcomes since He alone is omniscient and omnipotent. Moreover, as part of Jesus’ Sermon on the Mount, He tells us to focus on the Kingdom, not on worldly matters (Matthew 6:31-33); the idea of luck is worldly, not a Kingdom concern. Instead of prioritizing the things of this world and trying to get them through “good luck,” our focus should be on pursuing God before everything else. Ultimately, we don’t need to worry about trying to force a certain outcome because we know that God works all things for good for His children (Romans 8:28).
The word "luck" does not appear in the Bible (except in the problematic paraphrase translation called The Message, which uses it as slang or to mean "blessing"). Luck has two somewhat contradictory meanings. The original term is related to destiny as pre-determined by a deity or force—what we might call providence. Eastern religions in particular believe luck can be somewhat controlled by superstitious actions. Religious rites are performed (like rubbing the stomach of a Buddha statue or lighting incense) to induce supernatural powers to change the fortune of adherents.
Today, luck more often refers to an event that is out of the control of those involved and has significant repercussions, whether good or bad. This type of luck is related to the chaos theory which points out that most situations are affected by so many elements the outcome appears random and certainly unpredictable.
The Bible rejects these. God cannot be manipulated to endow good fortune through superstitious practices. And His omniscience precludes the existence of any truly random event. The Bible does use the word "chance" on occasion, but not as a completely unforeseen event; it generally indicates that the people involved had no way of knowing something would occur, but it doesn't follow that God didn't know.
The idea of luck brings up a difficult theological discussion: does God ordain everything that happens to us, or does He let nature and human choice play out to their inevitable end? The answer seems to be "both." We do often bear the repercussions of our and others’ choices without the apparent interference of God. In other cases, He acts in a way we call "miracles." How, when, and why He acts are usually hidden from us. But whether He ordained it or allowed it to happen, He did allow it. He is in control, orchestrating natural consequences and miracles in a way that will bring honor to Him and salvation to us.
That being said, should a Christian own a lucky charm or engage in superstitious actions such as wearing the same socks to every baseball game? If the charms, such as a rabbit's foot, a horseshoe, or an elephant with an up-raised trunk, are non-religious and used in a way that represents a culture and not in a way that causes another to stumble or attempts to gather actual fortune, it's probably all right. Rituals may calm nerves or mentally prepare for an event. But we should all recognize that nothing is truly random, and God cannot be manipulated by four-leafed clovers or dirty socks. Time would be better spent by following God, preparing for that game, and not risking anything too dear in poker.