Should we believe in predestination or luck?
I don’t think those two things are a forced decision. Predestination has a lot wrapped up in it. I think the opposite of luck is probably Sovereignty. God is Sovereign in the aspect that everything is in His purview and everything is in His control. So in the purest form of the word “luck” it doesn’t exist. In fact the idea of luck is contrary to itself. Luck implies that there is an intentional force orchestrating uncontrollable events.
But we do believe that God is in control. But a part of that is that God has set up the world in a way that works without His immediate intervention. For example the coin toss at the start of the Super Bowl. Is God divinely intervening in that coin toss? Probably not. But what determines that coin toss? It’s not blind chance. It’s the physics of the coin, the strength of the wind, the weight of the coin, the force of the flip etc. etc. What we might see as “luck” is really just God’s creation at work.
We can call it luck, I don’t think that’s so bad. But we must understand that in the end and over all, God is sovereign and could intervene and that there is nothing He is not aware of.