Playing Pool is a great example of this because you can math out the angles of a shot relatively easily, but the best pool players do it all intuitively. Some of the greatest don't bother with "advanced" pool tactics. They have spent so much time watching the cue ball strike other balls that they have a tacit understanding of what needs to happen. Part of practicing well is just watching balls hit each other so your brain starts to intuit what those collisions result in.

What is really fascinating for me is that my subconscious will lose interest in pool before my conscious does, and once that happens I struggle to aim correctly. It feels like the part of my brain that is doing the math behind the scenes gets bored and no matter how hard I try to consciously focus I start missing.