When I was young kid and teenager I would spend a lot of time playing checkers with my father. My father wasn't master or grandmaster level but he played well. We would sometimes spend entire evening playing dozens of fast paced games.

When friends asked me how it is possible to calculate so many moves in advance in such short time (I would typically have response prepared for whatever move they made) I realized I don't really know. Only occasionally I would spend time really analyzing the future state of the board and I was typically able to imagine how the board would look like in many moves in advanced and was even able to predict which moves would look tempting in half a dozen moves in the future.

It did not feel as if I was playing the game. Retrospectively, it felt more as choosing from menu of options but I did not know or cared to know where the options came from.

I came to conclusion after so many repetitions the brain gets somehow wired and runs all those simulations "behind the scenes" so that the conscious part of the mind is relatively free to make very high level decisions.