In descriptive set theory, a game (e.g., the Choquet game or the Banach-Mazur game) is usually played by two players, who take turns selecting some subsets or/and elements of a given set X. At least at first sight, this roundabout game procedure can hinder a direct intuition of the set X.
If we want to study a certain property of some set(s), why not take other approach? Do the games provide any insightful viewpoints that other approaches can't? Why do mathematicians study the games in descriptive set theory?