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When I lived in Berlin a few years ago, I used to play basketball with the sport club of the Technical University https://www.tu-sport.de/index.php?id=31. It is open to people outside the university, too, and the costs are very low. Be sure to book in advance when the new semester starts/ends, because some activities tend to become booked out quickly. The gym for basketball (but I've seen people play Badminton there as well) is in West Berlin just outside the ring (S Messe SΓΌd).