Scrub black algae with a stainless steel brush and a chlorine tablet.
Yes, you can kill it, but chlorine alone won’t cut it. Black algae roots into the plaster and forms a waxy coating that shrugs off normal shock levels.
First, hit the spots hard with a stainless steel brush — the stiff bristles break the protective layer. Then take a chlorine tablet, hold it against a pole or wear a glove, and rub it directly on each spot. The concentrated chlorine gets deep into the roots.
After that, shock the whole pool with a high dose — aim for 10–15 ppm free chlorine — and brush every day for a week. Keep brushing or it comes back.
This is not a one-shot deal. Stay on it until the spots fade and stop returning.