Combine potatoes and water in a small stock pot or medium saucepan. Cover and boil until potatoes are tender, about 35 minutes. Drain cooking liquid into a large glass measuring cup. Reserve potatoes for another use.
Transfer 1 1/4 cups of potato liquid to large ceramic or glass bowl. Add flour, sugar and salt to bowl; stir to combine. Cover bowl with cheesecloth and let stand at room temperature until starter begins to ferment and bubble, about 4 days. Starter is now ready to use.
Storage and feeding of starter: Transfer to covered plastic container and store in refrigerator. Feed starter every 2 weeks. Begin each feeding by discarding all but 1 cup. Mix 1 cup flour and 1 cup warm water (105 to 115 degrees F) into remaining mixture. Cover with plastic; let stand at room temperature overnight. Replace lid; return to refrigerator.