1. Rinse tamarind pods. Bring 2 quarts water to a boil in a medium pot; add pods. Reduce heat to medium-low and simmer, covered, until just tender and the water is brown, about 15 minutes.
2. Strain water through a fine sieve into a 3-quart pitcher. Remove and discard skin from each pod. Using your hands, place as much pulp as possible from the softened fruit in a blender, discarding the seeds and fibers. Add 2 cups of the strained tamarind liquid to blender; purée until smooth.
3. Strain purée through a sieve into the pitcher. Add 1 quart water and enough sugar to make the liquid sweet but still tart and stir well. Serve over ice.