Place apples in a large stockpot and add enough water cover by at least 2 inches. Stir in sugar, cinnamon, and allspice. Bring to a boil. Boil, uncovered, for 1 hour. Cover pot, reduce heat, and simmer for 2 hours.
Strain apple mixture though a fine mesh sieve. Discard solids. Drain cider again though a cheesecloth lined sieve. Refrigerate until cold.
