Quarter each apple and remove the core. Place apple slices in a large stockpot and add water.
Stir in sugar, cinnamon, allspice, and cinnamon sticks. Bring to a simmer over medium heat, then cover the pot with a lid and continue simmering for 2 hours.
Stir well, then carefully strain the apple mixture through a fine-mesh sieve.
Discard solids from the sieve
Line the sieve with cheesecloth and strain the cider again.
Serve warm, or refrigerate for 1–2 hours until cold.