We consider the problem of identifying locations in New York City that are currently underserved with respect to access to pre-Kindergarten programs. We use two public datasets; the spatial distribution of four-year-olds, and the distribution and seating capacities of pre-Kindergarten programs in public schools and community based organizations. We implement a random allocation algorithm to identify and map underserved locations, then see how these locations change as capacity is added in a random fashion. Our model incorporates travel distance, and we measure the sensitivity of our results to variations in this parameter. We provide evidence that as the pre-Kindergarten capacity in our model increases, the effectiveness of this capacity - as measured by the number of unused seats - decreases, to the extent that when the total capacity in the city equals the number of children, almost 20,000 seats remain unused.