(Upper panel) Observed cumulative distribution function OCDF for Cube Set S1. In this case, the observed OCDF extends beyond the range covered by 1000 Monte Carlo simulations. The discontinuity at p_S = 0.5 in the theoretical distribution is less pronounced due to the large number of galaxies n_all ≥ 300 in the cubes selected for this set. (Lower panel) OCDFs for Cube Set S127 (see Table 4). The observed distribution (red), the theoretical binomial expectation (black), and the results from 1000 Monte Carlo simulations (cyan) are shown. The observed OCDF lies well within the range spanned by the Monte Carlo simulations.