If we compare GAS-PCHB with discarding-GAS and assume that the supergroup index i sg is known, and that the list of probability distributions for all supergroups are already available, the drawing of orbital pairs AB from p(AB; IJ; i sg ) is practically as fast as drawing AB from the corresponding FCI distribution p(AB; IJ). Computational overheads for the GAS-PCHB algorithm arise from the generation of the probability distributions (only at the beginning of the simulation) and from the evaluation of the supergroup index for a given determinant at runtime. In the worst case, if every determinant is occupied by exactly one walker, the supergroup has to be calculated for every walker and the time per excitation increases slightly. Such a dense CI wave function is rarely encountered in practical applications. In actual chemical problems determinants are occupied by multiple walkers and the supergroup index is calculated only once for each newly-occupied determinant. Thus, in practical GAS calculations, the evaluation of the supergroup index represents a negligible additional step and the time per excitation can be considered identical for GAS-PCHB and discarded-GAS.