Also, optimal combinations of uniform, fully-weighted, or fast-weighted sampling of particles or holes in double excitations have been identified for a variety of chemical systems, active spaces, and forms of the orbital basis (localized or delocalized). We conclude the We have also suggested an alternative method to draw from constrained subsets of precalculated probabilities that is 5 to 10 times faster than the sampling methods currently available, and scales practically constant, when keeping the particle number constant and increasing the basis set size. The details are discussed in the appendix. This improvement can be used in all implementations of PCHB, for both singles and doubles and improves the performance of fully-weighted sampling.