In the case of double excitation there is no approximation regarding the matrix elements that would break down because of the use of Hartree-Fock orbitals. This means that the PCHB weights for doubles are close to the correct weights and from the discussion so far we conclude that fast-weighted hole-selection is the fastest method, which we can confirm in Table . The probabilities for the first particle I are near-uniformly distributed, (compare discussion around Figure ), hence the fastest double particle-selection is either unif-unif or unif-full. The first one is faster per wall-clock time, the latter samples with higher quality. Looking at Table we see that purely uniform particle selection (unif-unif) is outperforming unif-full, which makes unif:unif unif-unif:fast-fast the fastest method for this system.