The different sampling schemes are compared by their variance reduction per wall-clock time (V • t) -1 . FCIQMC dynamics were entirely run in stochastic mode, i.e. no semi-stochastic propagation was enabled. For every system and every algorithm there were three calculations of 24 h, the efficiency was then averaged over these three runs. Since the variance of the projected energy has to be estimated at stationary conditions, all calculations started from walker population distributions of already converged wave functions. To guarantee the optimal ∆τ , p 1 , and p 2 for each algorithm we optimized these values for 5 • 10 4 iterations according to equations 9 and 10 ensuring that they kept constant after reaching stationary conditions. This means that every sampling choice was benchmarked with its own optimal set of parameters. The shift was adapted via a second-order scheme to keep the population close to the target population of 1 • 10 5 for every calculation. The initiator criterion was applied with a population threshold of three. Although we used the initiator approximation in all applications presented here, we would like to emphasize, that our new excitation generator applies also to the original (non-initiator) FCIQMC. The data analysis was performed using pyblock, pandas, numpy, and matplotlib. All efficiencies were normalized to the current PCHB algorithm in NECI. Sampling from constrained subsets uses our improved redrawing algorithm (Subsection 3.2) everywhere; more details in the appendix A.1.