Furthermore, particle indices, I and J, should preferably be guaranteed to be occupied in the starting determinant, |D i , while the hole indices A and B should be guaranteed to be empty, which requires additional work. This implies that there is a trade-off between (a) faster sampling, which cannot guarantee occupied I, J and empty A, B, versus (b) slower but high quality sampling, that can guarantee this. If the underlying probabilities are nearuniform, then the advantage of weighted sampling vanishes and it might be beneficial to return back to uniform sampling, which is faster and cheaply guarantees occupied I, J and empty A, B.