Mash distances and FracMinHash estimates of evolutionary distance (given in terms of one minus the average nucleotide identity [ANI]) between an original and a mutated Staphylococcus genome with introduced point mutations at a known rate (A) and between pairs of real bacterial genomes (B). Error bars indicate the confidence intervals surrounding the FracMinHash estimate calculated using Theorem 8. To obtain the FracMinHash estimates, k-mer size k = 21 and scale factor s = 0.1 were used.