“…In free and fair elections, last digits ∈ {0,1, … ,9} in turnout counts reported by individual precincts with at least 100 registered voters can be regarded as outcomes of identical and independent multinomial trials while individual digits, and, in particular, last digit zeros, should be observed with uniform probability = = 0.1. Last digit tests that pool data across polling stations in Russia's March 2012 Presidential elections, while ignoring the differences across individual regions, strongly reject the hypothesis that the probability of last digit zeros is 10 percent for turnout counts, valid vote counts, and votes cast for the March 2012 Presidential elections winner Vladimir Putin (Skovoroda and Lankina 2016), while the hypothesis of uniform distribution of digits 1 to 9 (excluding last digit zeros) is rejected for turnout counts.…”