Results obtained by tracking 100 particles for 1000 turns when initial coordinates are selected randomly, with the requirement that the total emittance be constant, are compared to results from 1000‐turn and 106‐turn runs when initial coordinates satisfy &egr;x(i)=&egr;h(i) andXi’=Yi’=0. For studies of ten distributions of magnetic field errors, the 100‐particle results give apertures equivalent to those from 106‐turn runs, have an aperture distribution of considerably less width, and yet require only one tenth the computer time.