We prove that any randomize dalgorithm for on-line scheduling jobs on
m identical parallel machines must have a worst case ration at least m
(m)/m(m)-(m-1)(m)) for every m, which tends to e/(e-1) approximate to
1.58 as m --> infinity. This answers a question posed in a recent pape
r by Bartal, Fiat, Karloff and Vohra.