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Message: [QUOTE="Mark Dickinson, post: 3534241"] No: if you interpret average to mean 'mean' (add up the (signed) rounding errors from the 20 cases you list and divide by 20) you'll find that the average rounding error is indeed 0 for round-half-to- even, and 0.05 for round-half-away-from-0, just as Mikael said. I'm not sure you'll get many takers for this point of view. If X is a random variable uniformly distributed on the interval [0, 1) then the probability that X == 0.5 is indeed exactly 0, using conventional definitions. (And if you're not using conventional definitions, you should say so....) Mark [/QUOTE]