I don't understand your logic?? There are 500 values,
    ie, 000 to 499, then there are 500 values in the top
    half, ie, 500 to 999. The dividing point is *immediately*
    before 500, ie, 499.999999999999999 (forever)

    So if it starts with a 5 it absolutely must be in the
    top half. There is no favoring, just accuracy.

No, because we're not talking about "number of values" when rounding, we're
talking about a "distance."  There are (always) an infinite number of values
between any two numbers, but .5 is exactly half-way between 0 and 1, so
going consistantly either up or down introduces a slight bias.

Or, looking at all the values of precision N+1 that round to a particular
value, you'll find that there are 5 values that round up to that value, and
only 4 values that round down to it (plus the value itself.)

A trivial pieces of software ought to be able to calculate the accumulated
error over a large number of samples, which IS the value you want to
minimize.  Right?

BillW

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