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Frank you wrote:
> you were on the right track but I think
> you missed the final point.

Hmm.  Its become an increasingly difficult point to miss!  Seriously,
thanks for this detailed explanation, and to Alex and Bill Noyce too.

> You should try your spreadsheet example again.

Yes, that's a good idea.  We are still considering a sample of 100,
each set the result of adding  6 values between 0.0 and 60.0 (it
occurs to me now they should have been 0.0 to 59.9) and then the
addition of those same values after they have been rounded to the
nearest whole number.

The next column shows the difference, and at the bottom of that column
the standard deviation is displayed: 0.7.  Excel file attached.

If I've understood correctly, the standard deviation should
approximate 1.22 (0.5xsqrt6).

While I find the result intriguing, I wouldn't want to make too much
of it (small sample, etc).

The Wikipedia article was also interesting, if potentially confusing.
I was struck by:
"As expected of a random walk with equally probable outcomes, the
expected value will come out to zero."
which seems to imply that, relating this back to our example, that the
equally probable average difference of 0.5 (between a value rounded up
or down) will ... tend to cancel themselves out!  No doubt I have
misunderstood.

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