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byrnema comments on Why the tails come apart - Less Wrong
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Are you talking about relative sample sizes, or absolute? The effect requires that as you go from +4sd to +3sd to +2sd, your population increases sufficiently fast. As long as that holds, it doesn't go away if the total population grows. (But that's because if you get lots of points at +4sd, then you have a smaller number at +5sd. So you don't have "plenty of points at all values".)
If you have equal numbers at +4 and +3 and +2, then most of the +4 still may not be the best, but the best is likely to be +4.
(Warning: I did not actually do the math.)
I don't believe we disagree on anything. For example, I agree with this:
If you have equal numbers at +4 and +3 and +2, then most of the +4 still may not be the best, but the best is likely to be +4.
By 'plenty of points'... I was imagining that we are taking a finite sample from a theoretically infinite population. A person decides on a density that represents 'plenty of points' and then keeps adding to the sample until they have that density up to a certain specified sd.