On Mon, Mar 09, 2020 at 08:41:01PM -0700, 'Brent Meeker' via Everything List 
wro> 
> It may seem counter intuitive, but as the sample length goes up the
> probability of each possible proportion goes down, including that of the
> true value.  It goes down because there are more possible exact values.
> 
> Brent
>

Yes, but that is not really related either. When talking about all
proportions that lie within (say) 1% of 50/50, the number of such distinct
proportions grows faster than the probability of each possible
proportion.

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