Running tally
What you just did has a name
You have now predicted the fixation fraction five times across different
combinations of p0 and Ne. Look
at your tally above — your guesses and the observed fractions both sit
near the line guess = p0.
Under pure drift, the probability that an allele eventually fixes equals
its current frequency: P(fix) = p0. Ne
does not appear. Bigger Ne means it takes longer to
resolve — not that the answer is different.
Why: every allele copy in the current pool is equally likely to be the ancestor of the eventually fixed population. There are p · 2N copies of the focal allele out of 2N total. The fraction is p. This is Bayes' theorem applied to neutral drift. You verified it by simulation before anyone wrote the formula.