Paper: Frequentism and Bayesianism: A Python-driven Primer (Jake VanderPlas)

This is the final version – ready to be reviewed.
> The approach above does not consider how :math:`p` may vary.

p doesn't vary.
The point is that we calculate the probability of winning based on the MLE point estimate of `p`, which does not take the randomness of the estimate into account and results in a biased estimate of the winning probability. (sampling distribution as in last sentence).

maybe mention that frequentist large sample results might not be good when applied to small samples