My only point is that any kind of analysis has to be careful about the way its mathematical assumptions relate to how the real-life experiment is conducted.
I'm not even going near the question of whether the Bayesian approach is "better" than the frequentist approach.
I was trying to point out that the frequentist analysis in the OP does make assumptions about the nature of the experiment (that you will run exactly N trials) and that if you break those assumptions by stopping the test for some N' < N because the answers are looking good, then you'd better understand that your earlier analysis did not apply.
And in another reply, I wanted to add that there is a frequentist answer (the Wald test) to the practical question: Can you widen the scope of the analysis so that I can stop early if I'm getting results that point strongly in one direction?
Being sure that your assumed sampling distribution matches the actual experiment is key, even in the Bayesian case.
My graduate statistics class was taught from Berger, your second link, so I'm broadly sympathetic to the "Bayesian choice" -- but more important, I wanted to give some usable insight to someone who just wants to do an A/B test.
