[Bozeman]

I think I know what you are saying. However, after five (hypothetically independent) trials failed, you can only reject the null hypothesis with 97% confidence. And you can only reject the 60%/40% hypothesis with 92% confidence. Thus, it is not clear that the 6th trial should use the past precedence as the Bayesian baseline for success here. In particular, a past success rate of 1/5 only rejects the null hypothesis with 81% confidence (or 62.5% confidence two-way).

Even assuming each trial is aiming to have 50+% success based on prior knowledge, it is not clear how much revision of prior probability should be done.

Thoughts?
Craig