In the paragraph 4th from last, page says the sequence HHHHHT "is assigned 1/30 probability by the Rule of Succession". Where does this number come from? They don't explain. I do understand the part about that same sequence being assigned 1/64 by the fair coin hypothesis, but the part about the rule of succession isn't so clear to me.
The second example, in the paragraph 2nd from last, is also confusing to me: the part that says that the sequence HHHHH HTHHH HHTHH gives the Bayesian a 19.5 : 1 chance of the coin being biased vs it being fair.