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How to explain these jump-discontinuities in the expected stopping time of a SPRT?

Suppose a sequential probability ratio test (SPRT) with $$\alpha=P(\text{Type I error})=P(\text{Type II error})=\beta = 10\%$$ is used to decide between $$\ H_0: p=1/2\quad\text{vs.}\quad H_1: p=b\,$$ ...