> Do you think the questionable response looks genuinely random and satisfies the instructions? We don’t. Could someone explain why putting sequences of same choice is invalid? Sure, a probability of having many tails continously is low but how is it not random?
P(all heads | bad faith) ≫ P(any given "random"-looking string | bad faith)
therefore
P(bad faith | all heads) ≫ P(bad faith | any given "random"-looking string)
So if you want to exclude bad faith responses, the best strategy (by Neyman–Pearson, if you want to think of it that way) is to remove "all heads" responses (and similarly for "all tails").