This can be explained using Bayesian reasoning. P(all heads | bad faith) ≫ P(any given "random"-looking string | bad faith) therefore P(bad faith | all heads

This can be explained using Bayesian reasoning. 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").