[notsurenot]

It is clear that there is a selection bias. Suppose there are 3 heads in a row, HHH, and we are going to estimate the probability of the next coin to be H. But we do it this way: if the outcome is H you don't count that as a H, a success, instead we proceed to make another estimation replacing HHHH as the initial condition. Since you don't count correctly the number of successes, this way of estimating probabilities constitutes a biased estimator of the real probability.

[LittlePeter]

It is not THAT clear. Hence that multiple other papers, as the article says, made mistakes.