You are indeed right; while has the added advantage of making the estimator unbiased -- i.e., not only strongly (epsilon,delta)-guarantees but also having an ex

You are indeed right; while has the added advantage of making the estimator unbiased -- i.e., not only strongly (epsilon,delta)-guarantees but also having an expectation of being correct). It wasn't easy to see that loop would have added benefit -- that's where Knuth's ingenuity comes in.