Given a sequence of independent, identically distributed random biased bits, von Neumann's simple procedure extracts independent unbiased bits. In this note we show that the number of unbiased bits produced by iterating this procedure is arbitrarily close to the entropy bound.
"Iterating Von Neumann's Procedure for Extracting Random Bits." Ann. Statist. 20 (1) 590 - 597, March, 1992. https://doi.org/10.1214/aos/1176348543