We give a characterization of how fast the block length k may grow in order to have the relative frequence of occurrences of Blocks of length k among the first n tosses of a fair coin be 'good' approximations of their probabilities. The borderline will roughly be the logarithm of n with base 2, with the details depending on the definition of 'good'. This extends results by Flajolet, Kirschenhofer and Tichy (1988)