Fun question/"brainteaser" I don't think this problem really counts as a brainteaser, because I don't know the answer. Consider a sequence like http://www.research.att.com/~njas/sequences/A097614 which works as follows: Given a constant (pi in this case), find the first position in the constant with a decimal "0". This is a1. Then find the first position in the constant with a decimal a1; this is a2, and so on. If the constant were 0.11777777770... instead, the sequence would be cyclic: 0, 11, 1, 1, 1, 1, ... What is the probability that such a base-b sequence is eventually cyclic on a random constant? Here, "random constant" means that each decimal place to the right of the decimal point has a 1/b chance of taking each value in 0, 1, ..., b-1.