http://answers.yahoo.com/question/index?qid=20070316083032AAdnW73Actually, if you assume pi is normal (not proven, but probably true), this is a nice application of Poisson distribution. If your string is n digits long, then there are 10^n total combinations. Using Poisson, the probability of finding the string in the first d digits of the decimal expansion is 1 - 1/(e^f), where f = d/10^n and e = 2.71828...