It's interesting to realize that any finite sequence of digits in the expansion of Pi is indistinguishable from a sequence of digits produced by a natural random process. One can use a Geiger counter to generate decimal digits from measurements of natural radioactive fission of, say, radium atoms. If we do that and stop after generating any such finite sequence, no matter how long, there is a non-zero probability that that same sequence will occur somewhere in the expansion of the digits of Pi.

In fact, that finite sequence is almost certain to occur in the expansion of Pi if we can continue generating digits of that expansion indefinitely!