Again, what people here are asking is "

*is pi
normal?*". That's the only way that makes sense.

hamandpineapple says:

*Or to put it a little more precisely, the probability that any given sequence isn't in the first N digits tends to as N tends to infinity*

[my links],
which is not the question at all. After all, the digits of

π are a

*fixed* string. Suppose I ask "do 20 consecutive

7's appear in the first

10^{19} digits of the

decimal expansion of π?" I don't know the answer to this question. But since there is no

randomness involved, the

*probability* of 20 consecutive 7's appearing in the first 10

^{19} digits of the decimal expansion of π is either

1 (if the answer to the question is "

yes") or 0 (if it's "

no").

It's best to make the question precise. Either ask if pi is a normal number or ask if every finite sequence of digits appears in the expansion of pi. And the answer to both questions (an affirmative answer to the first would imply an affirmative answer to the second) is unknown.