Just how random is $\pi$? If somehow converted to ASCII, would it contain the complete works of Shakespeare? If we take the infinite monkey theorem: https://en.wikipedia.org/wiki/Infinite_monkey_theorem, and with a bunch of "infinites" and "randoms", we can generate any text we wanted.
What about $\pi$? If we wrote down $\pi$ to an infinitely large file, and somehow converted the digits to ASCII values, would that file (and, with some transformation also $\pi$) contain all the Shakespeares works? And Harry Potter 8 book and 4k movie? Or is there some property of $\pi$, that makes that impossible? What about other numbers, eg 'e'?
 A: What you are asking is can be rephrased into the question: is $\pi$ normal? The answer to that question is "we don't know".
"Normality" is a fairly difficult thing to prove for numbers, and we don't really know that much about it. We know that there exist uncountably many normal and uncountably many non-normal numbers. We also know that the non-normal numbers form a null set, i.e. a set with measure 0. We know that rational numbers are not normal, because their digits repeat. Other than that, there are very few numbers for which we have proofs either way. We don't know if $\sqrt{2}, \pi$ or $e$ are normal or not.
That said, it's relatively easy to construct a number that is normal, and also to construct an irrational number that is not normal. For the first, just take
$$0.123456789101112131415161718192021222324\dots$$
which is "trivially" normal. For the second, take $$0.1010010001000010000010000001000000010\dots$$
which is evidently not normal, as none of the digits above $1$ appear in its expansion.
