Details escape me, but IIRC there's a 50/50 chance of finding any given ~300 digit (bits?) sequence in π computed to the same number of digits as there are particles in the universe.

Every string is in π, but you're not going to find Hamlet in there any time soon.

I think what your remember went something like this:

"if every particle in the universe was used to encode a digit of pi, there would be a 50% chance of finding an arbitrary 300 digit number therein"

I can infer this means you think its highly improbable that pi contains every number, let alone Hamlet.

If your convert "Hamlet" into binary we get this sequence of numbers:

01001000 01100001 01101101 01101100 01100101 01110100 00001101 00001010

You could test yourself to see if these set of numbers combined exist in pi. Although I think you will have a higher chance if you convert into the Ascii decimal values: 72 97 109 108 101 116 13 10