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
To quote you back "But that's not mathematics, that's arithmetic".
I can see your point of view, but arithmetic is one of oldest fundamentals of mathematics. This is the way I was thought.
http://en.wikipedia.org/wiki/Arithmetic
Its like the old saying "Its not what you say, but how you say it". In this day and age, people generally get the perception that mathematics is all about counting.
"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