The Numbers Are Staggering

Hamlet runs to tens of thousands of words. To reproduce it by chance, a monkey would need every space, capital letter, and punctuation mark to land in exactly the right place. The odds of getting it on the first try are so small that the number of failed attempts would dwarf the count of atoms in the observable universe.

If every atom in the universe were a monkey typing one key per second since the Big Bang, they would not have produced even a single page of Hamlet by now. The theorem works only because infinity is qualitatively different from any large number, no matter how large. The certainty lives entirely in the infinite, never in the finite.