It doesn't need to be perfectly random; you just need every sequence to have a nonzero probability of being generated. "to be or not to be" may be more likely

It doesn't need to be perfectly random; you just need every sequence to have a nonzero probability of being generated. "to be or not to be" may be more likely for a monkey on a keyboard to generate than a random string, actually. The keys to generate it are highly repetitive and relatively close together. That's true for any NL string: the lower entropy of NL strings are reflected in the keyboard layout. If the monkeys switch to Dvorak, they could probably generate Shakespeare even faster.