This strikes me as cheating — and defeats the very idea.
The idea is that infinity is...well, you know, infinite. As a result, if you have infinite monkeys pounding randomly at a keyboard, eventually one will create a word. It may be, say, one in a billion. Most monkeys won't type anything — but some will, and a few will hit on a word.
And then eventually one will accidentally write a whole sentence. This is much harder — maybe one in a quadrillion. The monkey who writes a word has to then write another word, and another, and another, purely by accident. And these words, just by chance, must make sense together.
And then eventually one will accidentally write several sentences. This is exponentially even more rare — maybe one in a google?
And then, with enough time, one will write something close to a work of Shakespeare. This is rare beyond imagining — one in a google to the power of a google, maybe?
And then, with even more time, one will write all the works of Shakespeare, perfectly. This is unimaginably rare — so rare as to be below the threshold of possibility, so rare that you might reasonably call it impossible. (To imagine how rare, think of all the monkeys that will have to have typed out nearly the entire works, but written "Tp be or not to be," thereby failing the test. Or accidentally written the entire works of Ernest Hemingway, instead.) And yet, with infinity, it's an absolute given. That's the point.
This misses that, by making it exponentially easier. They're only looking for the first step — monkeys typing words — and even at that step, are cheating by assuming that the monkeys type anything at all. Humans are then interceding to order and shape the typing — clearing out all the randomness and selecting the results. And of course that will eventually get what you want — because you're writing it.
Very interesting! I like it!
Consider this. If the universe is infinite, and lots of people think it might be, but the laws of physics are the same everywhere (and we have no reason to believe they aren't) that means matter will tend to arrange itself in similar ways over and over. Many places will be duplicates of us, indeed exact duplicates: including me typing this and you reading it. Right down to our thoughts which are governed by quantum electrodynamics.
Even the people who stopped reading after the first paragraph because they thought it was bullshit will have their duplicates. In some cases those duplicates will be similar copies but not exactly the same. Ones where Republicans have hearts and democrats have brains for instance. In one or more of those places a similar duplicate computer just typed the text of Shakespeare's Hamlet in order. Think of the day that programmer is having. He's sent out interns for champagne. Everybody's slapping him on the back. Even the pretty programmer who sits by the conference room came over to congratulate him. She finally noticed him and his nerdy genius. In some lesser number of places they are wed.
But for every one of those great ones there are even more who typed out misses, like every word of James Joyce's Dubliners in order. In those tragic cases the programmer committed suicide and the pretty girl only noticed him in death. (Since the laws of physics remain the same no other outcomes of the terrible Dubliners scenario are possible.)
Infinity. It's kind of sad.