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It's a theorem. And yes, it requires the monkeys to be random. And yes, it was tested with monkeys and the results were mainly the letter 's' repeated.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

Really all this proves is that if you had infinite Shakespeares and infinite time, one of them would write his complete works using only the letter 's'.

As you note, the real issue here is that the problem is poorly framed. Let's instead consider spherical monkeys in a vacuum...

I have random number generator which produces exact copy of a work of Shakespeare every time when I call it. '-)