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To be fair, I didn't watch the video to the part where he mentions monkeys writing Hamlet, but I thought the point of the monkeys is that they will stumble upon a Hamlet by accident at some point in time, by randomly pressing buttons on a keyboard. Obviously, it would take a long time, but it would happen at some point.

Obviously, it would take a long time, but it would happen at some point.

Has someone done the calculation whether it would happen before the end of the universe?

It would involve multiple, multiple universes (but not infinite) coming and going. Even with infinite monkeys.

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