I think if they were given enough time, and large means what it sounds like, then the expected value of number of monkeys that reproduce Hamlet, character for character, would be any number you like (so greater than 1 if there were enough monkeys).(adsbygoogle = window.adsbygoogle || []).push({});

Let's say you give them a special keyboard that has only letters, space, and a shift key. Then there are 53 different keystrokes. Only one in 53 is the correct first character in Hamlet.

So 1/53 of the monkeys will get the first character right.

Of those, 1/53 will get the second character right.

There are about 200,000 characters in Hamlet. So the probability a monkey will type out Hamlet is less than (1/53)^200000 which is around 1 times ten to the -344855 power. In other words, there are about 344850 ZEROS before the decimal point. So it's pretty unlikely.

I think a google is 10^100. If you have one google raised to the 3449 power, or so, monkeys, all typing, then the expected value is that ONE of those (google)^3449 monkeys will produce Hamlet. Anything less than (google)^3449 monkeys will PROBABLY not produce Hamlet.

This is to skirt the issue of how many of those monkeys will STOP at HAMLET and not keep going. If a monkey keeps going, that should DISQUALIFY it from being considered a real Hamlet.

So let's revise it and give each monkey the option to stop. So let's model that by having 54 keys instead of 53, where the new 54th key is STOP WRITING.

OK, now the probability that a monkey will type all the right characters in Hamlet and Stop at the right time, without adding extra stuff, is (1/54)^200000 or so which is about 10^(-346479), meaning that now you need (google)^16 times as many monkeys as before to get the expected value of 1 Halmet.

Bottom line: you'll average one copy of Hamlet per every (google)^3465 monkeys you have.

Given the comparison between a million, or even a trillion, to the sort of numbers involved here like needing (google)^3465 to get ONE Hamlet (on average), there is basically no way a million or trillion monkeys will do it, if everything is totally random. It's safe to say that (google)^3465 is incomprehensibly bigger than the number of monkeys that ever lived on earth or ever will and, so, realistically, no real group of monkeys will ever produce Hamlet.

But since i added the 54th key, I have ignored the fact that all the monkeys who press key number 54 stop and if they stop before Hamlet is finished, there is NO change they will ever get Hamlet. So consider these numbers as upper bounds.

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# Can a large number of monkeys write Hamlet?

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