one addition to that:
if you take a dice and dice a lot of times every number usually occurs equally often. you need a lot of bad luck to never dice one of the numbers with 6 choices: still it's possible.

but if you take a infinite sided dice: it is a whole other story. thats were the funny assumptions start.

but(to be clear): if you have a /set/ of numbers you want to see dicing with the infinte sided dice you have a good probability that one of the numbers from the set occurs if the set is /big/ enough. the bigger the set the better your chances to see one occur even with finite tries. and with the monkey: it's higher for every "letter" comes from a finite set. and you can give a finite set of combinations that may occur trying to form your "word". say the word is "eat". then you have codesize^3(ascii would be 255^3 ) combinations which is finite. with such finite probabilities you can calculate(thats a lower limit for the prob. , taking the "n out of m" in addition to that prob. increases a lot ...) . so you can give a probability but you don't know if it occurs even with infinite tries.

I absolutely love the fact that this conversation took a completely different path away from the original post. I am most amused.

why another path? this completely on topic :P

see?

Technically it's not an assumption, but a theorem with a specific proof. All it states is that as the number of tries approaches infinity the probability of any particular outcome not occuring approaches zero.

But that's just the theory. In practical terms we are constrained by lack of appropriate hardware, ie a universe of infinite dimensions to contain the proverbial infinite monkeys and typewriters, infinite mass to make them and/or an infinite lifetime to let them bang away on the keys. To quote the article:

And of course the also the pesky matter of noticing when interesting outcomes occur - do you know what your /dev/random produced last week?

If you had infinite monkeys, why would you need infinite time? Surely if you want to reproduce the works of Shakespeare, you would only need exactly as much time as it takes one monkey to type them out at a constant speed from start to finish without making mistakes.

that was my point all such proofs are errors in maths. proofen to be wrong in the thrties. see the links i provided(turing is easier to understand for computer folks i guess).

too your last sentence. i simplify what i statet:

you can state(calculate): within x tries you will find y occurences of z with a probability of p. as long as x is finite if its infinite you can't. and yes you can be on the ods of the probability: the one who gets the whole night the same number(look at it as a special poem - instead shakspeare - consisting of always the same letter).

example:
the code "eat" has the same probability to occur as the term "www" or the term " ". and so
if you take 7 letters the term "weather" has the same probability to occur as the term "......."

at least his is how we usually define "random" wich is also just a man made definition.

thats simple:
1. zaphod beeblebrox doesn't care about what they have to tell so they have to wait for an infinite amount of time.
2. for real: the probability that in a large number of "monkeys" many of them produce the same output is way higher then the probability that one gets a specified ouput. you need to increase the number of tries and not the monkeys. (thats the thing with the birthday)

-> http://en.wikipedia.org/wiki/Birthday_problem