Math of probability revisited

It seems to be a variation of the joke: if you had an infinite amount of monkeys hacking away on an infinite amount of computer keyboards you get Shakespeare's Hamlet, word for word.
So from probability wise, there is no implication that order is likely or inevitable. Mathematically, theoretically speaking, certainly a yes, observable in reality, No. "True" randomness is an assumption in the proof.

Order doesn’t figure into my query, just randomness and probability

Quite true Tor but the less the randomness the greater probability of repetition

What is missing on these types of questions is time. How long does a monkey take to type the required number of characters? Now take all the monkeys and all the remaining time in the universe and you will see that there is no chance of getting the works of Shakespeare.

Well, is chaos misunderstood order?

You wrote "we’d expect an occasional repetitions of an object or a collection of objects. Thus why not exact repetitions of entire galaxies or even Universes"

And to the scientific community real order is observable only on very specific scales. I'm not sure if "order" vanishes at the level of galaxies, but replicating entire galaxies, exactly, has lower probability than monkeys typing up Hamlet. As a function of time, I'm sure as n goes to infinity the probability goes close to "1" for the replication-of-galaxy-event, but good luck figuring out an equation to represent that. I know that someone came up with an equation for the monkey-hamlet scenario, and as the number of monkeys, n, goes to infinity, I think the probability goes close to one.

Then again, in reality, monkeys seriously lack concentration, so a monkey is more likely to defecate or urinate on the keyboard than try typing strings of letters on the keyboard.

But what if all the remaining time is infinite

People have no concept of infinite. There will be no monkeys and no people before infinite happens so once again, no works of Shakespeare.

...well "God" knows what happens to residual energy long after the last galaxy disintegrates...I find it totally inelegant that the Universe just ends without circular, completeness...I would gladly bet my neck on my instinct on this one...

Much like “forever.” However I wouldn’t put it exactly so. Though it’s impossible to “picture in the mind’s eye," we can certainly conceive of it

Eng you might have to elaborate on that observation for the benefit of the Average Clod among us (me). How can the infinite have a “before"

By coincidence Fil I feel much the same way. The term “circular” bothers me however as I envision sequential Big Bang, Expansion, Big Crunch’es as being a linear phenom without beginning nor end

But I’d agree that the idea of huge numbers of cold objects and particles mutually accelerating apart forever certainly qualifies as inelegant