Those are some of the conditions necessary for the probability calculation to result in a non zero chance of writing the works of Shakespeare. From the article:

Consider the probability of typing the word banana on a typewriter with 50 keys. Suppose that the keys are pressed independently and uniformly at random, meaning that each key has an equal chance of being pressed regardless of what keys had been pressed previously. The chance that the first letter typed is 'b' is 1/50, and the chance that the second letter typed is 'a' is also 1/50, and so on. Therefore, the probability of the first six letters spelling banana is:

(1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50) = (1/50)6 = 1/15,625,000,000.

The result is less than one in 15 billion, but not zero.

But if they weren't independent, say every time a monkey hits b their lack of fine motor skills causes them to also hit yhb all together, then even infinite monkeys with infinite time wouldn't be able to type banana. Or if after hitting b they keep hitting b and ignore all the other keys they would never type banana. Evenly distributed just makes sure they can hit every key, it can take some unevenness like you mentioned j and some other letters come up very rarely. But if they never hit a or e you're never going to get Hamlet.

[–] HeavenlySpoon@ttrpg.network 1 points 6 days ago

No, I agree that independence is necessary, not just because of “always”, but because if, as a crude example, your odds of hitting B halve each time you hit A, an infinite number of tries isn’t guaranteed to give you Shakespeare, even if the odds aren’t technically 0. My problem was that what you originally described wasn’t independence, it’s uniformity, which isn’t a prerequisite. And it’s up to 9 upvotes now so I don’t know what’s going on.

[–] ameancow@lemmy.world 1 points 1 week ago* (last edited 1 week ago)

In a literal and real universe, if you had real magic and could organize this in reality without it collapsing into a singularity instantly, then not only would you indeed get Hamlet instantly, you will also get monkey poop sculptures in every possible configuration, including models of us typing these words on PC monitors made entirely of monkey feces. They would just be fecal scultpures because, as you said, a monkey can't poop actual electronics so pooping an entire, working internet with two people chatting is impossible.... probably. You would get typewriters thrown around randomly until some collapse into black holes, until some accidentally form whole, working machines that do a vast array of functions, until some mix with the poop sculptures and create models of whole worlds. If you want to limit it to a mathematical thought experiment, then yes you can make points about key distribution and so on, you can make limitations that will constrain the outcomes, but in the real world all we really have to create those limitations is the speed of light and other fundamental conservation forces, which would constrain contradictory outcomes in an infinite model.

Again, the idea is to understand that infinity is an absurd idea, and we can't work with infinities in any meaningful way.