What? That’s not what independence means. They need to be independent, yes, because otherwise you might get into weird corner cases where the probably doesn’t converge to 1, but they don’t have to be equally likely. In fact, weighing the odds based on how often letters are used by Shakespeare should lower the expected timeframe. Heck, Shakespeare doesn’t use “J”, why would that key even be relevant? Where in the world do normal distributions even come into this? How does this comment have 4 upvotes? What am I missing here?
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.