I was under the impression that a uniform distribution is still considered random, but that there are simply many other random distributions. If you have a flat 1/10 chance of receiving a certain item, then sure, you might do the task 30 times without getting it. But if it were programmed such that you will always receive the item at some point within the first 10 completions of the task (i.e. 10% of players receive it after their first completion, 10% after their second completion, etc.) I would still consider that random, and not really more or less random than the 1/10 scenario. I'm not sure what you mean by "real randomness."
I can give you one simple argument. Ten items shuffled have 10! entropy, while ten independent rolls have 10^10 entropy. How is that not far less random?
The distinction is between independent identically distributed random variables, where it's possible to not get the item after 1/p tries, and what you described, which the events are not identically distributed. In the case you describe, the probability you'll get an item when you have a second completion is 1/9, not 1/10.
This is the distinction that the original article highlighted and gives rise to the Poisson distribution, which can have unintuitive results because it is not a uniform distribution. You are describing a uniform distribution. (A Poisson distribution characterizes the number of hits you would expect after running some number of iid random events.)
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I was under the impression that a uniform distribution is still considered random, but that there are simply many other random distributions. If you have a flat 1/10 chance of receiving a certain item, then sure, you might do the task 30 times without getting it. But if it were programmed such that you will always receive the item at some point within the first 10 completions of the task (i.e. 10% of players receive it after their first completion, 10% after their second completion, etc.) I would still consider that random, and not really more or less random than the 1/10 scenario. I'm not sure what you mean by "real randomness."
I can give you one simple argument. Ten items shuffled have 10! entropy, while ten independent rolls have 10^10 entropy. How is that not far less random?
Because amount of entropy has nothing to do with "amount of randomness."
I'm pretty sure that entropy is pretty much the only sane definition you could give of "amount of randomness".
> entropy is a measure of the uncertainty in a random variable
The distinction is between independent identically distributed random variables, where it's possible to not get the item after 1/p tries, and what you described, which the events are not identically distributed. In the case you describe, the probability you'll get an item when you have a second completion is 1/9, not 1/10.
This is the distinction that the original article highlighted and gives rise to the Poisson distribution, which can have unintuitive results because it is not a uniform distribution. You are describing a uniform distribution. (A Poisson distribution characterizes the number of hits you would expect after running some number of iid random events.)