After all, there’s no fundamental reason for why it can’t all just be a repeat of the same number. But it doesn’t look random, right? So what is randomness?
There are 10 trillion ways to combine a sequence that long, so I think you would expect to see that exact sequence every 10 trillion digits of a randomly generated decimal sequence on average, which isn’t that many to a modern computer, so almost certainly that has already happened by pure accident.
And randomness can be defined as entropy, which you check statistically. You can never be certain, you can only increase your level of confidence. Here is how random.org does it:
Here’s another set of random digits
1 1 1 1 1 1 1 1 1 1
:3
After all, there’s no fundamental reason for why it can’t all just be a repeat of the same number. But it doesn’t look random, right? So what is randomness?
The most popular lottery numbers are 1,2,3,4,5,6 because we are human and don’t understand randomness.
There are 10 trillion ways to combine a sequence that long, so I think you would expect to see that exact sequence every 10 trillion digits of a randomly generated decimal sequence on average, which isn’t that many to a modern computer, so almost certainly that has already happened by pure accident.
And randomness can be defined as entropy, which you check statistically. You can never be certain, you can only increase your level of confidence. Here is how random.org does it:
https://www.random.org/analysis/
And this shows you what some of those analyses look like in real time:
https://www.random.org/statistics/