Quote from: deisik on December 16, 2019, 11:24:29 AM

Quote from: Betwrong on December 16, 2019, 10:39:02 AM

Quote from: deisik on December 14, 2019, 02:31:36 PM

I would say that with random distributions there should be no apparent distinction as this is what you could rightfully expect from two identical distributions, where any random distribution should truly belong to, i.e. all random distributions should be alike (well, as I see it)

I may be wrong, but I see it differently. I think if we have two(or more) distributions which are alike, it means that the processes were influenced by the same factors. And if we knew the factors, those distributions would not appear random to us

You apparently make an obvious logical fallacy here

I don't remember how it is called (anyone welcome to chime in on this). What you say is true, i.e. if two distributions look alike, it may in fact mean they are the outcome of the same forces or processes running. However, this doesn't exclude random distributions as the latter are also an outcome of a random process. And they would be the same specifically because they are random. In other words, you can't have random in two distinctively different ways (with respect to resulting distributions, i.e. not how you technically produce them)

I think that random process is the one and only for which it's impossible to predict the outcome. I mean, if random distributions were alike, we could analyse it just once, and then we would be able to predict with a high likelihood the outcome of any random process. But the thing is that "randomness isn't uniform", as it is said in the great article by Wired from the link below

https://www.wired.com/2012/12/what-does-randomness-look-like/

So, in short, no, two distributions will not be the same "specifically because they are random". They can be, though, but that would be despite they are random, and that would be an extremely unlikely event.

Quote from: deisik on December 16, 2019, 11:24:29 AM

Quote from: Betwrong on December 16, 2019, 10:39:02 AM

I think, if we are getting similar patterns as the result of a process, it implies that there is some order in that process. But there is no order in randomness, and exactly for this reason all gambling strategies fail in the long run

And that's exactly the reason why the distinction between the two truly random distributions should be as random. You simply can't have it any other way

I agree with this, but I don't see how can two truly random distributions be alike as a result.