If they were to cheat, you would be losing either way (or rather any way)
Sorry, I meant a provably fair game and even then some systemic flaw and/or complacency from the player's side (e.g. not entering their own seed) would be required for the casino to attempt it. I though this was obvious from the context. If it's not provably fair then randomness doesn't matter, they can take your money any way they want.
But isn't it what I mean exactly? If something happened once, then expect more of it (read, rare is relative). Actually, it is not like I have invented this as there are quite a few witticisms and pieces of common wisdom regarding this phenomenon (e.g. an evil chance seldom comes alone, troubles never come singly, etc)
Sounds more like superstition. I can't take it seriously in a discussion about randomness.
Indeed galaxies are bound by gravity
But what makes galaxies in the first place? Why are there many and not just one conglomeration of stars, all tightly packed together? If this is random (in fact, it is kinda a scientific fact), you have to accept that patterns are a distinctive feature or property of randomness. The Universe has innumerable billions of stars, and that's more than enough to evaluate its properties
Universe is expanding and has been doing so since the Big Bang. So it can't be in one big clump. It would probably be a very neatly organized sparse cloud of particles if not for randomness, which caused it to stick into various blobs.
Besides, you can't have it any other way from a purely mathematical point of view (the approach which you seem to be particularly fond of). How come? The reason is simple. If it were not for patterns, you would have a uniform distribution which is not random by definition, as simple as it gets. Stated differently, you can't have a random distribution without patterns given sufficient sample size
Uniform distribution is a very distinctive pattern. The
definition of random is: "proceeding, made, or occurring without definite aim, reason, or pattern". So it's the other way round. Random doesn't stop being random because you spotted a pattern. It either wasn't random to begin with, or you're wrong and there is no pattern.