Technically if they are following some regulations on how the gambling site should work, it should be random and strictly no other codes attached to manipulate the outcomes. But since there are no such restrictions in the gambling platforms, I think there is still a bit of a hole where the luck favors the house most of the time. But still, it could be considered profitable if you are lucky enough.
The house has a built-in advantage called the house edge. Again, if they fiddled with the numbers it could turn against them. For example in some (most? all?) dice games the players can chose low or high, so if the house favored one outcome and players noticed that they would start bidding in the other outcome and clean the bankroll
If they were to cheat, you would be losing either way (or rather any way)
That said, I don't know how it can possibly trump "human perception of randomness" as this perception, as you call it, allows to override the randomness of something, and make decisions precisely based on that randomness (or rather its override). I don't know either how that can be construed as an impractical use of randomness as it is quite the opposite. To sum it up, if you encounter something ostensibly random and seldom, expect more of it in about or around
I don't know what this means, other than humans are bad at generating randomness? You also seem to say that random must be rare. It's not rare, it's random. It can happen 3 times today and then never again for 100 years
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)
Then what about stars being grouped in galaxies? This grouping is said to be entirely random as otherwise the whole theory of the Big Bang doesn't hold. I think you can't go beyond that as far as randomness is concerned as there is no manifestation of randomness of a larger scale. Is this an optical illusion too according to you?
Galaxies are not random, they're bound by gravity. If you mean the initial distribution of matter then, again, random doesn't mean uniform distribution so I think being random would actually explain clumps of matter forming and the coalescing into stars and so on. Big Bang is thought to have started with lower (than today) entropy and it has been increasing since then but it's a whole different topic
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
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