It's not about luck, it's about mathematical statistics. You mentioned casinos in particular and that means the majority of the games you'll play are going to be weighted towards the house. Even things like blackjack give the casino an inbuilt advantage where you are more likely to go bust than the dealer - they have second mover advantage and unless you're card counting you'll never beat their strategy. If you include poker rooms, where you're feeding the casino take but (hopefully) taking winnings from other players, then you could possibly walk away with a profit without luck being involved.
You wrote it right, but the point is that mathematics obeys the law of chance, and this is the law. And what determines which chance will fall out? Luck. There is a way to almost completely neutralize the influence of luck from any game: This is to create a large number of repetitions, and then luck becomes the same for everyone, according to the law of normal distribution. The main thing is that in this case, the player had enough deposit to play for a long time. But here there is a minus: for a large number of repetitions in many casino games, it will have time to collect a large commission from the player. I mean something like the number 0 in red-black.