I like your phrasing! Alienating in that it is an unknowable other. Alienating doesn’t need to mean hostile though, especial player-hostile when used in game designs.
If anyone else follows and enjoys board games, there is a certain “movement” on Boardgame Geek to remove all randomness from any game with random elements. I think it’s intellectually lazy and logically bankrupt. The reductive explanation is that I replace a 6-sided die with a deck of cards numbered 1-6. Any time I need to roll a die, I instead draw a card. I do this until the deck is depleted and then I shuffle the deck again. The perceived benefit is that I do not need to worry about my die rolls because I will get exactly the correct distribution of dice rolls. Now I can’t complain that I am mad at my dice because they are perfectly “fair”.
Problem is that this is diluted by game designs that expect expected value on multiple die as they don’t converge. You also now have dependent events (your die has memory and what you rolled/drew will influence your next roll). Depending on the number of times your game requires you to roll, it can shatter the game design. For example, as a toy problem, it totally breaks the design of Craps.
For the record, I don’t think people in this thread are arguing for this kind of reductive design, but I do think it’s an interesting symptom of our human inability to intuit how probability functions. Is it “fair” if we agree to roll a die and you win? Probably. Is it “equitable”? No. I think certain game communities conflate the words and use them interchangeably.
In conclusion, I’m a big fan of the Central Limit Theorem. And we know it works because Quantum Mechanics works. :-P