This is satisfying:
This is unsatisfying:
This is most relevant to competitive board games, but it can also sometimes matter for RPGs.
Luck provides uncertainty. Challenge-based games need uncertainty or else they'll become solved. Without uncertainty, every time you play, you would keep getting the same outcome. But too much uncertainty can undermine strategic integrity. Good luck and bad luck keeps everyone on their toes, but I do prefer games where good decision-making matters more than luck. After all, what's the point of putting effort into understanding a game, into forming a sound strategy, if that effort can't compensate for bad luck? To the competitive mind, there's nothing more thrilling than beating your opponent even though you kept rolling worse than they did, simply because you were better at the game than them.
Luck can also be a great tiebreaker for players who are otherwise evenly matched. Stalemates aren't very satisfying, so luck usually ensures that someone gets to walk away a winner. But I'm tired of playing games that only possess an illusion of skill. Where the winner looks at their own victory and has no choice but to admit, "I didn't really earn that. I just drew a better hand."
-Dwiz