If there was a game master personality test— something like Myers-Briggs, Type A/B, or even the Hogwarts sorting hat— one of the core dichotomies tested would be reliance on dice versus personal instinct and intuition. I'm not going to pass judgement on one method or the other, but we all have our own tendencies and I do think it is important to intentionally think about what we are doing.
Dungeons & Dragons was originally a lot more random that it is today, both in rules-as-written and in how the majority of people played it. The standard method of generating ability scores was 3d6 in order, rules for random encounters were much more explicit, and every creature in the Monster Manual had a range stating how many of them would be encountered at once. D&D can still be played in this way, but the emphasis is not quite as strong as it once was. And other tabletop roleplaying games, unless they are deliberately attempting to be "old-school," are generally even less random than that.
The more randomness is introduced into a roleplaying game, the more "gamey" it tends to feel. And as times have changed, the role of the game master has largely shifted from neutral referee to invested show runner. If you prefer that role, you're not only probably going to play a game system that supports that, but even be more likely to override the rules and the dice when you see fit.
Many, if not most, game masters freely admit to occasionally fudging dice rolls, often in the favor of the players. How much of this is too much? When so much of D&D is based on getting tiny increments of +1 to rolls, is it doing the disservice to knock over a zombie who really had one hit point remaining? Or is it better to consider the pace of the game as a whole, and wrap up an encounter that feels like it is dragging on?
As a thought experiment, I've considered what it would be like to run a session of D&D where I effectively ignored the dice. The players would still roll as they usually do, and I would drop some dice as expected, but by controlling factors like monster hit points and the difficulty of various ability checks, I have the ability to rule an entire game by fiat. To everyone I bring this up to, this is clearly cheating. But does it matter if the players don't find out? Don't I know better than the dice when the encounter should end?
(Interestingly, this seems to be more forbidden for D&D— which is really at its core a tactical war-game— as opposed to something like Fate or Apocalypse World.)
So I probably shouldn't run a completely de-randomized game. At least not if I want to be game master for those players ever again should they find out. So should I instead roll up nothing but random encounters for them? I'm sure I could rig up a completely randomly-generated campaign. But I probably shouldn't.
Unsurprisingly, it doesn't work super well to go to either extreme. In roleplaying games as in life. I bring up these examples to establish boundaries so that you can start thinking about the messy bits in the middle you may not consider.
Do you use random encounters in your games? Why or why not? They can add some variety that you didn't even realize was lacking. You or your players may come up with a theory as to how that random encounter connects to the larger plot, bringing depth to the story you never planned. Or it may be a speed-bump shaped like 2d6 bandits.
What about when creating entire adventures? The Dungeon Master's Guide has tons of tables to help seed your world with randomness. Something you weren't expecting could spark creativity. Why did the random monster generator give me so many oozes and orcs in this dungeon? Maybe the orcs are part of a cult of Juiblex worshipers.
How do you determine the attitudes and reactions of non-player characters? Do you keep it old-school and roll randomly to determine their initial feelings toward the player characters? Or do you just go with your gut? You can get some interesting gameplay from trying to figure out why this random group of goblins reacted to the party as if they were their new best friends.
Who are these NPCs? How does it break down in terms of male/female/non-binary? If you are creating NPCs based on what feels right for the role, do you think about this, or do you just assign gender to a role of the dice? What about race? When I was populating a town, I randomly rolled that several nearby shops were all run by halflings. Suddenly, I had a halfling district that I hadn't originally planned for, but added some great flavor to the town.
Think about your methods. Try new things. If you usually run combat extremely impartially, try fudging some stuff to make the story flow better. If you don't make very many rolls in social situations, try some randomization to take things in an unexpected and exciting direction. You can always go back to the way you prefer, but it's difficult to grow in any field if you don't experiment with alternative methods.