1. One roll stands for success or failureThere are many games and gamemasters out there who let players roll several times for extended tasks like sneaking or opening doors. As Burning Wheel teaches us that actually reduces the chances of success of the player. Therefore, I only let the players try once at a task until the circumstances change significantly. No retries without an in-game justification beyond "it didn't work the first time". I'd rather give a modifier, if the character takes his time instead of allowing multiple rolls.
2. Social stats/skills/abilities are not to be ignoredAll too often the social attributes, skills and abilities don't figure into the game at all. Players have spend their points on those stats, but they don't matter because they are never rolled. The players just play their characters convincingly and persuasively, even if their stats don't reflect that. Back in the 70ies when no social abilities beyond Charisma existed that was fine. But nowadays skills frequently model the social aspects of a character as well. I usually give a bonus to the social roll based on roleplaying, but I let people roll nonetheless.
A correlary to this rule is: gaming a social conflict like a combat encounter generates as much excitement and involvement as the combat encounter. But it should be reserved to the really important social conflicts.
3. Re-thinking failureAll too often we are in the habit of thinking of a failed roll that the character just wasn't good enough to succeed. But failure can have other dimensions. Apocalypse World/Monsterhearts/Dungeon World encourage the gamemaster to think about failure in different terms. Narratively, a failure means that the flow of the story doesn't move into the direction desired by the player. Instead it moves into the direction that the gamemaster desires. Doctor Who Adventures in Time and Space applies that principle by dividing results into a "yes and...", "yes", "yes, but...", "no, but...", "no" and "no and..." spectrum. Burning Wheel states "if you can't think of an interesting outcome based on failure, don't roll". Apocalypse World gives you tools to think of interesting outcomes.
I am going to apply that principle to all games in the future. Failure just moves the story in a different direction, but doesn't stop the story. Moreover, failure doesn't necessarily mean that the character failed in their tasks, but maybe just that success did have unintended consequences and side-effects.
Example from "In the Service of the Black King": Durgar tried to use the silver sword to destroy the Tome of the Forgotten and missed his move. The action was still a success, but both items were destroyed. If the roll had been a hit, the sword would not have been destroyed.
So, what did Indie gaming teach you?