@Maxperson,
@Bedrockgames.
I don't really follow your replies. You say that the GM is in charge, but you also say that the players "have input" and "help shape things". But they don't have "narrative power" (whatever that means -
narrative power sounds like the power to shape the fiction, so if players don't have that then I'm not sure what their input and shaping consist in, so maybe it means something else?).
Do you agree that there is an approach to RPG play in which the GM is empowered to determine the outcomes of action resolutions based on a prior conception of the fiction (whether that is sourced in notes or imagination)? And do you agree that there is an approach to play in which the answer to a player's question
what do I see or
what do I find or
what do I know about <this gameworld element the GM has just introduced> is typically provided by the GM making a decision based on his/her prior conception of the fiction, perhaps relying on a Knowledge check (or INT check or whatever the system dictates) to determine how much of his/her prior conception to share?
When we say narrative power, it is just a convenient term for describing games where the players can narrate things into existence like the GM, or possibly games where they have limited abilities to establish setting content as players, not as characters.
Also i don't think any of us disagree there is a difference between a game where players have that kind of power, versus ones where the GM is the one with power of setting. Where I think most of us disagree is your simplifcation of the latter to "The GM decides" "playing to discover the GM's notes". You are describing it like a very binary process, and I think it is much, much more organic than how you are describing it. There is simply more to it than that. And part of what that is is the GM is beholden to other things (dice, what the players do in the setting and what gets established by their characters)
For example if you say "What do I see", the GM isn't responding based on their prior conception of the fiction. That isn't how we conceive of play at all. It is not this unfolding fiction that is happening that gets built up in binary exchanges of players say X, GM decides. There is that component of the GM making his decision. But you are ignoring things like players can make a case outside character for things, and the GM will often be considering their words. It isn't as simple as "I decide". My answer needs to make sense too. And most GMs I have played with, will allow back and forth, where players often explain hwy they think something ought to be present. The players don't have direct power, but they have the tools of persuasion (expected to be used in good faith, not to advance their character's interest) to help smooth out this process. In a typical sandbox the GM is making his decision not based on the prior fiction, but based on the world, the ongoing situations in that world, and what has just previously occurred (I think this is a much better term than the fiction, because the fiction seems to sidestep or minimize the role of the world).
To take another example, if the players go to the head of phoenix moon gang and ask for her help finding the disappeared daughter of a local magistrate, the GM is going to respond, not decide, but respond, based on what the players say, what the leader's motivations are, weighing any rolls they might make, who the player characters are, etc. What the players say here could be very important. Then he might declare what the leader says or does, and even then he isn't often simply deciding. If he says the leader throws her crescent moon blade at the party (which would be out of character here, but let's use that as an example), he still has to roll her attack. He can say what she tries to do, but he is frequently just as bound by the dice as the players. I think a much better conception, one that many sandbox GMs invoke is the GM is playing the world, the players are playing their characters. If you want to reduce that to the players are playing to discover the GMs notes, or the GM decides what happens based on his prior understanding of the fiction, I think you can do that, but like I have said it is very reductive, and it oversimplifies something that will feel very different in play if you follow the oversimplification as a model or as a procedure.