Action resolution is for resolving actions. It's not about making decisions (except in specific cases where it specifically is). Deciding to sneak by the guard is not the same thing as resolving the attempt to do so.
I was replying to your remark about a murder mystery, not about deciding to sneak past the guards.
But in either case, isn't action resolution - applied systematically over the course of play - the way that we find out whether or not the PCs made a poor or mistaken decision?
For the guard, let's say the player decides they want to sneak past. Cool, I don't have anything to do with this as a GM and it doesn't task me to narrate new fiction. What does is when the player starts declaring actions for their character to actually do the deed. Likely, there will be a few actions declared that I let auto-succeed, like moving through the town to where the guard is and taking up a starting locations. This is action resolution, even if it's usually handled very informally, because the GM has to decide if it occurs like asked or if mechanics need to be involved or if it fails due to notes or whatever.
I've called out a few bits of your posts that I wanted to respond to.
For this one, I'd often treat getting to the gate as framing rather than action declaration. Unless a player particularly wants to get some advantage out of treating it as an action - less of an issue in D&D, but in other systems this coud be establishing some sort of augment eg for having a Superior Vantage Point.
Genre appropriateness has been presented as an input into GM adjudication of action in the sense of if it's not present the GM can fail the declaration without engaging the action. Like, not allowing someone to find a ray gun in the baron's closet, or asking a dragon to give away it's horde. These are not genre appropriate to a 5e game and so the GM can use that heuristic to not consider them and fail them without consideration.
In a lot of these cases I don't even think of it as action resolution. The "genre filter" operates at a prior stage: we don't get to resolution because no permissible action has been declared.
I don't see how it's the player's mistake if the GM frames only the gate and doesn't provide indications that the sewer might exist. That's a GM mistake. Not a horrible, end of game, terrible no good one, but the GM is responsible for outlining the basic options of play in scene framing in 5e. This is a critical duty because the players cannot introduce new fiction, only the GM can, so it's the responsibility of the GM to make sure relevant fictional pathways are at least available through foreshadowing even if not immediately presented as obvious.
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Oddly, I think this is much less true to not true at all for other games so much as it is for 5e (or other D&D). The more the players can propose new fiction and the more the GM is constrained in resolution of action declarations, the less necessary it is to provide the options in framing. I could frame a heavily guarded gate in other systems and be comfortable not providing any other avenues because the players can create them with action declarations.
Various versions of D&D have a Streetwise or Gather Information skill/ability (eg 4e, 3E, AD&D Oriental Adventures via the Yakuza class, even sages in AD&D and B/X). So even within the compass of D&D there can be action declarations that allow the players to try and expand the scope of future potential action declarations.
I have played with D&D GMs whose response to that sort of thing is to shut it down - ie the inquiries produce no new information or options, all the potential informants remain silent, etc. I personally regard that as terrible GMing.
I have also played with D&D GMs who don't shut this sort of thing down but string it out endlessly - leads lead to leads lead to leads lead to session after session of trying to "find the plot". I also regard that as awful.
Although D&D doesn't have the same sort of crisp framework as (say) Fate or Burning Wheel for handling this sort of stuff, I still think there are better and worse ways for a D&D GM to handle it, which relate to some of what we've been talking about in this thread like (i) does the GM treat his/her notes as "total" or as a springboard? and (ii) to what extent does the GM follow the fiction and the impetus of play?
To relate the above to the example at hand: if the GM narrates the guards, and hints at or foreshadows the sewer, what happens if the PCs start searching for a hidden postern they can enter through? I don't think there's a single best answer, because it's so contextual. If it looks like the players are themselves trying to string things out, or squib in some fashion, because they're having trouble screwing up their courage to try and enter the castle, then as a GM I think it can make sense to force them to confront the choice:
Come on, people, what's it going to be? The gate, or the sewer? But if there is something genuinely going on - eg one of the PCs is an engineer or architect and so has some special interest in finding and exploiting the postern - then I think the GM would do better to take it seriously and see where it goes.
(The engineer/architect PC is like my bakers and vintners from upthread.)
It's only a mistake is the other available options have been determined by the GM to be failures regardless of approach.
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Ultimately, though, 5e is GM decides, and that structure means that player attempting to introduce new fiction is always at the mercy of the GM, which is not conducive to the player's being able to rely on a consistent adjudication if the GM is rejecting introductions not through the mechanics but through their authority. Unreliable mechanics like that are critically based on table dynamics and trust -- it's very easy to start to feel like you're playing "GM may I?"
I think this is why it makes sense to talk about principle and approaches that can make for a better or worse play experience. 4e D&D made the GM's job easier, because at a certai point responsibility for following the fiction and working out what happens gets passed off to the skill challenge framework. Whereas in the 5e context there is a risk that everything all the way up to the point of ultimate success or failure is GM decides. But I reckon there must be methods even in 5e for avoiding this - eg whether the postern is discovered or not can be put onto some sort of check or spell use or triggering of a background ability; there are guidelines for establishing encounters on the other side of the postern; etc.
If there be things that cannot be made to work, attempting one of those is a mistake. Sure, one can narrate negative results on Ability Checks (in 5E) as mistakes--it's something I do from time to time--but that's not what I was talking about. Making a mistake while disarming a trap does not mean it was a mistake to try.
If the idea that the player has is genre and gameplay appropriate, then
cannot be made to work seems to mean
doesn't fit with what the GM had in mind. This is what I am focusing on; and I am saying that, in general, I think it can make for a bad play experience. Because it pushes play towards
working out what the GM has in mind rather than
engaging and following the fiction.
(To be clear: if we're playing OSR-ish/"skilled play" and we're talking about puzzling out the riddling statue, or the room of trapped demi-gods, or similar than it's a different kettle of fish. But most of this thread doesn't seem to be about that sort of play.)