Upthread I've talked about RPGing as "puzzle solving", and
@Manbearcat has mentioned Torchbearer in this context. Here are some actual play examples which will permit elaboration:
Nearly all the action of the session took place in Megloss's house. After the recap and the account of Korvin's arrival, the players decided that getting from the back room of the house into the front sections, while the occupants were there asleep, was too hard, and so decided to leave, but to grab the papers from the front room that had been mentioned in the previous session.
The Scout tests to get to the front of the house without awakening anyone with the light of Korvin's lantern were successful. So was the Criminal test to pick the front door lock. But the Scout test to look around before actually entering was not: and so they suffered a twist - the Cinder Imp who lives in the fire place came to the front door to speak to them, wanting their lantern.
They decided to turn this into an opportunity, luring (ie tricking) the Imp outside with the lantern, so that Golin could sneak in and snatch the papers. The players succeeded at this contest of trickery but owed a significant compromise (having lost nearly half their own hit points): when the Imp tried to snatch the lantern from Korvin, as Golin grabbed the papers, it fell to the ground and was smashed.
The angry imp then decided to try and set fire to the timber house.
<snip>
Korvin decided to read the papers, and succeeded on the Ob 2 Scholar test (for weird inscriptions). The papers mentioned Celedhring, an Elf who abandoned dreaming and the West and turned instead to the powers of the Outer Dark.
The players then decided they should do more research in the library of the Wizard's Tower, and Golin's player decided to do this - with his Will having improved to 4 during one of the conflicts, and with help from Korvin, and one point of persona left, he had a better chance of success than Korvin did. He succeeded at the Ob 4 Scholar test, and learned that Megloss's house had originally been the house of the wizard Pallando, who had built the house around a post from an Elven Dreamhouse that had been stolen by Celedhring.
The session started in town phase. Golin shared the information that he and Korvin had acquired in the previous session, and Fea-bella did some more research. I figured that with the information already discovered, she had a "Detailed description" of what she was researching, and and for Ob 4 could learn an interesting fact. The Scholar test succeeded, and the interesting fact was that Celedhring, after entering the Shadow Caves, had never left them! Golin's player conjectured a lich; and Fea-bella decided to purchase some holy water for battling the undead. I've been following the gear availability rules from the LMM pretty closely, which has limited what the PCs can buy in the Wizard's Tower without going to the black market (which in this context I'm construing as buying directly from townsfolk or peasants). Holy water is listed as availability 3, ie in Wizards' Towers, Religious Bastions and Forgotten Temple Complexes. I toyed with being a mean GM and saying that, for holy water, one of those is not like the other two. But then I reviewed my list of town facilities for a Wizard's Tower and allowed that there was a shrine, where holy water might be acquired. Golin offered help. But the Resources test (5 dice against Ob 3) failed - the shrine attendant sold Fea-bella the holy water, but only after berating her for her lack of regular attendance or offerings (ie her and Golin both had their Resources taxed down to 1).
<snip>
they returned to the wedge room, averting their eyes from the symbols, and going through the door. This took them to an area where their candles provided only dim light, and dim light was darkness. They could see an alcove in the wall opposite, but when they went to explore it they awoke the aptrgangr resting there, as well as its friends.
Golin's player decided that they should extinguish their lights, to try and get the aptrgangr's to return to their rest. The rules say that only riddling or fleeing are possible in darkness; I decided that this was a trick that was in the neighbourhood of riddling, and so was also an acceptable conflict, pitting the PCs Manipulator and Lore Master against the aptrgangrs' Hunting Nature.
The players were defeated in the trickery contest, with only a minor compromise owed by the aptrgangrs. In retrospect I think I was a bit lenient here - I decided where, on my map, the aptrgangrs had led the PCs to, and it did have the potential to put the PCs at a disadvantage, but that ended up not mattering as after some discussion the PCs decided to remain in darkness (rather than pulling out their glowing fungus) and flee. And so they didn't suffer much consequence from their failed trickery. I now think the Afraid condition would have been appropriate, but didn't think of that at the time.
The pursuit was a close thing, but the aptrgangrs won with one hp left, and so I decided that they had caught up to the PCs, and forced a confrontation; but with a significant compromise owed, I determined that they had all moved to the other end of the map, where natural light fell though an open "window" in the cliff-side - looking out over the lower hills and the plain - which removed the light penalties.
At this point I made what could be considered a GMing error - I had in mind the episode in LotR where the Hobbits are caught in the Barrow Downs and awaken with a blade across their throats, and so I decided the aptrgangrs would try and capture the PCs. Only once I declared this to the players did I realise that, at Might 2 vs Might 3, the aptrgangrs can't actually do that! But I felt locked in by my declaration, and so the capture conflict was on!
This time around the PCs did well, and defeated the aptrgangrs with a half-compromise owed. The rules suggest, as possible compromises, "the adventurers are injured, weapons broken, or armour rent and torn". During the conflict, when Fea-bella used a vial of her holy water to good affect against an aptrgangr, I had decided that if they got the chance the aptrgangrs would smash her other vials if they got the chance - and given that she had been dropped to zero hp while Golin had lost none, I put that forward as the compromise. Fea-bella's player protested a little, but when I said perhaps she could be injured instead, the player was happy to lose the gear instead.
The first sequence of play - in which the PCs try and sneak in to Megloss's house to steal the papers - is an example of the players exercising agency over the shared fiction. The broad goal is to obtain some sort of advantage, or leverage, by taking the papers from their enemy Megloss's house. The house itself, the locked door, and its inhabitants including the Cinder Imp, are all elements of GM-introduced adversity.
There are thus two broad conceptions as to how the fiction should go next - mine as GM, in the adversity role, is
that the Cinder Imp gets their lantern and they don't get the papers; theirs as players, in the role of advocating for their PCs, is
that they get the papers, which will be useful to them, and keep their lantern, and evade/escape the Imp.
Which of these two conceptions prevails is determined via the appropriate rules procedure, namely, a Trickery conflict (broadly comparable to a Burning Wheel Duel of Wits, or at a higher level of abstraction to a 4e skill challenge). As the post above reports, this ended up with the PCs successful but the players owing a compromise: thus they got the papers, but the lantern was smashed, and the Imp angered.
I've snipped what followed, to go to the town phase which involved four relevant player action declarations. The first three are these:
*Korvin reading the papers;
*Golin doing research in the library of the Wizard's Tower;
*Fea-bella doing more research.
These do not involve the players exercising significant agency over the shared fiction. Rather, the players are deploying their resources - in this case, tests made during a town phase, each of which adds to the Lifestyle Cost of the PC who performed it. Because each test in Torchbearer is normally its own reward - contributing towards advancement of the tested skill or ability - there is an element of sheer mechanics here: the players spending resources to accrue tests.
But the successful tests also obliged me as GM to reveal information. This information pertained to the Shadow Caves, a dungeon beneath Megloss's house that I had already written up. In the writing up I had had regard to thematic content introduced by the players - the nature and fate of Elves - but also included some ideas of my own. (As I've mentioned a few times upthread, this GM pre-authorship is one way that Torchbearer differs from Burning Wheel. This aspect of Torchbearer - GM pre-authorship, which the players can try and gain information about - is deliberately based on classic D&D.)
The players learned about 3 bits of my pre-authorship:
*Celedhring, an Elf who abandoned dreaming and the West and turned instead to the powers of the Outer Dark;
*That Megloss's house had originally been the house of the wizard Pallando, who had built the house around a post from an Elven Dreamhouse that had been stolen by Celedhring;
*That Celedhring, after entering the Shadow Caves, had never left them.
This is where the puzzle-solving bit came in: in particular, the players used some of this information to inform their planning for their excursion. And this is the fourth of the relevant town phase tests: the Resources test to acquire holy water. Because this failed, I as GM got to narrate the consequences in accordance with the rules, which I did: successful acquisition of the desired item, but with a condition (Taxing of Resources) being imposed. (Later in the town phase, but snipped in the above posts, there were more failed resource tests where rather than success with a condition I imposed a twist, in the form of a new enemy for one of the PCs.)
The final part of the quotes sets out the PCs' encounter with aptr-gangrs in the Shadow Caves. Here the play is no longer puzzle-solving: rather, it is very similar to the Cinder Imp scenario in its basic structure: as GM I have one conception of how things will go (ie
that the PCs are captured by the aptr-gangrs) while the players have a competing conception (at first
that their PCs will escape the aptr-gangrs, and then
given that they can't escape the aptr-gangrs, that their PCs will capture them instead!). That was resolved using the rules for a trickery conflict, then a flee conflict, then a capture conflict. As the post described, in resolving these conflicts the information that I had pre-authored - the dungeon map - provided material for framing and for narrating consequences (eg it gave places that were advantageous for the aptr-gangrs, or advantageous for the players) but resolution was not map-and-key based, which is to say there was no
adjudication of declared actions by reference to pre-authored material. The resolution took place via the conflict system.
This sort of toggling between play that involves a reasonably high degree of player agency in respect of the shared fiction, and play that involves the players getting information from the GM which serves as grist to their puzzle-solving mills, is central to Torchbearer play.