if I wanted more shared narrative control, I certainly wouldn't use a system like D&D that has so many onerous sim elements.
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If I wanted truly shared storytelling, I see nothing to be gained by having a player build a character using a class or roll a check at all.
By making it clear who adjudicates and who's in charge, I've fixed a lot of problems.
Story Now gaming is not purely a collaborative storytelling experience.
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Story Now games are still games
I agree with Campbell here. "Story now", or "indie", rpging is RPGing. Not conch-passing.
The function of checks is primarily to allocate authority to narrate situation and consequence. Checks do this in two ways: (i) by causing everyone in the game to become clear on what is happening in the fiction, and what is at stake from the player's point of view; (ii) by distribuing the authority to then stipulate what, in the fiction, happens in relation to that situation and those stakes. Without checks, (i) and (ii) would still have to take place. Otherwise, how would the game progress? And how would he group establish the content of the shared imaginary space?
One answer to those questions is: the GM would decide. Which suggests that checks are actually less important to a GM-driven game. (And I think this is borne out by the GMing advice in 90s White Wolf games and the 2nd ed books, which suggest that the GM disregard dice rolls; and by 90s modules that are written in a way that makes actual mechanical resolution irrelevant to the unfolding of the module's events.)
The allocation of narrative authority could be done via coin tosses (is that roughly how Prince Valiant works?), but that's obviously not the only way. It is possible to have fairly typical PC builds - with different bonuses in different attributes - that still work in an "indie" way.
From a process simulationist point of view, skill bonuses are typically read as measuring PC ability. But in "indie" play, the preeminent function of skill bonuses is to deal with (ii) and therefore create incentives in relation to (i). For instance, if my bonus in Intimidate is high, then when a check is made I am more likely to succeed. Which means if I, as a player, approach situations with my PC attempting to Intimidate, I am more likely to be the one who gets to narrate consequences. Conversely, if my Acrobatics bonus is low, and I bring my PC into, or find myself framed into, a situation which requires acrobatic flourish, it is more likely that the GM will get to narrate cosequences, including my failure to realise what I (and my PC) were hoping to achieve.
But this doesn't have to be understood in terms of competence or incompetence. It can be good fortune or bad luck; reptuation, in the case of Intimidation; bad ground, in the case of Acrobatics; or any other fictional element that the adds colour and further possibilities to the situation.
(A further design question: should low bonuses, which mean that a PC is likely to lose what is at stake in situations that test that bonus, be considered disadvantages - because the player is less likely to succeed - or
advantages - because they increase the likelihood that the PC will dominate the scene in question (by failing in some intereseting way) and thereby give the player spotlight time? 4e says "disadvantage". Burning Wheel says "disadvantage" for skills, but "advantage" for some traits like physical disabilities that will tend to make the character dominate the resolution of many scenes. The design choices interact with other decisions around stake-setting and rewards.)
The interaction between (a) player build choices, which give
them incentives and prospects for success, and that will showcase their PCs in different ways, and (b) GM framing choices, which push those PCs into particular sorts of challenges, leads to the outcomes of play, and is arguably more diverse when PCs are built in different ways with different checks having different prospects of success.
I like the Cortex games as my second system of choice because that's what they're about. It's a skill-based system (not class-based), but has a lot more explicit metagame horse-trading between player and DM, and significant metagame mechanics integrated in.
It does not, however, use them to enforce a degree of sameness between disparate character concept.
The only Cortex game I know is Marvel Heroic RP. It has a uniform resolution and resource system for all players. I have found it is very common to see criticisms of MHRP from a process simulationist perspective that are very similar to criticisms of 4e D&D: that it's a dice-rolling game; that PCs are all the same; that there is no mechanical difference between different power sources; etc.
In both games the difference resides in the fiction, and the play that is engendered by the interaction between mechanics and fictional positioning.
On the framing side of things, one of the most distinctive features of Marvel Heroic, to my mind, is the Doom Pool: once a scene is framed, there is a clear mechanical upper limit on how hard it can get, because the introduction of new complications unrelated to a failed check by a player (such as reinforcements for the bad guys) requires Doom Pool expenditure. This gives a degree of metagame transparency to players that is even greater than 4e, which has clear level-relative DCs but no formal mechanical constraints on how the GM may evolve scenes. (And my players have frequently noted that one fact that affects their play is the knowledge that I like to evolve scenes as they unfold, to introduce new opponents or new complications.)
I think the main function of this sort of transparency and mechanical consraint is to give players confidence to mechanically engage scenes in a gung-ho fashion, and to reduce incentives to the turtling and caution that are the absolute enemy of "indie" play, but via techniques other than GM fiat. (Fail forward is obviously another part of this.)