One of my kids likes to play imagination games - she and her friends all pretend to be other people (often superheroes) and do exciting and interesting things.
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In summary: on this account, the function of RPG rules is to help mediate and constrain the process of agreeing on the shared fiction; and not just by assigning authority ("It's your turn now to say what happens next") but by shaping what is said so that it is surprising and even unwelcome to all participants.
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There are probably other reasons too why RPGs have rules, other things that those rules can do.
For experienced GMs, some rules are meant to be broken. As an author of an entire RPG game, we've made sure that anyone running/playing our game knows that the rules are necessary for
fairness and balance of power among all callings/vocations/races and NPCs, but they are merely our suggested guidelines. The rules that we settled upon (after 15 years of game testing) and published in our rulebooks are just the ones we thought worked best with the system as a whole. To drive this home, we've included certain HARD CORE rules that GMs can include for their players. These Hard Core rules make GMing a little more challenging but also give the Players a heightened game play experience. But the game runs fine and swiftly without them (when I run the game, I include most of the HC rules, but then again, I wrote the game, so they are second nature to me, lol).
Example: In the game, a person can Travel (using a spell) to any place s/he's seen at least once. But a HC rule would be to require an Accuracy roll unless a memorized slot was used for that destination. This places more "balance" on the game, such that a Player just can't be a genius and basically remember every single location they've ever seen well enough to Travel there. But at the same time, the HC Rule is optional (as is any other rule) if the GM doesn't want to have to bother with that level of scrutiny in the game. But no matter what, the GM must, MUST, remain consistent as to the rules s/he is GMing by.
Incidentally, that particular Travel HC Rule originated in my mind when running Planescape (oh, about 25 years ago). People needed to have BEEN to the Plane (or Dimension) they wanted to return to, I believe the rules were at the time -- ugh it's been too long. But I wanted the Players to have a little more freedom for their missteps (so to speak), so as long as they've seen the Plane (as in a Divination bowl), they could go there. Or something like that. But I know I changed some rule in Planescape regarding that, lol.
Anyway, bottom line: Why Rules?: [1] They define the game system (and some systems ARE better than others); [2] they attempt to establish a baseline of FAIRNESS between players, and also for the GM's personalities; [3] they are ultimately necessary for an inexperienced GM, but mere (if strong)
suggestions for the most experienced Storytellers/GMs.
Finally, (if anyone's read this far, lol -- I try to keep it entertaining), I'd like to opine that not all rule changes in newer and newer editions are for the best. One of the reasons we wrote and published our own game was because D&D started watering down the rules (obviously targeting a younger, less experienced in Role-Play, audience). In the latest editions, you can have a character in 30 seconds and rejoin the battle, replacing the character you just lost. Well, that's great for hack 'n slash. But we older RPG'ers very much more enjoy the development over time of a Character (PC) with the challenge of making them Great (in spite of their flaws and challenges), and so we like to put some time (at least an hour!) into our character generation, tweaking everything we can, bringing food to the GM to bribe him/her for that extra 5% on the roll for Royalty or Ambidextrous traits, har har. And then, once we've poured parts of our souls into the character (alternate selves, to be sure), we set out to make them legendary heroes with GREAT stories.