Seems like many people have been reading Jon Peterson's The Elusive Shift. And that's great - the more people realize how many arguments and design considerations relating to role-playing games are just as old school as "old school", the faster we can all discuss these matters more productively now, fifty years later.
One recent blog post took a main question from discussions in fanzines, APAs, and magazines of the '70s, on the distinction between role-playing and roll-playing: that is, whether to play your character to best emulate how it would act in any given situation, or whether to play it to win - the battle, the war, the contest, treasure, whatever is achievable. The rest of that post tries to apply game theory to the question of whether to role-play or to roll-play. And I do like the idea of looking at role-playing games from the perspective of probability and decision-making, which make up game theory: one of my first posts was about the Monty Hall problem, and I've written a series of posts about the character sheet game framework, which is my attempt to condense the most mechanical and strategy-based portions of a role-playing game into a form amenable to analysis by tools from strategy game design and theory. However, I must take exception to the very framing of this problem, because as it stands, I think it's a false dichotomy.
Let me explain with an example from your favorite edition of Dungeons & Dragons. It's a class-based system, which originally supported three classes: the fighting man, the magic user, and the cleric. This did not capture every type of character anyone would want to play, so people homebrewed their own classes or variants - that's where the thief class came from.
Now you, having access to either the homebrew version of the thief, or a more official form of thief or rogue from later supplements or editions, decide to create or manage to generate such a character. The character, per the rules, is very good at sneaking around, picking locks, disarming traps, climbing sheer walls, and other such dubious activities. It is not very good at fighting directly, or at taking a lot of physical punishment. So if you decide to play this character as someone sneaky and devious, who likes to pick locks, disarm traps, and stab enemies in the back from hiding, it works. The rules encourage you, the dungeon master has an easy time setting up challenges for you, and you contribute appropriately to a team of adventurers who are also playing to their niches.
On the other hand, if you decide, with this class, that you want to play a brave warrior who charges into battle, sword drawn, you will have a harder time succeeding at the mechanical challenges. You will not hit as much as a fighter would, you will not cause as much damage, you might not even be able to use the best weapons for the job, and so you may easily find yourself killed and forced to create a new character, or you may hope to be saved by the other players` characters, or by DM fiat. Why is that? It's because you chose the wrong mechanical archetype to go with your character concept.
You may counter that you're trying to challenge yourself, that real role-playing is playing against mechanical advantage, that focusing on mechanical advantage is roll-playing, and that a good DM or GM should be able to accommodate that. Well, to that I would say that you have made a role-playing decision by choosing both this class, and this behavior that is at odds with it. So the holistic concept is what we should interrogate. Why is it important for you that your character mechanically be a sneaky thief, but have the behavior of someone who insists on charging into the fray? Is this character trying to fight its natural or trained affinity to sneaking around? That's an internal struggle it has with itself. And there are role-playing game systems where that kind of struggle can be rewarded mechanically.
Let's say that instead of using D&D, you decided to play a fantasy FATE game. You want to create this holistic concept of a sneaky conniver, who is nevertheless driven to be a strong hero, a Gray Mouser who dreams of being a Fafhrd. You could choose what is called an aspect to capture this: "a scoundrel too combative for their own good". Aspects in FATE are used in two ways: the player can invoke them to gain some kind of advantage, spending a Fate point; and another player or the gamemaster can "compel" them from the character, forcing a disadvantageous decision that is in line with them. In the latter case, either the player resists this by spending a Fate point, or they can accept it, and gain a Fate point for use later. This is why the rulebook recommends choosing aspects that are two-sided - that combine the positive with the negative - and "a scoundrel too combative for their own good" is a perfect example of that. Let's try it out!
You and your party want to steal a big diamond from the Duke's mansion. You're a scoundrel, which allows you to spend a Fate point to give you a bonus for rolling to come up with a sneaky plan to get in there, and the roll comes out very well. The plan is set in motion, and it's proceeding like clockwork - a big distraction draws most of the guards to the front gate, and you're sneaking 'round the back. There are only two guards there, and the plan calls for you to throw a rock to their left, then use a well-positioned tree to drop in behind the wall to their right. But before you can do that, the GM compels you: "now that you see the guards up close, they don't look so tough. You feel like you could just take them there and then." If you accept the compel, you gain a Fate point. If you don't, then you need to spend a Fate point, which will allow you to proceed with your plan. By penalizing you for sticking to the optimal fictional choice, while rewarding you for accepting a less promising one, the mechanics incentivize you to play into this dual aspect of your character: a competent scoundrel who nevertheless can't stop themselves from getting into fights. To get to the position where you have the Fate point needed to avoid this hiccup, you would have had to surrender to this or another compel earlier, or not to have expended the ones you start a scene with; meanwhile, this extra Fate point you get from leaning into the negative side of this aspect of your character now can be used to improve the situation later, either by making it easier for you to do something, by sacrificing this point so that you can avoid being compelled by your weakness at a more critical juncture, or otherwise to improve the prospects of the whole plan, and the overall success of the party's mission.
If you had instead been playing a thief in D&D, mechanically this would have been a problem. You would have probably failed in the combat against the two stronger, more able guards, and if nothing else, at least one of them would have been able to raise the alarm, and none of that would have intrinsically involved any advantage to you or your party, equivalent to a Fate point.
Now we come to what I think is a better question than role- vs. roll-playing, which is an issue of taste, and possibly of human psychology: does the fact that there's an extrinsic, mechanical incentive help you or hinder you from role-playing your character? Do you get what you get out of role-playing by roll-playing to this mechanic, or not? Does it instead make role-playing less compelling for you, because it overrides an intrinsic motivation you previously had for role-playing?
And how does this affect the rest of the participants in the game? If you get the same joy out of role-playing along with the mechanical incentives, this means that you can peacefully co-exist with players who are more interested in making the best of the mechanics of the system. And the GM also has an easier time, because they don't have to negotiate some kind of fudging, or fiat, or other ad-hoc methods to make sure that everything keeps merrily moving along. Instead of having to work both on preparing and running the system, as well as on intervening extra-mechanically, to avoid letting your role-playing against the mechanics interfere with the enjoyment of the roll-players, everyone can play the same game, even though they might not be playing it for the same reasons.
Finally, in addition to the question of whether this will satisfy people who are looking for role-playing, we can ask what type of system encourages people who start out thinking as roll-players to move towards role-playing, and whether that's a worthwhile goal. When introducing role-playing games to new players, this pedagogical consideration can be crucial. I have personally found that the game that most encouraged me to play in character is by some accounts (including its current marketing copy) not really a role-playing game at all, but a story-telling game: Fiasco. Despite the fact that the mechanics barely have anything to do with playing roles in themselves, as they do not correspond to adjudicating actions that would make sense to the character itself in the world, the very framing encourages you to lean into the character you play as it interacts with the characters played by others.
It is important to remember that systems are designed by people to serve functions. They are not necessarily modeling a situation that people will encounter, which is where a game-theoretic analysis would be most appropriate, to tease out how to look at a given situation as a rational actor. They can instead model genre conventions, or they can be built to encourage and reward certain behaviors, reducing and even eliminating the tension between playing to win and playing to a role.