You want theory?  I gots theory.  Three posts.

Let's start with a glossary of “Kinds of fun”.  It's not complete by any stretch, but here we go:

AGON is the thrill of winning against another person at the table. This is not quite the same as beating a challenge, or about winning against difficult odds; it’s about beating the other people at the table. It’s not the most common joy of RPGs - in fact, a lot of gamers want to avoid it, since problem agon is really, really bad stuff. But it does sneak in. When the GM takes on the role of adversary, playing not just to embody the challenge fairly, but in an attempt to whup the players, that’s agon. When a couple of players engage in creative one-upmanship, trying to spout the coolest thing (in theatre terms, trying to upstage each other rather than collaborate), that’s agon again. Agon can be good, but only if it’s acknowledged and used, rather than festering quietly.

ALEA is the gambler’s thrill - the fun of taking a big risk, the tension that comes with it, win or lose. Games with dice rolls, and especially ones where big stakes are riding on that one throw of the dice, are good at giving alea.

CATHARSIS is a feeling of release that follows an intense or overwhelming experience. Not necessarily a tragic or traumatic experience, but usually an emotional one. Catharsis is served best by very particular kinds of phrasing in play - notably, talking in the first person regarding your character is often deeply helpful.

CLOSURE is the feeling that there is nothing more that need be done, and that the thing is finished. Closure requires resolution to whatever the matter at hand may be. This goal isn’t especially tied to any of the modes, but does require that either the GM make the in-character goals and end points clear, or that they actively listen to the players (in a way that often has some features like slow-moving collaboration).

EXPRESSION is the simple desire to be creative at the table; expressive players often spend plenty of time on description, might draw the characters, might write seriousbackgrounds (though big backgrounds also mark Kenosis and Kairosis)

FIERO is the feeling of TRIUMPH, of winning, of defeating a challenge, or overcoming adversity. People looking for that feeling are on the lookout for adversity – and they tend to want adversity where they can be partisan for their characters and the GM is actually playing against them a bit. If it’s not a real challenge, with real dangers, then there’s no payoff for a fiero-chaser. If you’ve ever died again, and again, in a computer game, and then finally manage to succeed, and felt a rush where you could stand on your chair and scream? That’s fiero.

HUMOUR… Games can be played for laughs, and often are. A player that really pushes for humour will often end up pushing for collaboration, even to the point of attempting to dictate the actions of other player characters, because some of the humor that comes to mind most easily can step outside the specific ideas of “who is in charge of what" often setups lay down.

KAIROSIS is the feeling that of fulfillment that comes when an arc of fictional development completes – a character is tested and changes, a situation grows more complex, and is then resolved, and so on. Actively seeking kairosis often means authoring, though it may only be authoring certain details relevant to you (revealing yourself from stunt-level disguise in Spirit Of The Century, picking out character developments from Fallout in Dogs in the Vineyard). If you find yourself saying "that was a good ending to that bit", you're probably experiencing Kairosis.

KENOSIS is the feeling of being deeply engaged in their character or in the fiction as a whole; it’s one version of “immersion”. Players looking for this (especially really serious kinds) often aim for a lot of characterisation. They also often (but not always) want to avoid types of collaboration that will pull them “out of the groove”. Serious kenosis is one of many “flow states” that goes on in tabletop gaming.

KINESIS is tactile fun. Miniatures, maps, game book illustration, tokens, and dice are all visual and tactile things that are enjoyable about RPGs. I haven’t yet met anyone that considers these things their number one priority, but it ranks in the top five things for quite a few.

LUDUS is for people who take their rules seriously. The tinkerers and the optimal builders are chasing this kind of fun. To someone looking for ludus fun, the rules are the game, a toy that the group is here to play with. Wherever the mechanics of the game are, whatever modes they attach to, that’s where ludus-seekers go. In order to support ludus, there needs to be enough complexity in the rules to allow someone to actually spend time exploring and playing with them as something interesting in their own right. D&D and Exalted both tend to satisfy ludus-oriented players.

NACHES is the enjoyment of seeing someone that you have taught, or are responsible for, go on to do well with that knowledge. If there’s a player at your table who is always happy to teach the others about how things work, chances are they like their naches. Many GMs, unsurprisingly, get a lot of good naches and enjoy it. Some players can get this same kind of enjoyment from seeing a student or smaller ally of their character do well.

PAIDIA fun is free-wheeling player fun, where rules are a convenience. Players looking to get some Paidial fun would prefer winging the rules-calls, going for whatever feels right at the moment. If there are involved adversity-resolving rules, Paidial players avoid adversity. Novelty and wonder are often, but not always, associated with this goal. Goofy characters are sometimes signals that someone wants this kind of fun.

SCHADENFREUDE is delight in the suffering of another - the thrill of seeing the villain get what they deserve is a pretty common expression. A game session can only provide this really well if it has characters that players “love to hate” and whom they inflict real damage (not necessarily physical) on without serious guilt.

SOCIABILITY is pretty central. For most gamers, the game and the acts that make up “playing the game” are a way of being social (for others, the event is also – or only – an excuse for being social outside of play). People looking to get especially significant gameplay-as-socialisation often try to match their other goals with the rest of the group, but do want to chat in general –if they aren’t engaging in characterisation, they will often enjoy general table talk.

VENTING is, simply, the desire to work out player frustrations or other emotions, using the game as a means. After a rough day working, smacking the hell out of some monsters can be pretty enjoyable.

Post numbah 2.   Now, let's talk about supporting those kinds of fun.

SUPPORTING: ALEA

Alea, the thrill of gambling, is supported in games by random elements that create and release tension.

Therefore, to support Alea, a game need tense moments, resolved randomly - which is a little more complex than just “has random”.

Critical hits that one-shot an enemy aren't typically sources of Alea unless the combat itself already had tension (but if it did, they're jackpots). Save-or-die is strong Alea, because tension.

Swingy one-die systems support more Alea, but often less Ludus; if the stats matter less, you can't satisfy the desire to work the rules. Dice that give a low-random probability curve go the other way.

Which is not to say a system can't do both. Texas Hold'em is strong both ways; the dice in Dogs in the Vineyard can be, too (though not as heavily).

Heavy Alea goes well with heavy Paida; a lot of old school play is high-random goofing around, with loads of character death on a lost roll. This style leaves little room for Kairosis and Kenosis, however, though it can absolutely do one strain of Catharsis in the form of “Holy crap we survived”. 

SUPPORTING: LUDUS

The rulesy fun of Ludus is often most strongly served by, unsuprisingly, games with big sets of rules and interesting tactical choices. Pathfinder, Exalted, and so on.

Ludus is also often provided in the form of “lonely fun”; building characters and talking optimization has no shortage of it.

However, at the table, high-ludus play can get a bad run in traditional games. If not all players are on board, they can feel dragged in and bored. Worse, if a Ludus-seeking player has significant system mastery and aren't paying attention to other people's fun, they can pull the whole game focus into being on their thing… And because it IS a game, with rules, this seems reasonable.

Traditional games are chronically bad at handling these issues, but some solutions exist. Paranoia demands that you never show any knowledge of the rules, you traitor. Old School play often quashes the time it can occupy by emphasizing rulings as needed. Many games have aimed to give Ludic (and Agonic) play a specific domain in combat, sometimes to an extent that alienates some (D&D 4th comes to mind). And, of course, some games just don't support Ludus much at all, having lighter or non-tactical rules.

Less traditional games, aiming to align the rules with the focus of play, go all over the place in terms of Ludus. Some deliver, some don't, some are resistant to “Ludus seeker can screw it up”, while others are even more vulnerable to it (and more insufferable when it happens). 

SUPPORTING: KAIROSIS

Kairosis is the satisfaction of ‘literary fulfillment’, of a narrative arc working out nicely around a character or group of characters, often including characters changing and growing (in sympathetic, often emotive ways, more than in level-up ways). There are a number of ways RPGs can serve up Kairosis, which include:

Traditional gaming often has GMs built a loose campaign structure, often centered on a major villain or threat, thereby creating a plot ahead of time. There are reams of critical talk surrounding how much structure is too much, in terms of “railroading” and the like, and how much pre-planning is just good situation building. Some Kairosis-seekers find their fun spoiled by knowing the story is largely prewritten; others don’t.

Traditional gaming also often assumes the GM will use their authority to bend things towards satisfying conclusions in one way or another (White Wolf especially did this). Again, this approach has significant critical talk about whether the GM should cheat, about making player choices illusions in the service of sneakily pacing the story, and so on. And again, some Kairosis-seekers find that this spoils their fun, while others don’t.

Less traditional games often aim to build naturally-occurring emergent narrative into the game, cutting down pre-planning and GM-driven story-making. These are replaced by mechanics that drive character arcs, or attempts to load up situations with things to resolve that will theoretically create story arcs however the players choose to go. Kickers in Sorcerer are a naked example of the first; town creation in Dogs in the Vineyard and clear example of the second. Countdown clocks in Apocalypse world are a weaker, more sandboxy version of the second, as well (and the exhortation to “play to find out” is a hard shove away from pre-plotting).

Kairosis is also linked to some experiences of ‘immersive’ play, where the player wants to vicariously experience meaningful moments of development for/as their character. When this is the case, any meta-mechanics that aren’t linked directly to the fiction (countdown clocks that measure something other than actual in-fiction time, for example) can break the vicarious experience and thus ruin the Kairosis. 

SUPPORTING: AGON AND FIERO

Fiero is the feeling of triumph, of overcoming adversity, requires a sense of opposition. If there's no opposition and no risk of loss, there's no Fiero.

Agon, meanwhile, is the competitive thrill of one-upping another player. If there's no competition (and opposition counts), then there's no Agon.

Obviously, these two kinds of fun overlap in many games, but just to keep them sorted: Gimli and Legolas have Agonic fun with each other while killing Orcs while getting Fiero from the Orcs. To a player in a battle royale, on the other hand, Agon is build-up, and Fiero is payoff.

Relatively few tabletop RPGs pit players with equal resources against each other in serious Agon (though there are a handful). Most instead look to the GM (a quite unequal player) to set up challenging scenarios, and take on a semi-Agonic role temporarily during their execution (which is typically combat). While this damps down the Agon, many traditional games also bring in plenty of interesting rules tied to it, allowing a good bit of Ludic fun in with the weaker Agon. Additionally, many games paint combat adversaries as irredeemably awful, which gives the delivered Fiero a nice touch of Schadenfreude to go along with it.

The traditional complex of good stuff served up can also pitch a long grind of semi-Agonic material (often in the form of a dungeon). This can deliver Catharsis (as in, whew, that was a hell of a thing). 

SUPPORTING: HUMOUR AND PAIDIA

Humour and Paidia are another linked set, just as Agon and Fiero.

An improv group that's working off each other is pursuing (and achieving) Paidia - and is fairly likely being humorous as well. A jazz group that's jamming is getting Paidia, but not Humour. A comedian doing a well-rehearsed set is dishing out Humour but not engaging in Paidia at all.

Rigid, comprehensive rules and strong Paidia-seeking don't generally mingle well; if you can't improvise with the rules, you can't chase Paidia in them… Which means Paida-seeking players can feel let down when mechanics are engaged.

Humour can be split up a lot of ways; some is in-character, some in-fiction in other ways, and some just social at the table. That said, the division I’ve found most useful is to split in-fiction Humour between what emerges naturally from Paidia in play, and deliberate jokes.

This division is because when there's a problem with humour (other than the group just going off track socially), it's often because deliberate jokes in the fiction are risky. Such deliberate jokes can easily push play towards silliness - and specifically, silliness that nobody will further engage, and which requires added suspension of disbelief and the like to deal with. Really silly character names, for example. Such jokes are a drag on the group; one or two laughs, and then carry that thing around as dead weight anytime it comes up. That's fine for cartoon-level comedy, where you can always flog it some more, but it’s much less so for many other games, interfering with seeking other kinds of good stuff. 

SUPPORTING: SOCIAL FLOW

Socializing and some degree of creative Expression are going to happen in and around an RPG by default. Beyond the obvious need to have a group that can function socially, the heaviest concern with these things is what form of Kenosis they support (if any). This is also a concern in term of Ludus and other bits, but it's especially easy to describe here.

Kenosis, as a flow state, comes in two main flavours - deep engagement with fiction, and deep engagement with character. Other possible flow states exist (from Paida, Ludus, and mixes of other things) as well, but pay off other ways.

Deep engagement with either fiction or character require that one can maintain that engagement. That is, if the play pushes regularly for full mental engagement with something else, it'll break… and if the creative expression and socializing at the table don't match it, it'll break.

Which leads back to this: During play, are players primarily expressing themselves and socializing around the game, through the procedures of the game, or as their characters? Do the rules pull them to a specific “voice” that they then hang around in? 

SUPPORTING: ENDINGS

Closure, Catharsis, and Schadenfreude are notable in that they all usually depend on some form of ending - and most of the ways that Venting is offered up employ them as well. 

The traditional structure incorporating all of these is the campaign villain and their disposable henchthings, with rising action - however, this is common to the extent that laziness in presentation and tropes can make the whole thing feel “stock”, cheapening the whole bundle.

Notable on the front of bad tropes - “The villain escapes again” can act as a cheat on the bundle just as easily, offering up this stuff and then snatching it away. Escapes when the players aren't actually invested in that villain are fine, but once they're out for blood…

Outside the bundled complex, even harder Catharsis is often hit through intensity of emotive play. Bluebeard's Bride is a Catharsis engine, among other things.

Post numbah 3.  

AAAAAAAAND FINALLY: PLAYSTYLES

So, as a quick review of the previous bits:
~ There are loads of kinds of fun.
~ Each has requirements to happen.
~ They often cluster up.
~ They are not all compatible in all forms.

Okay, so, Playstyles! A playstyle is the body of mechanics and techniques a group uses to pursue a particular bundle of good things. Every group playstyle is unique, group playstyles change over time, and a group's playstyle changes to some extent, by definition, when they change games (though they often carry over things they find “core” to their overall meta-style).

A playstyle can be dysfunctional, trying to serve contradictory things - but very few stay that way for long. Either the group falls apart, they drop one of the conflicting pursuits, or they cobble together some solution.

Whew!

Happily, playstyles also tend to cluster up, forming identifiable types. Some of those clusters have semi-common big heavy names already, like “Narrativism” and “Immersionism” and so on… which I'm going alter slightly before using here, to demarcate them so you can say things like “Your narrative playstyle cluster isn't really Narrativism” if you want to.

Here's a quick list of seven clusters that many individual playstyles fall into one (or more) of. This is not a comprehensive list:

...

Narrative playstyles focus on providing Kairosis, Expression, and fiction-engaged Kenosis. Sorcerer is an example of a game which drives and supports a group of playstyles in this cluster.

Tactical playstyles focus on the cluster of Ludus, Agon, Fiero, and Venting. D&D 4th edition is a game that drives and supports a group of playstyles in this cluster.

Immersive playstyles focus on character-engaged Kenosis; most immersive playstyles also have features that tie them to some other cluster, but will rarely connect to heavy Ludus or fiction-engaged Kenosis; there's conflict there. Game systems that support this style are ones that the group doesn't need to heavily engage mentally; they are “in the background”.

Improvisational playstyles are high Paida, high Expression, and a grab bag of other things (humour is common but not critical). Baron Munchausen is improvsational-supporting; Theatrix certainly wanted to be.

Classical playstyles (distinct here from traditional, below) have high Alea, Catharsis of the “Wow, we lived” variety, and a toned-down version of the tactical set that's less Ludus-centric. Early D&D dungeon crawls, full of save-or-die and the like, drive classical playstyles.

Traditional playstyles are those that attempt to pile in as many of the good bits as possible, with no absolute focus, and often aim to do so as efficiently as possible. Most traditional games can support styles in this vein.

Affective playstyles aim for, in order, emotional Catharsis, character-engaged Kenosis, and Kairosis. Colloquially, these are supported and driven by indie “feelings and index cards” games. 

This is definitely an interesting model to look at game design from! I can definitely see some value in looking specifically at the end user experience, even if I don't believe that to be the be all, end all. It can absolutely be a lens to use amongst many when examining a design.