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