Something esoteric I happened across this week that I thought was fascinating: in a book from 1968 (https://en.wikipedia.org/wiki/Man,_Play_and_Games), it's suggested that all forms of play combine 1 or more of 4 forms, each with names that sound like RPG stats:

Agon - Games where the players have equal chances and compete to win based on skill, strength, etc.

Alea - Games that depend on chance, like dice rolls, card draws, etc.

Mimicry - Roleplaying, storytelling etc.

Ilinx - Something like "physical disorientation", like swings, rollercoasters, skiing, etc.

It also defines games as fitting somewhere on an axis between "Ludus" and "Paidia", where Ludus has strictly-defined rules and Paidia is more spontaneous.

I'm not sure it really nails it - I feel like there are plenty of nuances that don't fit neatly into these categories, but it got me to thinking about where different games sit on the Ludus>Paidia axis and how they combine the 4 aspects.

For example, I don't like D&D so much, I like games like Dungeon World and Monster of the Week much better. On the Ludus>Paidia axis, D&D would be much more towards Ludus and maybe that's a simple explanation - there's a point on that axis that is ideal for me, while others have a different preference. I guess it's what's often referred to as "crunchiness" by a different name, but maybe the other 4 metrics offer a more interesting classification.

I'd say that D&D runs relatively high on Agon and Alea, with strictly-defined combat rules and a D20 offering a large random range, but Mimicry is somewhat incidental to the system. Meanwhile the "PBTA" genre of games is much lower on Agon, not really trying to offer strategic wargame combat, and I'd argue lower on Alea due to the narrower dice roll range of 2D6, but that makes much more room for Mimicry.

...and I'm wondering if LARP would qualify as including Ilinx if it involves physical combat.

Then there's video games, that typically combine Agon, Alea and Mimicry in one way or another, but I've wondered if physics-based games like Surgeon Simulator, QWOP, Human Fall Flat etc. would qualify as including an element of Ilinx (and if this is why I don't like them).

There isn't really a question here; although I'm tempted to try to create a numerical classification system, I can't think of solid metrics to classify against other than "vibes". It is interesting to think about where different games fall comparatively in these metrics, though. Was "Into The Breach" so popular because it provided pure Agon without the Alea? Are slot machines popular because they provide pure Alea (arguably with a side of Ilinx)? ...and then we're crossing into human psychology and asking why we enjoy these particular things.