I am in Symmetry

KateMaxPaint, DeviantArt

Symmetry is one of the rarely-referenced parts of TTRPG Design. You'll hear about balance the most - that is, how the choices made for player characters compare to each other. Symmetry, in this context, is how the system looks from either side of the table - from the players' perspective and from the gamemasters' perspective. This is before anyone has sat down at the table (literal or virtual), before the characters are created. It's not something that can be easily fixed by any one group or table, because it's a series of assumptions baked into the design of the system at it's core.

A Symmetrical system is one where the players and game master are governed by the same collection of assumptions. This isn't specifically about the resolution system (in most cases, that's going to be relatively the same across the board) but about how the people playing the game relate to the game itself. The most stark example of this, to me, is "3.P" - that is, the blend of D&D 3 & "3.5", and the Pathfinder 1e offshoot of that system.

In Symmetrical systems, everyone is approaching things the exact same way. When a player creates a character, they do the normal character creation things in a D&D-like: create stats, select things like class, race, background, class features, feats, spells, and equipment. That's a well known setup. The Game Master, when they're creating a non-player character, does the exact same thing. This seems relatively straightforward, and almost common sense. The problem lies in the imbalance of work between those two people. A player creates a character slightly more than once per game, on average - maybe slightly more in a particularly lethal system or unlucky streak. The GM, however, is populating the rest of the 'world' those PCs are playing in - each bandit, each beast, each guard, everybody. That's where the system breaks down... Where you have each minion, lieutenant and wandering monster that has a complete stat block, complete with feat chains, equipment, spells (or supernatural abilities) and maybe even class levels.

Example NPC from Technoir

This problem is then multiplied beyond belief because of the sheer amount of content that was created for the system. There were so many supplements and additional texts for these games (that didn't all communicate with each other, as there were multiple different publishers) that the norm for players to be limited to two core books and only one supplement... But no such limit for the GMs, which had an ever-expanding library in which to draw from.

Having Symmetry isn't a D&D exclusive thing, either. The World of Darkness games, Technoir, and several of the d100 games are all symmetrical. 

So what does an Asymmetrical system entail? That would be one where the system works differently for the GM then for the player.  My favorite example for this is the Cypher System. Also a d20 system, Cypher doesn't have the GM roll dice at all - when the players engage with the world, they roll to effect it; when the world effects the player characters, those PCs roll to evade or otherwise endure it. Because of this, they're created in completely different ways. Each Player Character has 3 pools to represent their stats, but each monster or non-player character is mostly contained in a single number. This creature is a level 4 character, so to hit it, you need to roll at or above a 12 (as everything in Cypher is in sets of 3); to find it when it's hiding, roll a 12; if it's attacking you, you have to roll a 12 to get out of the way. There's a bit more to it than that - you might have a particularly stealthy creature that is a step up in difficulty if it's sneaking, or a particularly large, powerful creature that counts as a lower level when being attacked, because they're so big.

Blades in the Dark SRD

This type of resolution system is very common in the more narrative-focused games. The Powered By the Apocalypse (PbtA) and Blades in the Dark (BitD) systems are probably the most well-known of this type of game. The resolution system of those includes degrees of success, and the GM makes their "move" when the dice say that they fail. There are some systems that are somewhat asymmetrical, like the relatively new Daggerheart - the players have relatively complex setups and use a 2d12+mod roll-over system, while the GM uses more simplified stats and a d20+mod roll-over. 

The benefits of an Asymmetrical system is that by simplifying some of the game, that frees up the GM to focus on other parts of the game. It also speeds up the game - There is no "mother may I" back and forth with the GM. That is the "Roll, Add, Declare Total to GM, GM says yes or no, React" flow that trad-RPGs are built around. Rolling an Asymmetrical System means whoever is rolling can look down and instantly know exactly where they land.

Between the two, I am 100% going to make this system asymmetrical.