RPG System Symmetries
This page is a description of desired symmetries in an RPG system. In this sense, a symmetry is a transformation of the game world or characters that has no effect on the rules used to describe them. Any help in expanding these lists, including examples of systems that do and do not exhibit these symmetries would be appreciated.
Trivial symmetries are those that are so obvious they're not really worth mentioning. A couple will be listed as examples though, and the category might be of interest for those looking for ways of making their system particularly strange. I know of no current systems that do not exhibit these symmetries. (These also tend to be symmetries that exist in the real world.)
Frames of reference
Systems should not change between different frames of reference with the same overall acceleration. That is, nothing mechanical should change between the frame of reference inside a moving train (on a straight level track) and the frame of reference inside a stopped train. (Note that a stopping train has a different acceleration to the other two.)
Systems should not change between two moments in time. That is, anything that works mechanically now, should work the same in any other time, assuming the situation was otherwise identical.
These are the symmetries that not every system deals with, but that they should really consider looking into. Such situations tend to come up eventually, and a system that lacks one of these symmetries can cause problems as people may assume things will or should work in different ways.
Systems should work the same if everything were shrunk or expanded uniformly. This should apply without having to change the absolute reference of the size scale. That is, if everything were shrunk by some percentage, you shouldn't have to redefine an inch just to make the system work. This doesn't mean that other absolute values related to size wouldn't change, but that all the rules still work the same just with the new stats.
The distinction between the rules changing and the stats changing isn't entirely clear. Sometimes the rules may be consistant mechanically, yet fail logically. An example of this would be in GURPS (at least with RAW, there are official-unofficial addenda for a few of these). Two ants would have a large, negative size modifier, which would apply as a penalty on their chance to hit each other. This means that the two basically have no chance to hit each other.
A more successful implementation of this symmetry can be found in the scaling rules from Mekton Zeta, and more fully realized in its advanced technical supplement, Mekton Zeta Plus. It presents a series of scales: Human (1/10 scale, for people and personal equipment), Roadstriker (1/5 scale, for Powersuits and small vehicles), Mekton (1/1 scale for most mecha, large vehicles, small structures), Corvette (10/1 huge mecha or vehicles, buildings, small ships), Starship (100/1 scale for capital ships, fortresses, and similar), and Excessive (no specific scale factor, reserved for relative comparisons among colossi such as the Death Star, the Midgard Serpent, Ego the Living Planet, the Zentraedi Base Station, or similar titans). Guidelines are also presented for defining custom scales, for example: 1/20 Pet scale, 1/100 Pest scale, or 1000/1 City scale could all be easily implemented.
Within the MZ+ scale framework, qualities such as height, weight, cost, range, and damage capacity all vary in one way or another with respect to scale, but things like to-hit rolls within a common scale are not effected. Only when differently scaled actors come into direct conflict do modifiers to action rolls appear. Off-scale components are also possible, such as a strike-fighter with anti-ship torpedoes or a battleship with anti-aircraft guns. The symmetry is not quite absolute, as special rules come in to play at Starship scale for crew actions and disabling ships' systems, and slightly different damage methods are used at Human scale for compatibility with other Interlock-system games (Cyberpunk 2020, et al).
I don't know of any system that fully exhibits this symmetry. Mekton Zeta largely succeeds, despite some inconsistencies and overlap potential here and there. GURPS tries, but in some places the asymmetries cause strange problems that require hand-waving on the part of the GM. In contrast, D&D has traditionally made only token efforts to be symmetrical with respect to size, giving rise to humorous situations where weasels or domestic cats may be more effective combatants than some low-level characters.
In systems that define contested actions, characters with the same relative skill should have the same chances against each other. Note that relative in this case could refer to either a linear scale, a logarithmic scale or any other appropriate scale. So for one system, characters with +10 skill should always have a 90/10 chance, while in another system characters with x2 skill should always have a 75/25 chance. The important point is that this holds for some consistent scale.
Most systems are good about this as it's usually a prominent design decision that's fixed early on.
This can be extended to a broader range of results than just success/failure, though that may not always be appropriate. (Imagine the outcomes of a contest of strength between two regular guys and between two copies of the Hulk. Success/failure rates may be the same, but critical rates may not be.)
NPC vs PC
Systems should have no mechanical differences between a player character and a non-player character. For the purposes of this discussion, it's only important that NPCs could be dealt with the same way as PCs. Extra rules to speed up one-vs-group combat, for example, wouldn't count against it.
This symmetry is purposely broken in some games to create a cinematic mood. Effectively the system provides rules to limit resources to some NPC's, typically called "mooks" and give an easier opponent for PC's to interact with.
That is, using the same mechanics to describe different kinds of activities and conflicts. It's not as easy as rolling d20 (or 3d6, or pool of d10s, or whatever) for everything - it's also about similar granularity, similar relation to character's stats, etc. If a game uses a map, describes attacks and counts HPs in combat while it resolves social conflicts with a single roll (or a few rolls, counting successes), it does not have a resolution system symmetry.
No game I know of fully exhibits this symmetry, though most games try.
These are further symmetries that some systems may exhibit, but that aren't likely to come up very often, exept perhaps in a game designed to take advantage of such a symmetry.
Symmetry with respect to body plans would imply that as far as the system is concerned a limb is a limb, and there are unified rules for dealing with characters with arbitrary body plans. This also means that while a humanoid body plan should also work, it shouldn't be the default with everything else being exceptions.
D&D pretty much ignores body plans except for granting extra attacks and a few other occasional details. GURPS tries to deal with this, but it's done as a series of exceptions to the humanoid standard. (Not to say that there's anything necessarily wrong with either approach. That's why this is under the unusual symmetries.)
A game has this kind of symmetry if all situations that cannot be distinguished by observations in-game are identical in game mechanics. Things like deterministic durations that cannot be measured in game (no observation may tell an effect that will be active a few more hours from one that will end in minutes), HPs that do not describe real wounds and fatigue or clearly meta-game resources break this symmetry.
This symmetry is only borderline unusual. Most games would exhibit traces of this without having been designed to do so. What makes it unusual is that few, if any, games were designed with this in mind as breaking this symmetry can make some design decisions much simpler.