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

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.)

Time

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.

Non-trivial Symmetries

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.

Relative Size

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. A good example of this would be in GURPS (at least with RAW, there are official-unofficial addendums 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. In this case all the rules still work mechanically, but they fail logically.

I don't know of any system that fully exhibits this symmetry. GURPS tries, but in some places the asymmetries cause strange problems. On the other hand, D&D makes very little effort to be symmetrical with respect to size.

Relative Attributes

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.

Unusual Symmetries

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.

Body Plans

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.)