Filling Out Factions With Combinatorics And Colour

One of the three most important codified innovations of game design in Magic: The Gathering is the colour wheel system. It’s not that this is the first card game ever to have factions (after all, what are suits, really), but of having an uneven number of factions, who match up with one another in terms of alliances and opposition. It’s a prime number, so there’s no even way to divide them up to create coalitions, everyone works together and against one another, and also, notably, it gives players an immediate philosophical flavour onramp saying hey, does this work for you, and then you can act on that. They are five essential operating vibes.

A lesson you can use from the Magic: The Gathering colour wheel, and which you can use in your own worldbuilding or game design is creating matrices of combinatorics. Or rather, you can give your players colours to fly.

If you’re following this blog for my worldbuilding, I’m going to talk a little bit about it but not about the specifics and more about the tools I use to create negative space. It’s generally applicable, though, I don’t intend to make this homework that requires you to know my other stuff already.

Okay, look so you want to give players a place or an idea to belong to in your game. You may have a very limited number of ways to do that, a very specific set of choices – Magic The Gathering starts out with five factions at base, and a lot of game design can run just fine with only two factions. Letters from Whitechapel, for example, gives players two choices; either Jack the Ripper, or the London Police, which are between them probably equally likely to kill sex workers. That’s a pretty easy faction structure to work with for getting buy-in, but also the flavour you give each faction changes the tone of the game. Consider the game Letters from Whitechapel, but instead of chasing Jack the Ripper as he leaves grisly trophies around London, you’re a bunch of vigilantes pursuing Christopher Skase in Majorca –

What do you mean not even other Australians get that reference.


What if you’re a bunch of black suited government agents, trying to track down a lone hacker, a crimew or a Edward Snowden? Suddenly you’ve got a different vibe on the villains or the heroes of the piece. What if instead of murder it was about theft? A cool sneaking stealthy thief opposing private security? I’m not talking about changing the mechanics of the game, here, not the way the system entangles you, but just changing the fiction.

(And if you think ‘well, changing the flavour doesn’t change the rules, you might be surprised.)

That’s a pair of factions. As you add more factions it gets more complicated, and I recommend, in general, trying to have a prime number of factions if you want them to be mechanically distinct from one another. It discourages perfect symmetry and makes it harder for players to naturally assume they know what every faction does when they engage with one faction. What though, if you want to make a lot of factions. Like Wargame factions. Like RPG Setting lot of factions.

This is where I recommend you start with signifiers and combinatorics. Signifiers can be things like values or ideologies, like the Magic: The Gathering colour wheel presents its colours, but they can also be colours. They can just be colours!

What you want to do is make a list of your signifiers. Let’s use The Locked Tomb as an example so it’s not so obviously self-indulgent. In the setting of The Locked Tomb you have nine houses, which represent different kinds of necromantic magic and also other things, but if you start from the position that (as they are revealed to you in the first book by a semi-ignorant viewer) the 9th house does bones and all houses do something necromantic, you wind up with a list that looks a bit like:

  • Absoring life energy from the living
  • Absorbing death energy from the dead
  • Blowing up corpses
  • Talking to ghosts
  • Connecting ghosts to their history
  • Preservation of death and souls, halting death
  • Soul siphoning, doing something weird with souls as they’re alive
  • Bones, Motherfucker

You notice pairs there too – life energy from the living, death energy from the dead – and there’s obviously a reason to only go up to nine houses; there’s also only eight things there, because one of the houses is completely absent. But these signifiers let you create effectively eight different methods within the category of necromancers, even if there are things that each do better, more specifically.

That’s an example of what you can get to when you start with a number of slots, and have a linking thematic space for them. I can easily imagine ways to bring this number of slots up or down depending on what the story needed, but The Locked Tomb has its nine houses (hence ‘Gideon The Ninth‘). Each of these are used in the story in different ways, and, if you’re at all familiar with fandom, quietly present people with ways to create OCs.

What if you have some factions in mind, know you need more, want more, but can’t quite think of how to start? Well, you can work on the way I handled things with the factions in Cobrin’Seil. This D&D setting is meant to represent a large world, a world big enough to have adventure happening all over it, with cities and countries and factional divisions. When I approach something so big, I struggle, because I am always afraid of thinking too small, of creating a small amount of space and then blowing it up big – a city of a million souls with four features that instead gets treated like a little town that’s inflated ala, a bouncy castle.

What I needed for my purposes is a way of proliferating these spaces without just laying out empty chairs. I didn’t want to say ‘oh there are two thousand player factions’ and then have them just these empty boxes maybe with a token name. That’s how the nation of Dal Raeda spent twenty years as ‘Kyngdom,’ a name I still sting at.

Signifiers don’t need to be something complex like a method, though. They just need to be a thing that distinguishes themselves from one another. The way I handled it, at first, was to take something of which I already had a set of signifiers, and do math to it.

First, we take one of the most well-developed player factions in the setting, the knights of the Eresh Protectorates. There are four knightly orders, and they each are signified by a pair of colours:

  • Tzarumites are purple and black
  • Lethenites are grey (silver) and red (rose)
  • Raguzans are blue and yellow (gold)
  • Chardunists are grey and green (jade)

That right there presents seven signifiers, in pairs. What I then did was take that set and punch it into a Combinatorics Calculator. The list goes in like this:

purple, black, grey, red, blue, yellow, green

That’s seven, that’s a list. Turn off ‘order important’ and turn off ‘repetition allowed,’ and then press ‘list.’

  • purple,black
  • purple,grey
  • purple,red
  • purple,blue
  • purple,yellow
  • purple,green
  • black,grey
  • black,red
  • black,blue
  • black,yellow
  • black,green
  • grey,red
  • grey,blue
  • grey,yellow
  • grey,green
  • red,blue
  • red,yellow
  • red,green
  • blue,yellow
  • blue,green
  • yellow,green

Okay, great, that’s a big list of combinations. Right? But what if I now want to suggest that the colours signify things? What if all the blue colours are somehow associated with royalty? Or if all the black groups have a reputation as being evil?

What’s more, with this array, I can start pushing things away from one another. A purple and red faction shouldn’t show up near the Church Knights by default, because anyone making a faction in that space would see the way the red and purple overlap with the Tzarumites and the Raguzans, which makes them less distinct. People make symbols and signifiers out of their experiences.

In a Rokugan-style arrangement with clans that have subfamilies, you might want a bunch of colours to be your ‘primary’ colours, and then underneath those primary colours you have the subfamilies – in that case, you could turn on ‘order important’ and suddenly a yellow-black is different to a black-yellow.

Add a signifier, you get more details. But you don’t even have to have them be colours – you could have a list like:

yellow, silver, swords, catfish, clouds

And then you’ll get another list of (seeming) nonsense that still asks you to explain what a silver-catfish is and a yellow-cloud is. You get to make those choices, and the tool presents you with a list that’s both non-redundant but also not bottomless. You can start blocking these things out as spaces.

This is a tool, and obviously it’s not going to be useful for everything. But I recommend if you want to work on factional spaces, where players get to belong to things, take an approach that gives you space to work with and groupings that need to be differentiated from one another. It clearly communicates ideas separated from one another, it gives you a tool for building, and it also lets you attach plain-language terms to an otherwise difficult task.