(Further) Ruminations on the color wheel

I have always (meaning, since I had learned about Magic’s color wheel) been fascinated with the intricacies of the relations between the five colors and with finding connections I didn’t realize were there immediately. For example: Each pair of friendly colors has a counterpart in an enemy-color pair – are you aware what the counterpart of Rakdos is? It’s Simic – do you know why? Well, since there are five colors in the color wheel, there is only one color related to Rakdos in an unique way: White, its shared enemy. In the same vein, there is only one color related in an unique way to Simic: White, its shared friend.

Actually, unique relations can only come into play once you look beyond relations between single colors – that is just the nature of the color wheel: Each color has two friends and two enemies. Things become interesting, though, once you treat color pairs and triples as separate entities! I have come to think of Magic as containing 25 “colors” (quite a useful perspective when you design asymmetrical cubes): five singles, five allied pairs, five opposite pairs, five shards and five wedges.

Thus you get the following unique relations:

1. Between singles and allies (each ally has a shared enemy color)

2. Between singles and opposites (each opposite has a shared friendly color)

3. Between singles and shards (by the central color befriending the other colors)

4. Between singles and wedges (by the central color hostile to the other colors)

5. Between allies and opposites (the shared enemy of the ally is the shared friend of the opposite)

6. Between allies and shards (the two colors not contained in the shard make up the ally)

7. Between allies and wedges (the wedge made up by adding the shared enemy to the ally)

8. Between opposites and shards (the shard made up by adding the shared friend to the opposite)

9. Between opposites and wedges (the two colors not contained in the wedge make up the opposite)

10. Between shards and wedges (those sharing the same central color)

Since these relations are transitive, another way to look at them is that each color is connected with one ally, one opposite, one shard and one wedge each:

White – Rakdos – Simic – Bant – Dega.

Black – Selesnya – Izzet – Grixis – Necra.

Green – Dimir – Boros – Naya – Ana.

Blue – Gruul – Orzhov – Esper – Ceta.

Red – Azorius – Golgari – Jund – Raka.

Now, five is a prime, so there is no way to split up, for example, the five single colors evenly over any number of sets higher than one and lower than five. As a cube builder, this means that if I am to build a cube consisting of several cube sets (cube sets would define which cards can show up in which booster round, just as regular sets do in a regular draft), I can not split up colors unless I am willing to do it in an asymmetric way. (Five sets are just too many. I can at least conceive using four sets – one four each booster round – but not five, and I’m actually not sure it makes sense to use more than two.) It IS, however, possible to split up all pairs between two sets, just as it is possible to split up all triples.

When I talk about splitting up pairs or triples evenly between two sets, I certainly do not only mean that each set gets five of them; I also mean that each color is represented an equal amount in each set. As I already explained in my previous entry, this leaves only 6 options when splitting up pairs: The obvious split between allies and opposites, and five splits corresponding to one color each putting three allies in one set and three opposites in the other. For reference, here are those splits again:

Ally / opposite split: Azorius, Selesnya, Gruul, Rakdos, Dimir / Boros, Orzhov, Golgari, Simic, Izzet.

White as the defining color: Selesnya, Azorius, Rakdos, Golgari, Izzet / Boros, Orzhov, Simic, Gruul, Dimir.

Black as the defining color: Dimir, Rakdos, Selesnya, Simic, Boros / Golgari, Orzhov, Izzet, Azorius, Gruul.

Green as the defining color: Gruul, Selesnya, Dimir, Orzhov, Izzet / Golgari, Simic, Boros, Azorius, Rakdos.

Blue as the defininig color: Dimir, Azorius, Gruul, Boros, Golgari / Izzet, Simic, Orzhov, Rakdos, Selesnya.

Red as the defnining color: Rakdos, Gruul, Azorius, Simic, Orzhov / Izzet, Boros, Golgari, Dimir, Selesnya.

Once I had worked this out, I realized how useful this information could be for me in future cube building (or maybe I’m just a geek…), and I did the same for triples. Note that you can only split up pairs or triples evenly regarding single colors: Each pair split puts, by necessity, two guilds featured in any triple in one set and the third guild in the other (it’s trivial they cannot be split up evenly, as you cannot divide three by two, but they also cannot be split up 3-0) – that is true when you split up pairs as well as when you split up triples; you cannot do both splits evenly at the same time.

When you split up triples evenly, you once again have six options: The obvious split between shards and wedges, and five splits defined by a single color each (in this case, rather simply: You take the three shards the color is in and put them in one set together with the two wedges it is not in, leaving a set with the three wedges it is in and the two shards it is not in).

So, in case you’re interested, here are the possible even splits for triples over two sets:

1. The shards / wedges split – Bant, Naya, Jund, Grixis, Esper / Dega, Necra, Ana, Ceta, Raka.

2. White as the defining color – Bant, Jund, Grixis, Necra, Raka / Naya, Esper, Dega, Ana, Ceta.

3. Black as the defining color – Grixis, Bant, Naya, Dega, Ana / Jund, Grixis, Necra, Ceta, Raka.

4. Green as the defining color – Naya, Grixis, Esper, Necra, Ceta / Bant, Jund, Ana, Dega, Raka.

5. Blue as the defnining color – Esper, Naya, Jund, Ana, Raka / Bant, Grixis, Ceta, Dega, Necra.

6. Red as the defining color – Jund, Bant, Esper, Dega, Ceta / Grixis, Naya, Raka, Necra, Ana.

So, if at any later time, Wizards will return to Alara, introducing wedges this time, and MaRo will explain how they arrrived at the perfect split between color triples over two sets, you know that, given that they aim for an even split, they have exactly these six options to choose from before they can add any other goals. (But maybe you’ll find it a tiny bit more practical to reference these splits when designing your own cube?)

Oh, and before I forget: The fourth part of my (German) Return to Ravnica limited preview is online on PlanetMTG!

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