Cool Beens' Wacky Faction Guide

Written by Cool Beens, graphics and editing by crushcastles23.

Introduction

A sentiment I hear a lot, mostly from myself, is something along the lines of “I want to make a faction set, but all the faction setups have already been done!” While wrong, this is not an unreasonable thought- by my count, there have been 17 canon faction sets, and a likely near infinite number of custom sets exploring what seems like a pretty limited pool of total setups. How much unexplored space could there possibly be?

That’s where I come in.

In this “article”, I’m going to explain and demonstrate every faction setup possible under a few conditions that most sets are expected to follow:

1. Each color must be represented equally

2. No faction can contain the whole color identity of another

3. Monocolor factions don’t exist.

4. Four and five color factions also don’t exist.

5. There are exactly five colors of Magic represented in the set.

2-Faction Setups

Y’all are smart people, I’m sure you’re able to figure out what a 2-faction setup could look like. So I’m going to use this space to discuss an essential principle that will be used throughout.

The APPF Test

For a set of factions to pass Rule 1, the total number of pips in the set of factions must equal a multiple of five. For instance, in Guilds of Ravnica, each color is represented twice for a total of 10. In addition, in compliance with Rule 3 and 4, each faction must represent either 2 or 3 colors. This means that the average number of colors per faction must be between 2 and 3.

Thus the APPF (Average Pips Per Faction) Test: 2 ≤ 5p/F ≤ 3, where p is the number of times each color is represented across the set of factions, and F is the total number of factions. For a 2-Faction setup, the only p value that passes the APPF test is 1. Therefore, each color can only appear once.

Final Possible Setups

• The Two-Party System: Any set of three colors (henceforth called a trio) + the pair that shares no colors with it

  • e.g. WUB + RG 

3-Faction Setups

Interestingly, no p value passes APPF for a 3 faction setup. p = 1 yields 1.667, which is too low, and p = 2 yields 3.333, which is too high. Thus, a 3-faction set is simply impossible.

Final Possible Setups

None.

4-Faction Setups

For a 4-faction setup, the only legal p value is 2, with an APPF of 2.5. This means that any 4-faction setup will have two 3-color factions and two 2-color factions. However, this still gives us a good amount of wiggle room, so now I get to get into the good stuff.

Setup Sleuthin’

For a while here I had a long-winded section on my procedure for finding every possible setup, but it was exhausting and boring and made very little sense, so you’ll just have to trust me that I got them all. Long story short, there’s a lot of different ways that 3c factions in particular can overlap, and it’s important to consider all of them.

Final Possible Setups

• The Ixalan: Any trio + a trio that shares only 1 color with the previous + two non-overlapping pairs, each comprised of one color that wasn’t the shared color from each of the trios

  • e.g. RGW + RUB + GU + WB

• The strictly worse Ixalan: Any trio + a trio that shares two colors with the previous + two pairs, where one of their colors is the only current nonrepresented color and the other color is one of the colors with only 1 pip of representation so far. This one sucks

  • e.g. RGW + RGB + UW + UB

5-Faction Setups

This is canon MTG’s bread and butter. Successful p values are both 2 (5 2c archetypes) and 3 (5 3c archetypes). Not a lot to say here.

Final Possible Setups

• The Half-Ravnica: Five pairs that each overlap each one of their colors with exactly one other color.

  • e.g. WU + UR + RG + GB + BW

• The Alara: Five trios, each comprised of two pairs that are each shared with exactly one other trio and one unique pair. (In Shards of Alara, Bant shares GW with Naya, and WU with Esper, but keeps GU as fully unique.)

  • e.g. WUB + UBR + BRG + RGW + GWU

6-Faction Setups

Now this is the good shit. We’re entering unexplored territory, but our process is the same. The only successful p value is 3, so we’re working with 3 trios and 3 pairs. Real dedicated Cool Beens fans will note that I wrote about 6-faction sets in #project-design once before, but those people also don’t exist so

Final Possible Setups

• The Triangle Strategy: Three trios that each share exactly 2 colors with each of the other two trios, forming a little triangle + three pairs, each comprised of the currently nonrepresented color and one of the colors that not all of the trios share

  • e.g. WUB + WUR + WRB + GU + GB + GR

• The Ravnalara: Two trios that share one color + a third trio that shares two colors with each of the previous trios + three pairs constructed in such a way as to not violate Rule 2, good luck

  • e.g. WUB + WRG + WUG + UR + RB + BG

• The Scaffolded Triangle: Three trios that all share a pair + the three pairs that don't use the color of the pairs the trios share

  • e.g. WUB + WUR + WUG + RG + BR + GB

7-Faction Setups

You didn’t think this would be possible, did you? You underestimate my power. Legal p values include both 3 (six pairs and one trio) and 4 (six trios and one pair).

Final Possible Setups

• The Trio Stands Alone: Any tri + six pairs comprised of a color from the tri and a color outside of the tri

  • e.g. WUB + WR + WG + UR + UG + BR + BG

• The Pair Stands Alone: Any pair + six trios comprised of a color from the pair and two colors from outside the pair

  • e.g. WU + WRB + WRG + WGB + URB + URG + UGB

8-Faction Setups

This is some weird shit. Our only legal p value is 4, with 4 trios and 4 pairs to work with. As far as I can tell, there’s only one way to do this, and you’re not gonna like it.

Final Possible Setups

• The Japanese Fan: 4 trios in such a way that none of them include a certain color + 4 pairs comprised of every possible pair involving that certain color

  • WUB + UBR + WUR + WBR + GW + GU + GB + GR

9-Faction Setups

This, to me, is the most interesting thing I found out during this document’s painstaking creation. There are two legal p values for 9-Factions, both 4 and 5, but neither are actually possible. p = 4 involves one trio and eight pairs, which is impossible under Rule 2, and p = 5 involves 7 trios and 2 pairs, which is impossible for similar reasons which are harder to explain.

Final Possible Setups

None.

10-Faction Setups

Back to basics, with legal p values of 4 (10 pairs), 5 (blatantly impossible), and 6 (10 trios), I bet you can guess what these are going to be.

Final Possible Setups

• The Dragon’s Maze: Every possible pair

• The Double Masters 2: Every possible trio

N-Faction Setups

Fun fact(ion): Past 10, every single faction setup fails to pass Rule 2. Ten is just a hard cap.

Final Final Possible Setups

None

Conclusion

While I frankly doubt this article has helped you, I hope it has been at least somewhat entertaining and maybe just a little bit inspiring. If anyone ever makes a set with The Ravnalara or The Japanese Fan, please @ me.

Until I’m bored again, stay Cool.