Math & Statistics of the Dragon's Maze Prerelease

So I've spent a couple of days working on the math of the prerelease, and I even had a statistics guy (El Tigre from the Sorn vs. Tibalt deck test video) look over my work. And he says that it I did my math right. I'm not bad at math, but I had to have a second opinion. So here are my findings:

Most stores have 80 prerelease boxes. It used to be 16 for each guild split by 5. Now we split by 10, so there are going to be 8 boxes per store. Of course, I'm pretty sure the number is 80, but I could be wildly off. Who knows...

We also know that there are secret guilds with the guild we choose. It is one of the four guilds from the opposite set that shares one of the colors of your guild's color pair (ex. Izzet can be paired with Dimir, Boros, Gruul, or Simic).

So... I've worked out what probability each guild will have at a particular shared color. Let me explain a bit...

Given the Izzet example, I did this for all the guilds. And I came up with this:

Guild	Color 1	Color 2	Color 3
Azorius (White/Blue)	50% - Black	25% - Green	25% - Red
Orzhov (White/Black)	50% - Green	25% - Blue	25% - Red
Dimir (Blue/Black)	50% - Red	25% - White	25% - Green
Izzet (Blue/Red)	50% - Green	25% - Black	25% - White
Rakdos (Black/Red)	50% - White	25% - Green	25% - Blue
Golgari (Black/Green)	50% - Blue	25% - Red	25% - White
Gruul (Red/ Green)	50% - Black	25% - White	25% - Blue
Boros (Red/White)	50% - Blue	25% - Black	25% - Green
Selesnya (Green/White)	50% - Red	25% - Blue	25% - Black
Simic (Green/Blue)	50% - White	25% - Red	25% - Black

So, essentially, this tell you what guild to choose for a tri-color pair. Or at least the best chance of getting the pair you want (which is 50%).

So, if you want the Esper Shard you should choose Azorius, Dimir for Grixis, Gruul for Jund, Selesnya for Naya, and Simic for Bant.

Don't know the shards? Quick explanation:

• Esper = W/U/B
• Grixis = U/B/R
• Jund = B/R/G
• Naya = R/G/W
• Bant = G/W/U

If you want enemy wedges, choose the following: Orzhov for Necra, Izzet for Ceta, Rakdos for Dega, Golgari for Ana, and Boros for Raka.

Don't know what those are? Tristamicus commented about them on this post. But here is a quick breakdown:

• Ana = U/B/G or BUG
• Ceta = U/R/G or RUG
• Dega = W/B/R or Kaalia of the Vast's colors
• Necra = W/B/G or "Junk"
• Raka = W/U/R or "America"

But there's more! Just like with the extra colors, of course you could get different shards or wedges. We're just talking high probability here...

Guild	Color 1	Color 2	Color 3
Azorius (White/Blue)	50% - Esper	25% - Raka	25% - Bant
Orzhov (White/Black)	50% - Necra	25% - Esper	25% - Dega
Dimir (Blue/Black)	50% - Gixis	25% - Ana	25% - Esper
Izzet (Blue/Red)	50% - Ceta	25% - Grixis	25% - Raka
Rakdos (Black/Red)	50% - Dega	25% - Jund	25% - Grixis
Golgari (Black/Green)	50% - Ana	25% - Necra	25% - Jund
Gruul (Red/ Green)	50% - Jund	25% - Naya	25% - Ceta
Boros (Red/White)	50% - Raka	25% - Dega	25% - Naya
Selesnya (Green/White)	50% - Naya	25% - Bant	25% - Necra
Simic (Green/Blue)	50% - Bant	25% - Ceta	25% - Ana

I took the math just a little further... I decided to see which guilds had more allied and more enemy color pairs.

Guild	% Allied	% Enemy
Azorius	75%	25%
Orzhov	25%	75%
Dimir	75%	25%
Izzet	25%	75%
Rakdos	50%	50%
Golgari	25%	75%
Gruul	75%	25%
Boros	25%	75%
Selesnya	75%	25%
Simic	50%	50%

Of course, it shouldn't be a surprise that the allied color guilds have more of the shards and the enemy color guilds have more of the wedges, but... Wait, Rakdos and Simic? What is their problem?

I went back and did this twice, and I also had someone look over my work... Rakdos and Simic both have an equal chance of being an allied pair or an enemy pair with your secret guild.

Anyway, long story short, if you want to know which guild to choose for the higher chance you'll get the color pairing you want, take the math from the first table. But remember this:

If a store has 80 boxes, and each guild has 8 boxes in all, in a statistically perfect situation, 4 will have the color pairing you want, and 4 won't, but hopefully of the 4 that won't, 2 of them will have a pair you're okay with. So for instance, if you want Grixis, go with Dimir, but if you know you want an allied shard if you can't have Grixis, Dimir is probably your best bet (since 50% will be Grixis and 25% will be Esper).

I'd like to use Boros and Simic, but Selesnya might be better in place of Boros since I'd like Naya, and for Simic, since I want RUG/Ceta, I'd be better off with Izzet since I have a better chance.

Anyway, I hope you like my assessment. Good luck in you're prerelease, and enjoy playing with Dragon's Maze!