Wednesday, April 24, 2013

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:

GuildColor 1Color 2Color 3
Azorius (White/Blue)50% - Black25% - Green25% - Red
Orzhov (White/Black)50% - Green25% - Blue25% - Red
Dimir (Blue/Black)50% - Red25% - White25% - Green
Izzet (Blue/Red)50% - Green25% - Black25% - White
Rakdos (Black/Red)50% - White25% - Green25% - Blue
Golgari (Black/Green)50% - Blue25% - Red25% - White
Gruul (Red/ Green)50% - Black25% - White25% - Blue
Boros (Red/White)50% - Blue25% - Black25% - Green
Selesnya (Green/White)50% - Red25% - Blue25% - Black
Simic (Green/Blue)50% - White25% - Red25% - 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...

GuildColor 1Color 2Color 3
Azorius (White/Blue)50% - Esper25% - Raka25% - Bant
Orzhov (White/Black)50% - Necra25% - Esper25% - Dega
Dimir (Blue/Black)50% - Gixis25% - Ana25% - Esper
Izzet (Blue/Red)50% - Ceta25% - Grixis25% - Raka
Rakdos (Black/Red)50% - Dega25% - Jund25% - Grixis
Golgari (Black/Green)50% - Ana25% - Necra25% - Jund
Gruul (Red/ Green)50% - Jund25% - Naya25% - Ceta
Boros (Red/White)50% - Raka25% - Dega25% - Naya
Selesnya (Green/White)50% - Naya25% - Bant25% - Necra
Simic (Green/Blue)50% - Bant25% - Ceta25% - 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!

3 comments:

  1. I pulled Izzet hoping to play ceta or raka , my favorite combos. However, I got no removal outside of paralyze, renounce the guilds and krasis incubation. So, I ended playing bant ( I got the new armadillo cloak too) . Needless to say deck was not too good and I lost a tiebreaker that kept me out of top eight. There may be something said for designing to these paradigms. The top deck was an azorious esper deck. The second best was selensya / necra/ junk.

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  2. Oh my secondary guild was simic.

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  3. Izzet/Simic? Not a bad combo. I chose Selesnya/Boros first, Golgari/Simic second, and then my third prerelease was Izzet/Gruul. First and last times I got Top 8, but didn't get past the quarterfinals. At least I won a couple packs each time. I'm going to go over deck techs and put videos of pulls within the next week or so once exams are over. I feel my first choice was by far the best, and it seems that most people went with some combination of Boros since most of the packs with Boros were gone. (Deck idea: Phytoburst, Trained Caracal, Gruul cards with Bloodrush).

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