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Expected Numbers of Specific Cards in Dominaria Limited


Dominaria has 269 cards that appear in booster packs: 101 Commons, 80 Uncommons, 53 Rares, 15 Mythics, and 20 basic lands. This is the same as recent large sets. There are another 11 cards that don't appear in booster packs, so they don't affect Limited formats, and we will ignore them for the purposes of this analysis. We'll also ignore foil cards in this analysis since the chance of getting a specific foil is low enough that it has relatively little impact on Limited.

Impact of the Legendary Slot

The most important difference between Dominaria and other large sets is that every pack is guaranteed to have a Legendary card (not necessarily a Legendary creature). Unlike the double-faced card slot in the Innistrad sets though, there isn't a Legendary slot replacing a Common. Instead, there's a slot behind the Rare that sometimes contains a Legendary Uncommon and is sometimes not present. Unlike with double-faced cards, you can have more than one Legendary in a pack and you can't get more than one Rare unless your pack has a foil Rare. 

Since the Legendary slot only contains Legendary Uncommons, I wanted to determine whether Legendary Uncommons occur more frequently than non-Legendary Uncommons. I watched a video of six box openings to try to figure out whether the presence of a Legendary slot affects the expected number of specific Legendary cards relative to non-Legendary cards at the same rarity. Here are some observations:

  • If the Legendary slot is used, it always contains a Legendary Uncommon, and the pack only has two non-Legendary Uncommons in front of the Rare.
  • Packs always contain at least one Legendary card, but may contain up to three (not counting foils, as in the rest of this analysis).
  • There are six different variations for the Rare/Mythic and Uncommons:

Legendary Uncommon
in Legendary slot?

Rare/
Mythic

Uncommons

No

regular

1 Legendary, 2 regular

No

Legendary

3 regular

Yes

regular

2 regular

Yes

regular

1 Legendary, 1 regular

Yes

Legendary

2 regular

Yes

Legendary

1 Legendary, 1 regular

  • The only packs that contain 2 Legendary Uncommons contain a Legendary enchantment (On Serra's Wings or In Bolas's Clutch) in the regular slot and a Legendary creature in the Legendary slot.
  • There does appear to be some kind of a print run pattern. For instance, packs that contain Squee, the Immortal or Marwyn, the Nurturer don't seem to contain anything in the Legendary slot, but other Legendary Rares still have a Legendary Uncommon in the slot.
The six boxes opened contained the following number of Legendary cards (not including foils):
  Mythics Rares Uncommons
Box 1 3 17 28
Box 2 6 16 25
Box 3 5 16 31
Box 4 4 16 27
Box 5 3 15 28
Box 6 3 15 28
TOTAL 24 95 167

This admittedly small sample size suggests an average of about 4 Legendary Mythics, 15.8 Legendary Rares, and 27.8 Legendary Uncommons per box. Since a box is expected to contain 4.5 Mythics, 31.5 Rares, and 108 Uncommons, that means that Legendary cards were 89% of the Mythics, 50% of the Rares, and 26% of the Uncommons.

Now let's compare that to the percentage of cards at each rarity that are Legendary.
  • 87% of Mythics (13 out of 15) are Legendary, so we saw slightly more Legendary Mythics than we would expect.
  • 47% of Rares (25 out of 53) are Legendary, so we saw slightly more Legendary Rare than we would expect.
  • 28% of Uncommons (22 out of 80) are Legendary, so we saw slightly fewer Legendary Uncommons than we would expect.
Oddly, there were actually fewer Legendary Uncommons than we would expect, instead of as many or more. However, the difference is small and Legendary Rares and Mythics vary in the other direction, so it seems more likely that this is just due to our small sample size. I think it's safe to conclude that Legendary cards occur at the same frequency as non-Legendary cards at the same rarity, or that any discrepancy is small enough that it won't materially affect our expected value computations.

Putting it All Together

Each booster pack contains ten Commons, three Uncommons, and one Rare or Mythic. As usual, one out of every eight packs contains a Mythic instead of a Rare. Let's use this information to determine how likely we are to see a specific card at a given rarity when opening booster packs, bundles, and booster boxes.
  Contents Common Uncommon Rare Mythic
Booster pack 10 Commons, 3 Uncommons, 7/8 Rares, 1/8 Mythics 0.10 0.04 0.017 0.008
Bundle 10 booster packs 0.99 0.38 0.17 0.08
Booster box 36 booster packs 3.56 1.35 0.59 0.30

You're about 2.6 times as likely to see a copy of any given Common as you are to see a copy of any given Uncommon, 2.3 times as likely to see a copy of any given Uncommon as you are to see a copy of any given Rare, and twice as likely to see a copy of any given Rare as you are to see a copy of any given Mythic.

Now let's apply this information, along with the numbers of packs used for each format, to determine how likely we are to encounter copies of specific cards at each rarity in various Limited environments. I will use this information in subsequent articles to determine how viable various draft archetypes are, how strong some cards are in draft, and whether certain situational spells are playable maindeck in sealed.

Draft

An eight-person Dominaria draft uses a total of 24 packs and will, on average, contain 2.4 copies of a given Common, 0.9 copies of a given Uncommon, 0.4 copies of a given Rare, and 0.2 copies of a given Mythic.

Sealed

Individual sealed uses six packs of Dominaria, so each player has access to a quarter as many copies of any given card as in an eight-person draft. A sealed pool will, on average, contain 0.6 copies of a given Common, 0.23 copies of a given Uncommon, 0.1 copies of a given Rare, and 0.05 copies of a given Mythic.

Team Sealed

Three-person team sealed uses twelve packs of Dominaria, so each player has access to half as many copies of any given card as in an eight-person draft. A team sealed pool will, on average, contain 1.2 copies of a given Common, 0.45 copies of a given Uncommon, 0.2 copies of a given Rare, and 0.1 copies of a given Mythic.

Two-Headed Giant

Two-Headed Giant sealed uses eight packs of Dominaria, so each player has access to third as many copies of any given card as in an eight-person draft. A Two-Headed Giant sealed pool will, on average, contain 0.8 copies of a given Common, 0.3 copies of a given Uncommon, 0.13 copies of a given Rare, and 0.07 copies of a given Mythic.

 


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