Expected Numbers of Specific Cards in Eldritch Moon Limited

Eldritch Moon has 205 cards (not including basic lands)—21 more than most small sets to accommodate double-faced cards.  There are 74 Commons, 70 Uncommons, 47 Rares, and 14 Mythics. The 21 double-faced cards include four Commons, ten Uncommons, five Rares, and two Mythics. These counts include cards with meld, since those cards appear in the same slot as double-faced cards. Individual double-faced cards appear at roughly the same frequency as regular cards, but are distributed differently across packs.

Each booster pack contains a double-faced Common or Uncommon, nine regular Commons, three regular Uncommons, and one Rare or Mythic. In addition, one in every eight packs contains a Rare or Mythic double-faced card in place of a regular Common. One out of about every six packs also contains a foil card, which replaces a Common, so you can actually end up with three Rares/Mythics in a pack if you're extremely lucky. However, foil cards are sufficiently rare that they have relatively little impact on Limited formats, so we won't consider them in our analysis.

Given those numbers, here are the chances of seeing a specific card at any given rarity in an Eldritch Moon booster pack, fat pack, or booster box.

If double-faced cards had exactly the same frequency as regular cards, we'd end up with 36.25 Commons plus Uncommons, and 4.5 Rares plus Mythics in a box. The second number matches what we'd expect if one in each eight packs has a double-faced Rare or Mythic. The first number is slightly higher than the 36 we'd expect, but if there are 4.50 copies of any given double-faced Common instead of 4.56, then we end up with exactly 36 Commons plus Uncommons. This means that you're only 1.3% less likely to see any given double-faced Common as you are to see any given regular Common, and as likely to see any given double-faced Uncommon, Rare, or Mythic as you are to see any given regular Uncommon, Rare, or Mythic. (In Shadows over Innistrad packs, you're 5% less likely to open a specific double-faced Common than a specific regular Common, 12% less likely to open a specific double-faced Uncommon than a specific regular Uncommon, and as likely to see any given double-faced Rare or Mythic as you are to see any given regular Rare or Mythic.)

For both regular and double-faced cards, you're about 2.5 times as likely to see a copy of any given Common as you are to see a copy of any given Uncommon, 2.4 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.

I'd previously computed similar numbers for Shadows over Innistrad, and am including these here for reference, since we will use them to determine how likely we are to see cards from both sets in different Limited formats. Note, Shadows over Innistrad has more cards than Eldritch Moon, so you're less likely to see a specific card at any given rarity.

Now let's apply this information, along with the pack distributions listed in the Magic Tournament Rules, to determine how likely we are to encounter copies of specific cards at each rarity in various Limited formats. We can use this information to determine how likely we are to be able to draft the cards needed for an archetype, or how likely we are to face a particular card or group of cards in sealed formats.

Draft

Since we're drafting two packs of Eldritch Moon and one pack of Shadows over Innistrad, an eight-person draft will, on average, contain the following numbers of copies of cards at each rarity:

• Eldritch Moon: 2.03 copies of a given Common, 0.80 copies of a given Uncommon, 0.33 copies of a given Rare, and 0.17 copies of a given Mythic. Double-faced cards occur at almost exactly the same frequency as regular cards at the same rarity.
• Regular cards from Shadows over Innistrad: 0.70 copies of a given Common, 0.30 copies of a given Uncommon, 0.13 copies of a given Rare, and 0.07 copies of a given Mythic.
• Double-faced cards from Shadows over Innistrad: 0.64 copies of a given Common, 0.27 copies of a given Uncommon, 0.13 copies of a given Rare, and 0.07 copies of a given Mythic.

This means you're about three times as likely to see a given Eldritch Moon Common as you are to see a given Shadows over Innistrad Common, and about 2.5 times as likely to see a given Eldritch Moon Uncommon, Rare, or Mythic. You're 10-20% less likely to see a specific Shadows over Innistrad Common than a specific Eldritch Moon Uncommon, a specific Shadows over Innistrad Uncommon than a specific Eldritch Moon Rare, or a specific Shadows over Innistrad Rare than a specific Eldritch Moon Mythic.

Sealed

Individual sealed uses four packs of Eldritch Moon and two packs of Shadows over Innistrad, so cards from the two sets will occur in the same relative proportions as in draft, although a player will only have access to a quarter as many copies of any given card. A sealed pool will, on average, contain the following numbers of copies of cards at each rarity:

• Eldritch Moon: 0.51 copies of a given Common, 0.20 copies of a given Uncommon, 0.08 copies of a given Rare, and 0.04 copies of a given Mythic. Double-faced cards occur at almost exactly the same frequency as regular cards at the same rarity.
• Regular cards from Shadows over Innistrad: 0.18 copies of a given Common, 0.08 copies of a given Uncommon, 0.03 copies of a given Rare, and 0.02 copies of a given Mythic.
• Double-faced cards from Shadows over Innistrad: 0.16 copies of a given Common, 0.07 copies of a given Uncommon, 0.03 copies of a given Rare, and 0.02 copies of a given Mythic.

Team Sealed

Three-person team sealed uses eight packs of Eldritch Moon and four packs of Shadows over Innistrad, so cards from the two sets will also occur in the same relative proportions as in draft, although a player will only have access to half as many copies of any given card. A team sealed pool will, on average, contain the following numbers of copies of cards at each rarity:

• Eldritch Moon: 1.01 copies of a given Common, 0.40 copies of a given Uncommon, 0.17 copies of a given Rare, and 0.08 copies of a given Mythic. Double-faced cards occur at almost exactly the same frequency as regular cards at the same rarity.
• Regular cards from Shadows over Innistrad: 0.35 copies of a given Common, 0.15 copies of a given Uncommon, 0.07 copies of a given Rare, and 0.03 copies of a given Mythic.
• Double-faced cards from Shadows over Innistrad: 0.32 copies of a given Common, 0.14 copies of a given Uncommon, 0.07 copies of a given Rare, and 0.03 copies of a given Mythic.

Two-Headed Giant Sealed

Two-Headed Giant sealed uses six packs of Eldritch Moon and two packs of Shadows over Innistrad, which is a different ratio than the other Limited formats. A Two-Headed Giant sealed pool will, on average, contain the following numbers of copies of cards at each rarity:

• Eldritch Moon: 0.76 copies of a given Common, 0.30 copies of a given Uncommon, 0.13 copies of a given Rare, and 0.06 copies of a given Mythic. Double-faced cards occur at almost exactly the same frequency as regular cards at the same rarity.
• Regular cards from Shadows over Innistrad: 0.18 copies of a given Common, 0.08 copies of a given Uncommon, 0.03 copies of a given Rare, and 0.02 copies of a given Mythic.
• Double-faced cards from Shadows over Innistrad: 0.16 copies of a given Common, 0.07 copies of a given Uncommon, 0.03 copies of a given Rare, and 0.02 copies of a given Mythic.

This means that you're roughly four times as likely to see a given Eldritch Moon Common, Uncommon, Rare, or Mythic as you are to see a given Shadows over Innistrad Common, Uncommon, Rare, or Mythic. You're 45% less likely to see a specific Shadows over Innistrad Common than a specific Eldritch Moon Uncommon, a specific Shadows over Innistrad Uncommon than a specific Eldritch Moon Rare, or a specific Shadows over Innistrad Rare than a specific Eldritch Moon Mythic.