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Expected Numbers of Specific Cards in Modern Masters 2017 Limited


Modern Masters 2017 has 249 cards: 101 Commons, 80 Uncommons, 53 Rares, and 15 Mythics. This is the same number and distribution as Kaladesh. 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.)

In addition, there's a foil in each pack instead of a basic land. While it's difficult to determine exact distributions, it seems that a box of Modern Masters 2017 contains roughly 15 foil Commons, 6 or 7 foil Uncommons, 1.5 foil Rares, and 0.25 foil Mythics. I will assume that each box has 15.75 foil Commons and 6.5 Uncommons, so the total adds up to 24 foils per box. Assuming that foils are evenly distributed among the cards at each rarity, this means that each booster pack effectively contains 10.656 Commons, 3.271 Uncommons, 0.938 Rares, and 0.135 Mythics.

Let's use this information to determine how likely we are to see a specific card at a given rarity when opening booster packs and booster boxes.

  Contents Common Uncommon Rare Mythic
Booster pack 10.656 Commons, 3.271 Uncommons, 0.938 Rare, 0.135 Mythic 0.106 0.041 0.018 0.009
Booster box 24 booster packs 2.53 0.98 0.42 0.22

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 about 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 Modern Masters 2017 draft uses a total of 24 packs (a booster box) and will, on average, contain 2.53 copies of a given Common, 0.98 copies of a given Uncommon, 0.42 copies of a given Rare, and 0.22 copies of a given Mythic.

Sealed

Individual sealed uses six packs of Modern Masters 2017, 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 0.63 copies of a given Common, 0.25 copies of a given Uncommon, 0.11 copies of a given Rare, and 0.05 copies of a given Mythic.

Team Sealed

Three-person team sealed uses twelve packs of Modern Masters 2017, 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 1.27 copies of a given Common, 0.49 copies of a given Uncommon, 0.21 copies of a given Rare, and 0.11 copies of a given Mythic.

Two-Headed Giant Sealed

Two-Headed Giant sealed uses eight packs of Modern Masters 2017, 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 0.84 copies of a given Common, 0.33 copies of a given Uncommon, 0.14 copies of a given Rare, and 0.07 copies of a given Mythic.


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