Expected Numbers of Specific Cards in Oath of the Gatewatch Limited
by Sameer Merchant // Jan 25, 2016
expected numbers Draft Sealed team sealed two-headed giant 2HG
Oath of the Gatewatch has 70 Commons, 60 Uncommons, 42 Rares, and 12 Mythics — a slightly different rarity distribution than most other small sets. Given those numbers, here are the chances of seeing a specific card at a given rarity in a booster pack, a fat pack, or a booster box.
| Contents | Common | Uncommon | Rare | Mythic | |
|---|---|---|---|---|---|
| Booster pack | 10 Commons, 3 Uncommons, 7/8 Rare, 1/8 Mythic | 0.14 | 0.05 | 0.02 | 0.01 |
| Fat pack | 9 booster packs | 1.29 | 0.45 | 0.19 | 0.09 |
| Booster box | 36 booster packs | 5.14 | 1.80 | 0.75 | 0.38 |
Wastes occur twice as often as other Commons, and Zendikar Expeditions appear at roughly the rarity of a foil Mythic. The Expeditions affect the expected value of a box of Oath of the Gatewatch, but have little impact on Limited, both because they occur so infrequently and because they are all lands. We will ignore them for the purposes of this article.
Battle for Zendikar has 101 Commons, 80 Uncommons, 53 Eares, and 15 Mythics, so the corresponding numbers for the set are as follows:
| Contents | Common | Uncommon | Rare | Mythic | |
|---|---|---|---|---|---|
| Booster pack | 10 Commons, 3 Uncommons, 7/8 Rare, 1/8 Mythic | 0.10 | 0.04 | 0.02 | 0.01 |
| Fat pack | 9 booster packs | 0.89 | 0.34 | 0.15 | 0.08 |
| Booster box | 36 booster packs | 3.56 | 1.35 | 0.59 | 0.30 |
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 environments. We can use this information to determine how likely we are 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 Oath of the Gatewatch and one pack of Battle for Zendikar, an eight-person draft will, on average, contain the following copies of cards at each rarity:
- Oath of the Gatewatch: 2.3 copies of a given Common, 0.8 copies of a given Uncommon, 0.33 copies of a given Rare, and 0.17 copies of a given Mythic. Wastes are twice as common as other Commons, so there will be an average of 4.6 copies in an 8-person draft.
- Battle for Zendikar: 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.
This means you're about three times as likely to see a given Oath of the Gatewatch Common as you are to see a given Battle for Zendikar Common, and about 2.5 times as likely to see a given Oath of the Gatewatch Uncommon, Rare, or Mythic as you are to see a given Battle for Zendikar Uncommon, Rare, or Mythic.
Sealed
Individual sealed uses four packs of Oath of the Gatewatch and two packs of Battle for Zendikar, 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 copies of cards at each rarity:
- Oath of the Gatewatch: 0.6 copies of a given Common, 0.2 copies of a given Uncommon, 0.08 copies of a given Rare, and 0.04 copies of a given Mythic. Wastes are twice as common as other Commons, so there will be an average of 1.1 copies of it in a sealed pool.
- Battle for Zendikar: 0.2 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.
Team Sealed
Three-person team sealed uses eight packs of Oath of the Gatewatch and four packs of Battle for Zendikar, so cards from the two sets will 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:
- Oath of the Gatewatch: 1.1 copies of a given Common, 0.4 copies of a given Uncommon, 0.17 copies of a given Rare, and 0.08 copies of a given Mythic. Wastes are twice as common as other Commons, so there will be an average of 2.3 copies of it in a team sealed pool.
- Battle for Zendikar: 0.4 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.
Two-Headed Giant
Two-Headed Giant sealed uses six packs of Oath of the Gatewatch and two packs of Battle for Zendikar, 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:
- Oath of the Gatewatch: 0.86 copies of a given Common, 0.3 copies of a given Uncommon, 0.13 copies of a given Rare, and 0.06 copies of a given Mythic. Wastes are twice as common as other Commons, so there will be an average of 1.7 copies of it in a Two-Headed Giant sealed pool.
- Battle for Zendikar: 0.2 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.
That means you're roughly four times as likely to see a given Oath of the Gatewatch Common, Uncommon, Rare, or Mythic as you are to see a given Battle for Zendikar Common, Uncommon, Rare, or Mythic.
