BFZ: Expected numbers of copies of a card

Battle for Zendikar has 101 commons, 80 uncommons, 53 rares, and 15 mythics. This means that an 8-person BFZ/BFZ/BFZ draft will have an average of 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.

ORI: Expected numbers of copies of a card

Magic Origins has 101 commons, 80 uncommons, 55 rares, and 16 mythics. This means that an 8-person ORI/ORI/ORI draft will have an average of 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.

MM2: How many bounce lands is too many?

A lot of good players like to play as many bounce lands as they can get their hands on, but doing so also increases the risk of having to mulligan hands where your only lands are bounce lands. It may seem unlikely, but it happened to me thrice in my first 8 matches of Modern Masters 2015. (I had 3-4 bounce lands in each of those decks.) Was I just unlucky? Let’s try to quantify the risk.

An 8-person draft has about 1 copy of any given uncommon on average and there are 10 bounce lands, all at uncommon, so the typical draft will have about 10 bounce lands. This is only about 1.25 per player, but for our analysis we’ll consider decks with up to 10 bounce lands. We’ll also assume 40-card decks with 17-18 lands and where each bounceland replaces about 1.5 lands. I’m also going to ignore the case where you only have 1 bounceland and no other lands, since you wouldn’t usually keep a hand with only 1 land in most Limited games, but the risk of this does increase slightly since you’re running fewer lands in the deck.

# bounce lands # other lands P(2+ bounce lands & no other lands
2 15 0.07%
2 14 0.09%
3 14 0.26%
3 13 0.35%
3 12 0.47%
4 12 0.85%
4 11 1.12%
5 11 1.71%
5 10 2.23%
5 9 2.88%
6 9 3.93%
6 8 5.03%
7 8 6.41%
7 7 8.13%
7 6 10.24%
8 6 12.43%
8 5 15.53%
9 5 18.16%
9 4 22.55%
9 3 27.81%
10 3 31.60%
10 2 38.74%

With 3 bounce lands and 14 other lands, the probability of all the lands you draw being bounce lands is only 0.26%, and with 4 bounce lands and 12 other lands, the probability only goes up to 0.85%, so the risk isn’t as high as it seemed from my small sample size. As long as you have fewer than 6 bounce lands, the probability is less than 3%, which is well worth the virtual card advantage of drawing a bounce land, and the greater density of spells in your deck. The risk involved with running 6+ bounce lands might still be worthwhile if you compare it to the lowered probability of getting stuck at 2-3 mana sources, the increased mana you have available for multikicker/X spells, and the ease of splashing cards from other colors and maximizing sunburst cards. But it’s always better to enter such situations with a good understanding the risks involved.

MM2: Expected numbers of copies of a card

Modern Masters 2015 has the same rarity distribution as Khans of Tarkir: 101 commons, 80 uncommons, 53 rares, and 15 mythics. However, each pack also has a foil card. According to some sources, a box typically has about 16 foil commons, 6 foil uncommons, and 2 foil rares (presumably 1/8th of which are mythics). This means that an 8-person MM2/MM2/MM2 draft will have an average of 2.5 copies of a given common, 1.0 copies of a given uncommon, 0.4 copies of a given rare, and 0.2 copies of a given mythic.

KTK/FRF: Expected numbers of copies of a card

EDIT: I didn’t realize when I posted this that the gain lands were going to take the basic land slot. I’ve updated the post to reflect the new numbers.

Fate Reforged has 165 cards (not counting the gain lands, which take the basic land slot): 60 commons, 60 uncommons, 35 rares, and 10 mythics.

Let’s consider the expected number of copies of any given common, uncommon, rare, or mythic from both sets in the block for a few different formats.

8-person draft (8 pack of Fate Reforged and 16 packs of Khans of Tarkir at the table)

Fate Reforged Khans of Tarkir
Commons 1.33 1.58
Uncommons 0.40 0.60
Rares 0.20 0.26
Mythics 0.10 0.13

Individual sealed (3 packs of Fate Reforged and 3 packs of Khans of Tarkir per person)

Fate Reforged Khans of Tarkir
Commons 0.50 0.30
Uncommons 0.15 0.11
Rares 0.08 0.05
Mythics 0.04 0.03

Team sealed (6 packs of Fate Reforged and 6 packs of Khans of Tarkir per team)

Fate Reforged Khans of Tarkir
Commons 1.00 0.59
Uncommons 0.30 0.23
Rares 0.15 0.10
Mythics 0.08 0.05

Some observations:

  • An 8-person draft will only have 0.6 copies of any given Khans of Tarkir uncommon, so you shouldn’t draft towards an archetype that relies heavily on one until after you’ve actually drafted a copy. In fact, there are only 1.6 copies of any given Khans of Tarkir common, so you probably shouldn’t expect to see any specific one of those either, unless it tends to not be valued by other players.
  • Drafts will have 1.2 – 1.5 times as many copies of a specific Khans of Tarkir card as of a specific Fate Reforged card at the same rarity, not 2 times as many copies as one might expect from the pack distribution.
  • The expected numbers are roughly reversed for sealed, with 1.3 – 1.7 times as many copies of a specific Fate Reforged card as of a specific Khans of Tarkir card at the same rarity, despite an even pack distribution, so the small set should have a big impact on these formats.
  • Sealed now has half as many copies of Khans of Tarkir cards. This means that the team sealed deck patterns previously observed are likely to change since there will be fewer copies of Savage Punch, Secret Plans, and the Warrior tribal cards, which enable the R/G, Sultai morphs, and B/W/x Warriors decks respectively. (The Sultai morphs deck does get Mastery of the Unseen, Temur War Shaman, and Whisperwood Elemental, but those are all rare or mythic. And while Fate Reforged has 2 Warrior tribal cards, neither of them has a particularly strong interaction with Warriors.)
  • An 8-person KTK/KTK/KTK draft had an average of 24 gain lands, or 1 per pack opened. Since Fate Reforged also has 1 gain land per pack, the average number of gain lands in a draft won’t change. We will lose 1.5 tri-lands and 0.7 fetch lands per draft, but that is not likely to have a huge impact on the format.

KTK: Expected numbers of copies of a card

Khans of Tarkir has the same rarity distribution as Magic 2015: 101 commons, 80 uncommons, 53 rares, and 15 mythics. This means that an 8-person KTK/KTK/KTK draft will have an average of 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.

M15: Expected numbers of copies of a card

Magic 2015 has 249 cards: 101 commons, 80 uncommons, 53 rares, and 15 mythics. This means that an 8-person M15/M15/M15 draft will have an average of 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.

Note that this rarity distribution is different than that of Magic 2010 through Magic 2014, all of which had 60 uncommons and so had an average of 1.2 copies of a given uncommon in an 8-person draft of that set. This difference will need to be accounted for when deciding on the viability of archetypes that require specific uncommons.

JOU: Expected numbers of copies of a card

In BNG/THS/THS, an 8-person draft had an average of 1.3 copies of a given Born of the Gods common, 0.4 copies of an uncommon, 0.2 copies of a rare, and 0.1 copies of a mythic. Similarly, it had 1.6 copies of a given Theros common, 0.8 copies of an uncommon, 0.26 copies of a rare, and 0.13 copies of a mythic. While there were twice as many packs of Theros as of Born of the Gods, there weren’t just twice as many copies of a card at a given rarity because small sets have a different rarity distribution (60 commons, 60 uncommons, 35 rares, and 10 rares).

JOU/BNG/THS draft has half as many packs of Theros, so there is now half as much a chance of seeing a given Theros card at any rarity. Journey into Nyx has the same rarity distribution as Born of the Gods, so there is an identical chance of seeing a given card from either set, regardless of rarity. Here are the expected numbers for a given card from each set at a particular rarity for an 8-person draft:

JOU BNG THS
Common 1.3 1.3 0.8
Uncommon 0.4 0.4 0.4
Rare 0.2 0.2 0.13
Mythic 0.1 0.1 0.07

So a JOU/BNG/THS draft will, on average, have the same number of any given JOU, BNG, or THS uncommon, but will actually have significantly more of any given common, rare, or mythic from either small set as it will of a THS card at the same rarity.

If a given Theros common has a very close analog in both Born of the Gods and Journey into Nyx, you’ll now have access to 3.4 copies of the card instead of the 2.9 copies you would have had in a BNG/THS/THS draft. If only Born of the Gods had a close analog, you’ll now have access to 2.1 copies instead of 2.9. And if only Journey into Nyx had a close analog, you’ll now have access to 2.1 copies instead of 1.6. Similaly, if Journey into Nyx has a close analog of a Born of the Gods card, you’ll now have access to 2.6 copies of it instead of 1.3 copies. We’ll use this information in future posts to determine the impact of the new set on existing archetypes.

BNG: Expected numbers of copies of a card

In triple Theros, an 8-person draft had an average of 2.4 copies of a given common, 1.2 copies of a given uncommon, 0.4 copies of a given rare, and 0.2 copies of a given mythic. Now that we’re down to 2 packs of Theros, we have fewer of the key cards for our familiar archetypes.

An 8-person BNG/THS/THS draft will have 2/3rds as many copies of a Theros card at a given rarity: 1.6 copies of commons, 0.8 copies of uncommons, 0.26 copies of rares, and 0.13 copies of mythics. While there are half as many Born of the Gods packs as Theros packs, the draft won’t just have half as many copies of a given Born of the Gods card at the same rarity since the set has a different rarity distribution (60 commons, 60 uncommons, 35 rares, and 10 rares). Instead, it will have an average of 1.3 copies of a given Born of the Gods common, 0.4 copies of a given uncommon, 0.2 copies of a given rare, and 0.1 copies of a given mythic.

This means that while you will see 1/2 as many copies of a given uncommon, you will actually see about 3/4ths as many copies of a given Born of the Gods rare or mythic, and 0.85 as many copies of a given common, which is more than you might have expected. In fact, if a given Theros common has a very close analog in Born of the Gods, it means you’ll now have access to 2.9 copies of the card instead of 2.4 copies.

In future weeks, we’ll use this information, along with the prior analysis of what cards each THS/THS/THS archetype gains, to determine where the prior archetypes have gained or lost with the introduction of Born of the Gods.