The Math of Dominaria United

It’s become a tradition, and one that tests my limits for going back and redoing things, but here we are, with a new set and a whole new list of things to figure out.

As always, I want to figure out what the rarest of rare things are, and just how rare they are, especially as a historical comparison. Plus, I need to do some calculations about Legends boosters!

Let’s get into it.

The headliners, of course, are the ‘Lost Legends’ that have been added to these packs. One thing they did for us is they said, straight out, that 3% of Collector Booster packs will have one card from a Legends pack. Now that card can be any rarity, so calm yourself down. You have a 3% chance to open a Zephyr Falcon!

For those who want it, here’s the list of cards. We can break this down a little further, and in fact we need to.

Number at this rarity in the original Legends setHow many are excluded, for one reason or anotherNumber possible for the Lost Legends

We have the same distribution as always: 10 commons and 3 uncommons for every rare, so the pool for this slot is 1403. Therefore, your odds for getting a card at each rarity IF you hit a Lost Legend:

1150/1403 = 82%183/1403 = 13%70/1403 = 5%

Remember that these are only in 3% of packs, so we have to multiply each by .03, and so there’s a Common in 2.46% of Collector Booster packs, Uncommon in 0.4% of packs, and a Legends Rare in 0.15% of those packs.

Want a specific card? Buckle up. You’ve got to multiply the above numbers by their number of options. So for example, if you want to hit a Willow Satyr, it’s (3/100) X (70/1403) X (1/70), and now we’re getting into negative exponents.

Rarity of the specific card% of Collector Boosters that contain that card (approx.)Packs needed to open one (approx.)

We can estimate how many of each Legends card is about to enter circulation, too. If we’re using 100 boxes as an estimate for what got opened, that’s 54,000 cards. Divided by the pool, that’s a max of 38.4 copies of any particular rare, 115 of any uncommon, and 1150 of any common.

This number is almost certainly an overestimate, as some cards were just straight removed and new ones weren’t added back in, but it’s a good reference point to know that we’re not getting any appreciable supply of Legends cards added to the mix.

It’s almost as an afterthought that we have some sweet Dominaria United cards to look at and think about! 

Frame/Treatment# of uncommons# of rares# of mythics
Showcase (Stained Glass)402815
Textured Foil20147
Extended Art415
Legends Retold1010

It’s a relief to work with some normal-ish numbers here. Let’s look at how these frames are distributed:

Let’s go over this, from the top down. (If you open the pack this way, it’ll be from the back to the front)

Slot #1: Textured Foil Stained Glass U/R/M

They added uncommons in this slot, and that makes for quite rarer cards. We know that the distribution is 10c:3u:1r:0.5m, or to make it easier, 20 commons:6 uncommons:2 rares:1 mythic. Therefore the pool of cards in this slot is 215.

RarityPercentage of packs that hold any card of that rarityChance for a particular card of that rarity# of packs to hit a particular card

Slot #2 and #3: Foil-Etched or Nonfoil Alternate Border R/M (Stained Glass, Phyrexian, Borderless, or Legends Retold)

This is crazy. Wizards has a history of changing what they collate into different slots in order to get to the percentages they desire, but I can’t remember a slot having such a wide variety of treatments, and in nonfoil, except for the set of Legends Retold which can be in etched foil but NOT traditional foil! They are trying to make me lose my mind.

Stained GlassPhyrexianBorderlessLegends Retold
Rare Nonfoil28610
Rare Etched Foil10
Mythic Nonfoil152510
Mythic Etched Foil10

The pool here is 150, and so:

RarityPercentage of packs that hold any card of that rarityChance for a particular card of that rarity# of packs to hit a particular card

Remember that there’s two of that particular slot, so there’s going to be a lot of nonfoil rares from that grouping that get opened. The foil-etched mythics will be 1 per 75 packs, which is pretty common as these things go.

Slot #5: Traditional Foil Alternate-Border R/M

Too many options here, let’s organize it with a table: 

Stained GlassPhyrexianBorderlessExtended Art
Rare 28641
Mythic 152*5*5

The asterisk here is for the Phyrexian cards: Sheoldred, the Apocalypse and Ajani, Sleeper Agent. Sheoldred has a showcase and a Phyrexian frame, cutting your odds in half. Remember that more versions of a card does not mean that there’s more copies of a card out there. So if there’s 100 Borderless Liliana of the Veil (only one special version), there’s 50 each of Showcase Sheoldred and Phyrexian Sheoldred. There would also be 25 each of each of the Ajani variants.

Textured foil is different, because that’s a special subset put in Collector Boosters only.

Because there’s four extra versions, the pool is 173, and as a result:

RarityPercentage of packs that hold any card of that rarityChance for a particular card of that rarity# of packs to hit a particular card (except special versions of Sheoldred or Ajani)

With all of that calculated, let’s look at some example cards and see how they stack up against each other for a Collector Booster: 

Card with Rarity and TreatmentNumber of Collector Boosters needed to open to get one (approx.)
Textured Foil Stained Glass Jodah, the Unifier (M)215
Foil-Etched Sivitri, Dragon Master (M)75
Borderless Foil Liliana of the Veil (M)173
Phyrexian Foil Sheoldred, the Apocalypse (M)346
Foil Compleated Ajani, Sleeper Agent (M)692

One foil special Ajani, Sleeper Agent every 692 packs is among the rarest of drops we’ve had in Collector Boosters, except for two very special entrants: Hidetsugu and the Lost Legends. Let’s compare these numbers with a list of other big tickets.

Card/SetCollector Boosters to open one (approx.)Card/SetCollector Boosters to open one (approx.)
Phyrexian Foil Vorinclex (KHM)256Foil Etched Food Chain (2X2)280
Japanese- Language Alternate Art Time Warp Foil (STX:MA)309Textured Borderless Foil Emrakul, the Aeons Torn (2X2)160
Foil Extended Art The Meathook Massacre (MID)151Green Soft Glow Hidetsugu (NEO)444
Foil Fang Frame Sorin, the Mirthless by Ayami Kojima (VOW)171Red Soft Glow Hidetsugu (NEO)1,828
Extended Art Foil Jeweled Lotus (CMR)400Borderless Foil Liliana of the Veil (DMU)173
Phyrexian Foil Urabrask, Heretic Praetor (SNC)492Phyrexian Foil Sheoldred, the Apocalypse (DMU)346
Borderless Foil Ancient Brass Dragon (CLB)352Phyrexian Foil Ajani, Sleeper Agent (DMU)692
Phyrexian foil (or foil-etched) Jin-Gitaxias (NEO)544The Tabernacle at Pendrell Vale (DMU:LL)46,767

I hope that this breakdown helps you make decisions about what to buy. The biggest takeaway for me is that the special versions of Sheoldred, a clearly busted Commander card, will go for a pretty penny indeed. If Ajani takes off, those twice-as-hard-to-pull versions will hit the stratosphere. And whatever you do, don’t go cracking packs hoping to hit a lottery-ticket-level rare Legends card.

Cliff (@WordOfCommander) has been writing for MTGPrice since 2013, and is an eager Commander player, Draft enthusiast, and Cube fanatic. A high school science teacher by day, he’s also the official substitute teacher of the MTG Fast Finance podcast. If you’re ever at a GP and you see a giant flashing ‘CUBE DRAFT’ sign, go over, say hi, and be ready to draft.