The Math of Phyrexia: All Will Be One

Welcome back to this ongoing series of attempts to calculate exactly how lucky the luckiest pulls are for every set with Collector Boosters.

Phyrexia: All Will Be One (hereafter written as ONE) has some very interesting formulations, and every slot appears to have a variation in distribution. Thankfully, Wizards has given us a lot more information about ONE than they have for previous sets, making my task both easier and more difficult.

So let’s get into it, and calculate exactly our odds for opening certain packs, then compare those rates with chase cards from previous expansions.

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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.

The Comprehensive Collection of Relative Rarities

There have been nineteen sets (so far, ONE is #20) with Collector Boosters, and frankly, every one has had a slightly different formulation when it comes to calculating what goes where. 

I should know; I’ve had to figure out all of them. 

Each time I do, I put together a comparison table for rarities, but what I’ve made for our members now is a spreadsheet of the percentages and odds, sortable in whatever ways you want to use the data. I’m not a data scientist, just a Magic nerd who likes knowing precise things.

So here it is, the first comprehensive attempt at relative rarities!

For the spreadsheet, this is all for foils. Some of these are not able to be foil, such as Dominaria United’s Lost Legends inserts, but most of these are for the foils.

So here it is, the first comprehensive attempt at relative rarities!

Here you are, a link for this very useful tool:

The Comprehensive Collection of Relative Rarities

The odds that are listed are for you to pull a foil card of a certain rarity, in any version. Wizards has a method for cards that I think of as the double roll. First you roll to see what card you get, and then you roll to see which version of that card you get.

For example, in Kamigawa: Neon Dynasty, you have a 1/272 chance of pulling any given mythic from that slot in a Collector Booster. But because there are two different premium versions of Jin-Gitaxias, Progress Tyrant, the Soft Glow and the Phyrexian, you have a 1/544 chance for the Phyrexian version.

Sadly, there’s no simple way to create a database of the number of versions available. The workaround I’ve found is to find the card in Scryfall, and see how many options there are. 

I would also recommend that you do a search for my articles “The Math of…” in order to find a more comprehensive overview of which cards have which treatments. I try hard to keep things organized, and you should enjoy the fruits of this labor.

Those articles will also clarify why some sets have different entries for Showcase styles, or FEA. Wizards has done a lot of different formulations when it comes to which versions can be found in which slots.

There is a second sheet dedicated to the rarest versions of cards for each set, so we can keep track of which are the luckiest pulls.

As always, if you notice problems, please reach out in the comments or in the discord!

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.

The Math of Ikoria, Zendikar Rising, and Magic 2021

Yes, I’m finishing the cycle, the set, I’m covering all the bases.

This week, I’m giving us the math of the last sets I never wrote for, and after that, I can have a full comparison going on for every Collector Booster set. 

These aren’t terribly complicated, and frankly, I’m used to how these stack up, so let’s get to the sets.

Ikoria: Lair of Behemoths

We didn’t have anything fancy going on with the main set here, but we did get a slot dedicated to reskinned monsters. Remember when they had to rename ‘Spacegodzilla, Death Corona’ and it spiked as a meme-level interaction?

Also, the Showcase cards are separate from the FEA cards. The FEA are instead mixed in with the regular foil rares/mythics again. I appreciate that even though a sheet is 121 cards, they have found so many ways to mix and match.

Frame# at rare# at mythic
Regular5315
Borderless PW03
Showcase105
EA437
Godzilla67

For anything where different rarities are mixed, Wizards uses the booster pack model of distribution, as far as we know. This means for every one copy of a mythic rare, there’s 2 copies of a regular rare, 6 copies of an uncommon, and 20 copies of a common. So in the Godzilla slot, there’s going to be a whole lot of Mothra’s Great Cocoon going around. The pool of options for that slot is 20 Cocoons, 30 of the uncommons (6×5), 10 of the rares(5×2), and 7 mythics, a total of 67.

In the Showcase/Borderless slot, it’s 5/15/20/8 for the C/U/R/M numbers, and given our ratio, the pool of options is 218. Neat trick, pushing in 5 commons and 15 uncommons that will make up about 87% of the pulls from that slot.

For the FEA slot, we’ve got only rares and mythics, but a full set of the regulars mixed in. That means 53 plus 43, doubled, and then add the 22 mythics, for 214. So close!

Frame/Rarity% chance of any card with that frame/rarity% chance to open a specific card with that frame/rarityApproximate number of packs to open a specific card with that frame/rarity
Borderless Planeswalker – Mythic1.37%0.46%218
Showcase Rare9.17%0.92%109
Showcase Mythic3.2%0.46%218
FEA Rare20.1%0.93%107
FEA Mythic3.3%0.47%214
Godzilla Rare14.9%2.98%33.5
Godzilla Mythic10.4%1.49%67

Zendikar Rising

The return of Expeditions, and the unapologetic ‘everyone gets nonfoils as a box topper, but only Collector Boosters get foils’ of this arrangement. 

This was the first set where they just crammed all the good stuff into one slot, and then didn’t mix in the regulars. Separating the regular frame cards just made sure that the value dropped, as it used to be that regular foil mythics and borderless planeswalker mythics were dropping at equal rates. No more of that!

Frame# at rare# at mythic
Regular6420
Borderless 63
Showcase72
EA5115
Expeditions030

What we do get, though, is a whole lot. 64 rares, 50 mythics, for a pool of 178. Better odds than a lot of sets! The number of mythics is clearly goosed by the presence of all 30 Expeditions, each of which is classified as a mythic.

Frame/Rarity% chance of any card with that frame/rarity% chance to open a specific card with that frame/rarityApproximate number of packs to open a specific card with that frame/rarity
Borderless Planeswalker – Mythic1.6%0.56%178
Borderless Land – Rare6.7%1.1%89
Showcase Rare7.9%1.1%89
Showcase Mythic1.1%0.56%178
FEA Rare57.3%1.1%89
FEA Mythic8.4%0.56%178
Expedition Mythic16.9%0.56%178

Happily, this works out almost exactly to a point referenced in the Collecting article, that one in six Collector Boosters will have a foil Expedition land. I do love it when a plan comes together.

Core Set 2021

This is where things start getting unusual. This represents the first time that we got multiple versions of the same card, and it’s not just two versions of Ugin, the Spirit Dragon but a full four different versions of Teferi, Master of Time! Later on, they would adjust the collations so that no one card was more plentiful than the others, but this time, each version is expressly added to the pool as its own card.

Frame# at rare# at mythic
Regular5318
Borderless PW & Reprints48
Showcase59
EA457

The numbers don’t all add up this time, and that’s entirely due to the multiple frames. Irks me, really, but they fix this issue later.

There’s two slots we care about: The last one, with the foil Showcase and Borderless treatments, and the two middle slots that can give FEA rares and mythics. For this set, they dipped back into mixing regular frame foils in. What I haven’t been able to verify is which borderless cards from this set are uncommon. If you know, hit me up on Twitter or our Discord, tell me what research I missed, and I’ll adjust this table.

The Showcase slot has five commons and five uncommons, to go with 18 rares and 17 mythics, for a pool of 175. In the doubled-up slot, there’s 53 regular rares and 18 regular mythics to go with the Extended Art numbers, and that means our magic number is 221. However, there’s two bites at this particular apple, which the table will reflect.

Frame/Rarity% chance of any card with that frame/rarity% chance to open a specific card with that frame/rarityApproximate number of packs to open a specific card with that frame/rarity
Borderless Mythic4.58%0.57%175
Borderless Rare4.58%1.14%87.5
Showcase Mythic5.1%0.57%175
Showcase Rare5.7%1.14%87.5
FEA Mythic6.3%0.90%110.5
FEA Rare40.7%1.8%55.25

Normally, at the end of these articles, I put in a comparison table, but I’m reworking those tables into a living spreadsheet, which will allow me to rank where certain cards fall in comparison to each other. I can tell you, though, that these three sets had better odds than just about anything in more recent times, as Wizards figured out how to balance individual variations and lower chances. The set after ZNR was Commander Legends, where you had a 30% chance of having your foil rare/mythic turn into an Extended Art version, and that’s where the odds skyrocketed.

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.

The Math Of Throne of Eldraine and Theros: Beyond Death

While Throne of Eldraine has been out for several years, it represents the first set with Collector Boosters and therefore, the first time we had a real change in booster packs. Now we could get regular nonfoils, regular foils, Showcase/Extended Art nonfoils, and Showcase/Extended Art foils, the latter of which quickly became THE cards to have in Commander decks. Theros: Beyond Death follows suit, witha special slot for the Constellation foils

We’ve gotten a lot of variations on frames and special subsets since ELD came out, but I’ve had a few requests to run the math on the first sets and see how rare things were from those boosters, as compared to more recent sets.

So with that in mind, let’s do some Fae math!

Throne of Eldraine was the first set to systematically use Extended Art frames. Until then, we did get frameless/borderless treatments, but those always had new art. Extended Art was the same art as the original card, just zoomed in a little to show off more. It also turns the card type into white-text-on-black-background, a reverse of the card name. 

Impressively, Wizards showed some restraint when launching this project. Every card had exactly one variation:

Card Frame# at Rare# at Mythic
Regular5315
Borderless03
Showcase52
EA4810

You could get one of four versions of the card, ranging from most common (regular nonfoil) to most out there (special foil) and the prices of the cards reflects this range.

In the Collector Booster, Wizards had “One slot with 1 foil rare/mythic rare.” Given the incredible shenanigans of a Mystic Archive, Phyrexian Text, or the Lost Legends, this seems almost quaint. Thankfully for us, it’s also very easy to calculate the odds of pulling the more chase cards.

We know that Wizards follows a 10:3:1:0.5 rarity ratio when it comes to commons/uncommons/rares/mythic rares. That means there will be two of any rare for every one of a mythic, and the numbers are simple: 2×53 plus 15 is 121, but doubled because we’ve got all the regular foils and all the special frame foils.

It’s therefore that any particular foil rare is 1:121 to come out of a ELD Collector Booster, and any given foil mythic is 1:242. Interestingly, you have the same odds to pull a regular foil The Great Henge as you do an Extended Art version, but we’ve made the special frame that much more expensive.

Theros: Beyond Death is also a very straightforward calculation, made slightly more complicated by some of the choices Wizards made with the Showcase Constellation frames. Very little of this set is done with different art, something that they don’t really do anymore. 

Frame# at rare# at mythic
Regular5315
Borderless PW03
Showcase06
EA505

Sagas have no special version, and that’s why the numbers don’t add up cleanly. 

Luckily, Wizards had a handy graphic for what was in these boosters, explaining how Constellation cards wouldn’t be in the same slot as FEA cards.

One slot has the foil Demigods, Gods, and Borderless Planeswalkers. The Demigods are all uncommon, which means there’s six of each in the pool of cards for that slot, and only one of each mythic. You have a 1:39 chance to pull a specific foil mythic from that slot, and a 1:5 chance to get a specific foil Demigod.

That leaves only Foil Extended Art in the other foil slot, and with 50 rares and 5 mythics, plus the regular foils, the total pool of possible cards is 226. That means 1:226 for any particular foil mythic, and 1:113 for any given foil rare.

Card/SetCollector Boosters to open one (approx.)Card/SetCollector Boosters to open one (approx.)
Extended Art Foil The Great Henge (ELD)242Constellation Foil Klothys, God of Destiny (THB)39
Extended Art Foil Nyxbloom Ancient (THB)226Extended Art Foil Thassa’s Oracle (THB)113
Phyrexian Foil Vorinclex (KHM)256Foil Etched Food Chain (2X2)280
Japanese- Language Alternate Art Time Warp Foil (STX:MA)309Red Soft Glow Hidetsugu (NEO)1,828
Foil Extended Art The Meathook Massacre (MID)151Phyrexian Foil Sheoldred, the Apocalypse (DMU)346
Foil Fang Frame Sorin, the Mirthless by Ayami Kojima (VOW)171Phyrexian Foil Ajani, Sleeper Agent (DMU)692
Extended Art Foil Jeweled Lotus (CMR)400Foil Alternate-Art Teferi, Temporal Pilgrim (BRO)299
Phyrexian Foil Urabrask, Heretic Praetor (SNC)492Retro Foil Sulfuric Vortex (DMR)70
Borderless Foil Ancient Brass Dragon (CLB)352Retro Foil Sneak Attack (DMR)140
Phyrexian foil (or foil-etched) Jin-Gitaxias (NEO)544Borderless Foil or Retro Foil Force of Will (DMR)280

We can see that these first two Booster Fun sets have drop rates that are better than most of the more recent sets, when it comes to the most desired versions of chase cards. Nothing is extra-rare, even the mythics. It’s much easier to grasp these sets that have only a single special frame, instead of having a Showcase AND a Phyrexian AND a Borderless.

Eldraine and Theros cards have had some time for the prices to settle out, and we have a clear picture of what the cards go for. Those reprints should affect the prices, even things like Brazen Borrower being in The List, so plan accordingly. 

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