# 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.

All of today’s math will come from the Collecting Phyrexia: All Will Be One article, or explained using that math as a basis. That article has specific percentages, which I’ll copy over.

Also, we need to refer to this image to talk about what slot has what:

We are going to focus on the step-and-compleat slot, and the final slot with all of the Booster Fun treatments.

All of the numbers we’ve been given are percentages that have been rounded, and that’s a source of error I can’t control for.

In the Step-and Compleat slot, we’re given these percentages: “There are 6 commons (38%), 7 uncommons (29%), 26 rares (22%), and 28 mythic rares (11%)” Normally, I’d talk about the distribution of 10:3:1:0.5 that Draft Boosters have, but that math doesn’t work out. What we do know is that the cards which appear the least, the 28 mythics, make up 11% of your potential pulls.

What we do is multiply the percentage by the number of potential cards. In this case, that’s 11% times 1/28 to get a chance of 0.39% for a certain mythic. In terms of packs opened, you need to divide the denominator by the numerator, also known as taking the reciprocal. That gives you approximately 254.5 packs to open a certain mythic.

Let’s make this into a table for the Step-and-Compleat categories:

One thing we need to pay attention to: There are multiple versions of cards available in this slot, such as four different Elesh Norn, Mother of Machines with this foil treatment. You’ve got the same odds to pull any variation from the slot.

The other important slot is the final one, that compares everything possible except for the Step-and-Compleat versions. This includes something we usually don’t get: Foil Extended-Art versions of Commander and Jumpstart cards. Now here, we’ve been given some percentages for individual variations, rather than the overall number like we’re used to. As an example, we get “5 mythic rare Phyrexian-language planeswalkers (3%)” in the nonfoil slot. Because the nonfoil slot makes up 51% of the distribution of cards in the foil slot, I’m going to go ahead and run these rates in another table, taking the nonfoil rates and multiplying by .51:

The estimate of 500 packs is because Elesh Norn has two extra variants, the borderless manga and the Phyrexian, that the other Praetors don’t have in this set. Five variants in one set!

(If you really want the math: All copies of all variants for one card should be equal to all variants of another card at the same rarity. Since Elesh Norn has two extra variants, I split the rarity for the borderless concept Praetors, as those are all add-ins to this set. When we get to foils, these will be plenty rare enough. If I get more concrete data, fromWizards or large operations, I will update this and the running tally.)

Now we’re basically going to take everything in this table and multiply by .51, because we’re told that for foils, 49% of that slot is the extended-art rares from the set, plus select extended-art Commander and Jumpstart foils. They don’t tell us exactly which are foil options in the article, which is incredibly frustrating. When I have better information there, I will update the section about the FEA cards. There’s no FEA mythics in the main set this time around either–they all got one of the other variant frames.

So here’s the table with everything you can get in that slot, along with my estimates for the FEA cards.

Again, as I find out which FEAs are an option and which aren’t, I’ll update this table. This is the rarest possible outcome for the FEA rares/mythics, your odds will only get better from here.

I have also updated the Comprehensive Collection of Relative Rarities, so that you can sort out what the rarest pulls ever are. These special Elesh Norns are pretty high on that list!

As always, if you notice errors or want to talk about my methods, please reach out in the comments or the ProTrader 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.