## Collecting MTG Arena: Part 1 (of 2)

#### by caliban // Apr 26, 2019

*DISCLAIMER: The following advice is primarily aimed at players interested in collecting complete 4x sets on MTG Arena and doing so as efficiently as possible. If you're grinding for Mythic Top 1000 in draft or plan to do 100+ drafts of every set no matter what, then you might not need it. But you don't have to go! You can stay if you want, we're all friendly here.*

**Link for collecting MTG Arena spreadsheet**

Magic has meant many different things to me over the years, but one of the things I've always been is a collector. I got bit by the collector bug early, and I've always wanted to "own every card" in some form or other. I gave up on collecting paper long ago, but I did have a complete MTGO collection until recently. While MTG Arena is fun and very fast, it didn't really appeal to me as a collector. With no trading system, collecting an entire set on MTG Arena used to be VERY inefficient.

__The way it used to be__: To collect one of each of 53 Rares from a single set with no trading, you needed to open an average of **276** packs - just to get at least ONE of every Rare. You'd have plenty of duplicates of other Rares and ~35 total Mythics but finding those last Rares is always tricky; the gods of probability are Rarely merciful. To get up to the 4 copies of each you'll want, you would need to crack **~600 **packs on average to get the 4x Rare set. Of course, if you drafted it (which you definitely should do) instead of just opening packs, the bots do pass Rares, and you'll earn some reward packs. Depending on your assumptions, doing **100-140 ranked drafts **to get 4x each Rare was in the right ballpark.

Now, couldn't I just use wildcards for the last few Rares and notably cut down on the long tail? Isn't that what they're for? Sure, but why would I want to do that? If the last Rare isn't constructed playable, it feels terrible to use a Rare wildcard on it, just to know that I have the set. But if I don't, there's a little nagging voice in the back of my head saying that *I don't have the set*. Such is the mindset of a serious collector.

Here's an analogy: I'm the kind of person who, while playing a Final Fantasy game, almost always chooses the "FIGHT" option. FIGHT is free! Even though there's plenty of ways to recover spell points (or whatever equivalent that particular game had), why spend them if FIGHT is good enough 95% of the time? Maybe I'll need my spell points later, so why would I spend them willy-nilly? I don't care if my mage deals only 18 damage with his silver dagger, as long as the fighters can finish the battle. I would go entire games only using magic to heal between battles and for bosses. Some would find that boring. I found it to be the way that I most enjoyed playing.

So what I'm trying to say is that on MTG Arena I have a great reluctance to spend ANY wildcards, ever. (For example, I've been playing a Mono-Red deck without any Goblin Chainwhirlers. It's good enough to get a few daily wins, and he's rotating in five months. Works for me.) Because collecting without spending wildcards was so difficult (and wasn't all that much easier even if you did spend wildcards) I just wasn't that interested in MTG Arena, figuring I'd stay on MTGO.

**Then they introduced duplicate protection.**

Almost entirely because of duplicate protection, they have now 100% lured me in as a customer to start seriously playing on MTG Arena and spending money, while also still collecting Common, Uncommon, Rare sets on MTGO (though no longer Mythics, it's too expensive to keep that up). Good for them! And I've been having a lot of fun on MTG Arena, collecting via jamming drafts instead of (on MTGO) playing a handful of drafts and then collecting via trading/buying, as I used to do. Duplicate protection feels like a win-win for both *Wizards *and the players. And I'm here to share what I've learned in the course of collecting 4x all the Rares in M19, GRN, and RNA. (All advice subject to *Wizards *randomly changing everything about how you collect cards.)

**1) Don't open ANY packs until you reach the Critical Point**

It's tempting to open packs when you see the little dot at the top of your screen telling you that you have some packs just sitting there unloved, begging to be opened. If you are even vaguely interested in collecting the set and saving your precious wildcards, don't give in! Don't open any packs until you have reached the Critical Point.

Here's the formula to calculate how many more drafts you need to do to reach the Critical Point:

R = Total number of Rares of that set already in your collection

P = Total number of reward packs of that set already in your collection

N = Number of "new" Rares you pull from a draft on average (Higher earlier, lesser later, but an average across the set is fine.)

W = Average number of reward packs from doing the draft.

D = Number of drafts you still need to do.

The formula for the Critical Point is (solving for D):

D = (53*4 - P*7/8*11/12 - R)/(N+W*7/8*11/12)

Constants: 7/8 is an adjustment for non-Rares (ie, Mythics) in the reward packs, 11/12 is an adjustment for getting Rare (1/24) and Mythic (1/24) wildcards, and 53*4 is the number of Rares in a set you need to collect.

Variables: N is about 3.5 from my observations, and that already accounts for the fact you pick some Mythics, so no further adjustment needed there. W is about 1.38, assuming 55% win rate in ranked draft. You go up to 1.45 if you can maintain a consistent 60% win rate (while Rare drafting, see below).

If you solve for D for a brand-new set where you don't have any Rares or packs yet, it now takes **47 ranked drafts** to collect a 4x Rare set. After you do your 47th draft, you can open your packs. That's a huge difference from 100-140, and it's all thanks to duplicate protection. And as fast (and fun) as MTGA drafts are, 47 is a VERY reasonable number of drafts to do in ~3 months' time, and this number barely depends on whether you win or not. Of course, the number of gems you spend cares quite a bit about whether you win or not, but we'll talk about that in-depth next time.

Why do you need to wait to open packs? Just to be explicit, it's because it's quite likely that later on while drafting you'll open up copies of the Rares that you already got from your early-opened packs. And that means each pack you opened was "wasted" in that it didn't bring you any closer to completing the set. Whereas if you saved it, because of duplicate protection, that pack would open a Rare you didn't have yet.

The above formula doesn't count weekly reward packs you earn for that set. That and possibly improving the variables above means that 47 is really the **ceiling** for how many drafts you need to do, but it may end up being much lower. Example: For M19, you get a bunch of free Rares from the tutorial, and I managed to average 4.5 new Rares per draft instead of 3.5. So I ended up needing to do only **31 ranked drafts** to get the 4x Rare set. Quite a difference from 100-140!

**2) You have to take every Rare and Mythic (unless you already have 4 of that particular one)**

When trying to collect the set, though, you need to be absolutely RUTHLESS when it comes to taking Rare and Mythics. If the pack has a Rare or Mythic you don't already have 4 of, you should take it, period. End of sentence. Even if it's terrible. Because of this, I've found it difficult to maintain a consistent game win percentage (hereafter "win rate"). For M19 I was at 50%, for GRN I was at 55%, and for RNA I was at 60% win rate (+/-1% each). I'm always passing Uncommons/Commons that would be great in my deck for some crap Rares. If you don't have the mental fortitude for passing good cards for crap and still trying to win, this system may not be for you. I personally find it kind of fun to try and win with slightly underpowered decks.

Here's the thing: how fast you collect the set (how many drafts you need to do, which is proportional to how many gems you need to spend, since you can't "go infinite" with ranked drafts) depends MUCH more strongly on how many "new" Rares you collect each draft as opposed to how many games you win. Every Rare that you pass is -1 Rare. Going from 55% to 60% win rate is worth about 0.6 game wins on average, which is worth a measly +0.06 extra packs. And a pack itself is worth only 0.8 Rares. So, +1 Rare is a lot bigger than +0.05 Rares. Like, a lot bigger.

You can't be trading value like 1 Rare for 0.05 Rares. On average, moving from 55% to 60% wins nets you 80 gems (i.e., you lose 80 fewer gems). And sure, earning more gems is better and makes drafts overall cheaper. But then you'll have to do more drafts to get the Rares you didn't pick, and each draft costs more gems. If your primary goal is to collect the set, I'm telling you that you will spend less overall by ruthlessly picking Rares and Mythics than by drafting only to "win".

Example: If you have 55% win rate while picking 3.5 Rares per pack, and 60% win rate by picking 2 Rares per pack (ie, only ones for your deck), then the number of drafts you need to do to complete the set moves from 47 to 68. And you'll end up spending 1500+ more gems AND have to sit there and do 21 more drafts. No thanks!

If you're A) planning to do 100+ ranked drafts of this set no matter what and/or B) a pro-level player that can improve your win rate 8-10% if you don't take the bad Rares, then you may not need to pick bad Rares quite so ruthlessly. For everyone else, if you're planning to collect the set by spending as little money and wildcards as possible (i.e. most efficiently), you should.

Before I really did the math, it was hard to resist occasionally picking a Gate Colossus over Smothering Tithe, Mirror March, or Immolation Shaman, etc. But if collecting is my goal, then it was never correct of me to do so.

**3) You have to maintain a spreadsheet**

It's absolutely vital at all times to know which Rares you already have 4 of. If you open one of those Rares, you then have a "free pick" for whatever will improve your deck the most - an Uncommon, or that Rare/Mythic (which is now worth 20/40 gems to you).

You need to maintain a spreadsheet of all the Rares and Mythics in the set, have it open while you're drafting, and update it after every Rare/Mythic pick. You may want to track Uncommons, too. Luckily, I have **just such a spreadsheet created for you, updated for WAR.** (Same link as beginning of the article.) Feel free to download it and modify it as you see fit. I've found it enormously useful to have. (It's provided as is, no tech support or warranty implied.)

**4) Mythic sets are as hard to get as you would expect**

All of the preceding is based on collecting Rares. If you want to collect a full 4x set of Mythics, you're in for the long haul. When you reach the Critical Point and then open your packs, afterwards you should have roughly half of the Mythics in the set. For example, for RNA, I had 28 of the 60 (4x15) total Mythics. It will vary by set size and how many Mythics the bots deem "crap" and pass all the time, but half is a decent approximation.

At that point, if you want to collect all the Mythics in the set without spending any Mythic wildcards, you should again save all of your packs until you reach the new Mythic Point. You can use a variant of the above formula to figure it out.

M = Total number of Mythics of that set already in your collection

P = Total number of reward packs of that set already in your collection

N = Number of "new" Mythics you pull from a draft on average (Higher earlier, lesser later, but an average across the set is fine.)

W = Average number of reward packs from doing the draft.

D = Number of drafts you need to do.

The formula for the Mythic Point is (solving for D):

D = (15*4 - P*1/8*11/12 - M)/(N+W*1/8*11/12)

Note the factors of 1/8 instead of 7/8. N (the number of "new" Mythics you get every draft) is harder to estimate than for Rares. The floor should be near the 0.375 (3/8) Mythics you open per draft. But bots do pass (bad) Mythics. Based on the data I do have, it seems to be between 0.5 and 0.55 Mythics you can take per draft, though it should decrease as you get closer to the Mythic Point. I've been setting N to 0.5.

Solving that gives us **92 ranked drafts**, very close to double the 47 ranked drafts for the Critical Point, which makes a lot of sense. That's 45 additional drafts after you've collected all the Rares. This is very much "on average" and is much less certain than collecting Rares, because you may open 3 Mythics in a draft or you may go 10 drafts without opening any. Bots may pass or bots may not. Opening packs may yield 1 Mythic every for every 6 packs, or 1 for every 10 packs. You will probably want to go a bit over what the formula says to ensure you really get 4x every Mythic and really need to spend 0 Mythic wildcards. For Mythics, you absolutely MUST take every Mythic you have less than 4 of. Every one you take is 1.5 less drafts you need to do.

Note that 92 drafts is also conveniently about the number of days that each set is the "new" set. If you do a draft every day, and only open packs twice - at the Critical Point and then at the Mythic Point, you should be able to get the entire set without spending any wildcards. If you know you are going for the complete set of Mythics, there's an argument to wait to open everything just once, at the Mythic Point. I don't have that kind of patience, but maybe you do.

On the downside, ranked drafts for that set won't be available the entire 90 days. So you may have to work in some traditional drafts, which are riskier but potentially more rewarding, as we'll discuss next time. Of course, if you are able to jam 5 drafts a day, you should be pretty close to collecting the entire set in the typical 14-day window that it's available for ranked draft.

**5) As you get close to the Critical Point, you'll still need to work on the Uncommons**

If your goal is to get all the Rares and not worry about the Mythics (i.e., you'll spend wildcards as needed for the half of Mythics you don't have that you want to play), you'll find that you'll still be missing a decent chunk of Uncommons. Bleh. For both GRN and RNA, I was missing about 30 Uncommons out of the 320 total. For M19, it was about 40. There's no duplicate protection on Uncommons, and rewards packs only have 2 each instead of 3. Yikes. You're completely at the mercy of probability and what you can draft.