# From the Deck: From Pack to Playset

Hey everyone. First off, I’d like to open with some caveats: the first one being that simply opening packs is a terrible way to get a playset of cards (though it is the fastest). Just like in mobile games, you can pay more real world cash in order to expedite your experience of collecting your set. The next caveat is that there is some pretty complicated math behind this science, math that I am going to completely ignore because the end result becomes you needing an absurd amount of packs to open in order to near-guarantee a playset of 4 of every card. And in doing so you would end up with hundreds of extra rares and dozens of extra legendaries which you need to deal with.

What I am going to do is break down the math behind purchasing a minimum number of packs in order to get a playset, assuming you have perfect luck (spoiler alert: you won’t). First I am going to tell you that I am ignoring Commons and Uncommons here. If after cracking the amount of packs we are looking at you are still short commons or uncommons, you will likely be able to easily pick them up on the Auction House to fill out what you are missing at minimal expense. Next, we’re going to need some data on how often you get Legendary cards from packs. Through countless pack openings, it seems that the agreed upon rate is around 1 in 9 packs have a legendary card instead of a rare. This means that the chance of getting a rare is 88.89% and a legendary is 11.11%; if you bought 100 packs, 89 should have rares, and 11 should have legendaries instead. This is vital information to have, as we’re going to see.

Armies of Myth has 72 rares and 18 legendaries in the set. This means that in order to get a playset of rares you will need 4 x 72 rares or 288 rares from the set. For legendaries, we have 4 x 18, or 72 legendaries to get out of the set. Doing some quick napkin math based on the 88.89% rate for rares and 11.11% rate for legendaries, we can see that in order to even get 288 rares, regardless of what card they actually are, we are going to need 324 packs (288 rares divided by 88.89). That’s just to get 288 rares! The remainder of the packs will yield 36 legendaries, which you can see is half of the number of legendaries we need to have the 72 minimum for 4 of each legendary.

This means in order to get to 72 legendaries, we need to double the amount of packs we are buying: 648. Now, on average, we will get 72 legendaries out of that many packs, which is the bare minimum we need in order to facilitate a playset of 4 x 18 legendaries. 648 is a crazy number, and if you buy them direct from Hex Entertainment, you’d end up spending 129600 platinum (or $1296) just in packs alone. But don’t forget there is a secret weapon to reduce the number of packs we need to get: the primal pack.

A primal pack’s distribution of 2 legendaries and 13 rares makes it a far more efficient way to get to a playset than the 1 in 9 distribution from pack cracking, but let’s look at how often you find Primals when you are purchasing packs. Again, countless purchases have shown this number to be around 2%. A number this low is going to cause all sorts of standard deviations. I know many of you will be tempted to fill the comments with messages like “I got 4 primals from 20 packs once” to “I bought 300 packs and got 2 primals, so the rate is way less than 2%.” Trust me, in the grand scheme of things 2% has proven to be about right so that’s what I am going to use.

If I purchase 648 packs, a primal rate of 2% gets me on average 12.96 primals… let’s call it 13. Now, this removes 26 legendaries that we are looking for and so our 96 count drops to 70. Of course, this changes the math of how many packs we need to get, so after a quick recalculation (yay, Excel) we’re at 414 packs… but then this changes our Primal number again. Uhg. Fortunately, in excel I have a formula that lets me punch in a number of legendaries I am seeking and it spits out how many packs that would need, how many primals that should proc, and then I can figure out how many primal-generated legendaries I have to supplement my packs with.

Eureka! *I know my math teacher is turning over in his grave now for not creating a formula to arrive at the number I got, sorry Mr. Marschand.* If I put in that I need 53 legendaries, I will need 477 packs to get that many cards. 477 packs gets me 9.54 primals, and that many primals gets me 19.08 legendaries, which (rounded down) gets me my 72 legendaries that I was seeking.

Of course, the odds of me actually hitting on all these numbers that are only chances (1 in 9, 2%, etc.) are compounded by the random nature of the packs themselves. I will likely fall short of several legendaries and maybe even a couple rares, but each defect represents a surplus I’d other cards that I can sell on the Auction House or trade with teammates or in the trade channel to fill out my set. Still, 477 packs is nothing to sneeze at—it’s a huge amount of packs. You can now see why I didn’t do the math behind the “no trading, no auction house” scheme, but we’re talking a pack count of well over 1000, and you’re likely to have a ton of extras in the pursuit of just a couple more cards.

Now you can see the value of opening your packs in limited events like draft and sealed. In those events you have a chance to turn 3 packs into 4 to 8, or 6 packs into 8 to 12. You need to win in order to see your packs start to multiply, but there’s plenty of other articles here on FiveShards to help you in that area. *Also of note: in draft format, you can occasionally sacrifice a pick in order to grab a rare that’s missing from your collection.—Ed.*

I hope this was enlightening to you. For the record, I don’t think a full playset of Armies of Myth will even be worth 95400 platinum on day 1, so spending that much on packs (and still doing the trading and supplementing you need to do to complete a set) just isn’t worth it in my opinion. Also, only a completionist NEEDS a full playset of 4 of every card. Many cards aren’t great in constructed format to begin with, and plenty others don’t lend themselves to being included as a 4-of. Focus on what you need for the decks you want to play first, then you can always pick away at the rest over time.

*Edit—Below are my actual results buying 404 packs and 4 additional packs at 2400p each from the Auction House. Check it out to see how my math worked out in real life:*

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Love this idea, but you will miss a lot of cards with 477 packs 🙂