This article went longer than I planned, but it needed to explain booster collation so I’m not posting a TL:DR. It’s 2000 words, give or take.
Over the weekend, both paper Magic and MTGO had their prereleases for the new set, Dominaria.
Players were reminded just how good Icy Manipulator is in Limited, and got to play around with a whole lot of new legends.
The set has a real Kamigawa feel to it – there are Legends everywhere (albeit with names that are easier for an English speaker like myself to pronounce), and a number of intriguing build-around-me cards at the higher rarities. Although the Kamigawa block was polarizing, it has stood the test of time well, introducing at least two cards that are Legacy staples (Glimpse of Nature and Umezawa’s Jitte), many Modern staples and archetype-enabling cards, and it is one of the most significant blocks for casual formats like Commander.
I was hyped for Dominaria for this reason – and on top of that there’s the nostalgia of returning to the plane that the first set I experienced (Ice Age) took place on, and Saga cards that explicitly attempt to turn the stories of these sets into cards.
The MTGO prerelease, however, was marred by a significant issue.
Booster packs are not perfectly random, and this is by design.
Not considering factory errors, in paper Magic, you cannot open two of the same card in one booster. However, in packs with 10 commons, duplicates would actually be a very common occurrence if boosters were truly random.
To prevent this, Wizards de-randomize the packs. The first uncommon added to a pack is effectively random, but it then determines the other two uncommons in the pack. A more complicated system is used for commons, but the same principle applies – the first common put in the pack influences the other commons that can be added, and this is done in a way that prevents duplicates.
Foils break these rules (so you can open Dauntless Bodyguard and a foil Dauntless Bodyguard in one pack, but not two non-foil copies, assuming the system works).
So packs are not perfectly random. But this also applies to booster boxes.
If packs were randomized within boxes, players that opened entire boxes would regularly encounter duplicate and triplicate rares. While opening three copies of Steel Leaf Champion in a box would be a happy outcome, opening three copies of Two-Headed Giant would be disappointing or even infuriating. And most rares printed are not chase cards.
The probability of getting 3 or more non-foil copies of Steel Leaf Champion in a perfectly randomized box would be 2.148%. This isn’t high, but when you factor in that there are 53 different rares, you have around a 70% chance of having a triplicate rare in your box, around a 30% chance of having two or more triplicate rares, and a 10% chance of getting 3+ triplicate rares.
(Disclaimer: I’ve modelled these estimates with binomial distributions, which those of you with a statistics background will recognise are not perfectly accurate here. I’m confident that the estimate will still be close. If you want to run a Monte Carlo simulation of opening ten million boxes, feel free to report your findings, and the maths geek in me would be particularly interested in a rigorous analytical solution to this problem).
To avoid the extreme feel-bad of opening a box with three triplicate bad rares, Wizards of the Coast use a variety of sorting algorithms to decide which rares go into a box that minimizes duplication, just as they do with the commons and uncommons within a pack. They then add in further tweaks to reduce the predictability introduced, which led to the ugly phenomenon of ‘box mapping’ around six years ago.
The end result is a very complex collation system with a lot of moving parts, especially when paired with the 121 card print sheets Magic has used for a very long time.
Dominaria’s ‘every pack has a Legend’ adds to this collation complexity.
The MTGO Impact
That’s all been about paper Magic. Why does this matter for MTGO, where no informed customer ever cracks bulk boosters?
MTGO is designed to simulate paper Magic as accurately as possible, albeit with a few improvements (cheating is basically impossible, and the chess clock most judges would like to see in paper if it were feasible). It also has a few silly bugs, and an omniscient judge at every table.
MTGO is programmed to reflect most of the card collation decisions made in paper. This is true within packs (if you ever see two copies of Adamant Will in a Dominaria booster, one of them will be foil).
It is also true to an extent across multiple packs, making it impossible for a draft to open 3 copies of a given rare in one round of packs. I believe that the 8 packs opened simultaneously in each round of the draft are intended to mirror 8 packs that come from the same box. (This information is based upon my personal recollection of a now long deleted post on the old Wizards of the Coast forums from around ten years ago, so it may not be exactly correct).
This combines to give MTGO a very complex set of algorithims for card collation. And like we all know, when you have a very complex system, something can go wrong.
And in Dominaria, something did go wrong.
On MTGO, most players prefer non-foil cards, at least for cards in the various post-8E frames. The animation on foils performs poorly on many computers that can run MTGO just fine, and as a consequence people who open foils tend to dump them on dealers quickly. Dealers then compile them into complete sets, and these digital foil sets mostly get sold to paper MTG stores. These stores then use MTGO’s redemption program to swap these digital foil sets for foil sets of traditional paper cards. (Side note: Individual players can use redemption too, but it does not appear that these players are a large factor in the MTGO economy. Most redemption appears to be done by people intending to resell the paper cards).
A few hours into Dominaria prerelease events, the large MTGO dealer chain Goatbots realised that they were not being offered any copies of most of the foil Legends in the set.
Possibly because of the complexity of Dominaria’s collation, these cards simply did not get inserted into Dominaria packs online. At the time this article is being written, they still do not exist.
Why This Matters – for MTGO players
If you play MTGO and draft a lot, you probably sell most cards you open to dealers, in exchange for Event Tickets. You probably sell every foil you get, with the possible exception of nearly-valueless foil commons.
Dealers only pay for these cards because they are confident that they can compile sets and then onsell these sets in bulk to the owners of paper MTG stores.
Assuming one foil rare or mythic per 36 packs (this ratio has never been confirmed, and could be as low as 1:27, but I’ll write this assuming 1:36), every 4356 boosters of Dominaria opened online generates enough mythics for 36 normal sets and 1 foil set to be redeemed, as well as a bunch of excess foil commons through rares that don’t assist redemption as mythics are the bottleneck.
This isn’t quite true for smaller numbers of packs (e.g. if only 43560 packs were opened, variance would dominate and you would not have close to 10 of each mythic), but over the number of packs that are drafted during a set’s redemption timeframe on MTGO, these variances become less significant.
This sets a minimum price for cards on the MTGO secondary market. Assuming prices are reasonably similar to the last set of the exact same size (Amonkhet), 36 regular sets will typically sell early on for around USD 2520, and the foil set another 210. This $2730, spread over 4356 boosters, or approximately 60 cents per pack, is what I term the ‘redemption equity’ of boosters on MTGO – it’s the value boosters would be expected to have if you assumed that the only value of digital cards was to compile them into sets to sell to someone who will redeem them.
At the moment, it is impossible to compile a foil set of Dominaria. This means that foil cards have no redemption equity at all, and the redemption equity of each booster is consequentially around 5 cents lower than it should be, and this has been the case for every Limited event run so far.
We don’t know what caused the collation issue, and it’s entirely possible that the missing foils have been replaced by foil cards of the same rarity. However, this does not restore the missing redemption equity.
While a 5 cent rip off here and there doesn’t add up to much for an individual player – even if you entered six release events you’ve only opened 36 boosters of the new set for a grand sum loss of $1.80, it is still something Wizards should make good on.
Why This Matters – for Paper Players
If you don’t play on MTGO, this may seem like a storm in a teacup.
However, MTGO redemption has a large impact on the secondary market for foil cards in paper Magic.
Redemption is a huge source of cards – I know of one MTGO dealer (who is far from the largest one) that sells 600 digital sets a year to their third largest customer alone. Whilst I’ve never redeemed more than 20 of any given set, large paper chains redeem so many sets that they are sent on pallets.
And because foils are not particularly popular online but are hugely valuable in paper Magic, very large percentages of the available foils on MTGO are redeemed.
I won’t go through my methodology (as I’m not confident it is correct), but my best estimate is that about 8% of the copies of a given foil mythic in the paper game come from MTGO redemption.
If you are a paper player and desire foils from Dominaria, this will result in you paying more for them, and having a harder time finding them.
What’s The Solution?
I believe Wizards are right to have MTGO collation mirror paper collation, to ensure that booster draft online is a similar experience to paper draft.
And with systems this complex, mistakes will happen. Programmers are humans.
One of the best things about MTGO is that, unlike in the paper world where it is very expensive for WotC to replace a defective product once it has been sold to a wholesaler, then again to a dealer, then again to a player, on MTGO it is relatively easy for the system to retroactively give players additional digital objects for events they entered.
I believe the best way for WotC to fix this mistake is firstly, to fix the collation issue for future packs.
Then, they should give everyone that has participated in a release event a small promo pack for each prerelease they entered.
Some of these promo packs should contain one of the ‘missing’ foils, at a relative rarity that is carefully calculated so that these cards are no more and no less rare than other cards of the same rarity. My estimate is that about 1 in 5 packs should contain these foils.
For example, if there have been an average of 120 copies of each foil mythic in DAR ‘printed’ so far, the promo packs should be assigned probabilities that produce an expected 120 copies of foil Lyra Dawnbringer. The same should be done with the missing rare and uncommon foils.
Variance may then decide that there are 116 or 127 copies of a specific mythic foil legend printed, but that same variance would have applied to ‘normally’ printed ones anyway.
The remainder of these promo packs could then contain a tiny bogey prize – 5 or 10 play points, a random Modern-legal rare/mythic, or something similar.
Humans make mistakes. This mistake is pretty easily fixed, and should be fixed ASAP.
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