The Math of Universes Beyond: Lord of the Rings

Buckle up, people, because we’ve got a lot to talk about. Every set, Wizards gives us some information, and from that information, we can calculate very specific ratios and odds for what we can open out of Collector Booster packs.

So let’s get to it, and insert your own ‘find the precious’ joke here.

First of all, the whale in the kiddie pool. The One Ring (001/001) is the first serialized singleton in Magic’s history. There’s a couple other exceedingly rare, or one-of cards, in Magic’s history but those are prizes and giveaways. This time, someone’s going to open it. 

We’re outright told in the Collecting Lord of the Rings article that there’s less than a 0.00003% chance of opening the card. In math terms, that’s less than 0.0000003. If you remember reciprocals, that’s handy here as that decimal is also expressed as 1/3,333,333 and that’s how many packs we’re talking. 

Granted, there’s a ‘less than’ in that sentence, so it could be that there’s 3.5 million Collector Booster packs that are eligible. Or four million. We’re going to use the 3.3 million as a known figure, and know that the odds aren’t going to get better, just potentially worse. Wizards likes to be cagey about its actual sales numbers to the public, but this 3.3 million is a helpful guide for future sets.

So one pack in 3.3 million will have The One Ring. There’s three other serialized cards: Sol Ring with Elven art, Dwarven art, and Human art. Respectively, there’s 300 copies, 700 copies, and 900 copies. We know how many copies there are, and we know there’s at least 3.3 million packs, so we can estimate how many packs it would take to get one of those serialized Sol Rings.

# of copies# of packs needed% chance of opening in a Collector BoosterStated Odds
Elven Ring30011,1110.009%Less than 0.01%
Dwarven Ring7004,7620.0209%Less than 0.025%
Human Ring9003,7040.027%Less than 0.03%

That’s some long odds, but if Sam and Frodo could do it, don’t give up hope! Someone’s going to open these, and claim quite the windfall. 

Let’s talk for a moment about what we can get in terms of special treatments. Last week I wrote about the Box Toppers, and how every box gets a traditional foil. In Collector Boosters, those can show up in nonfoil in one slot, and Surge Foil in the final slot.

There are three special versions of LOTR cards: The Showcase Ring frame, the Borderless Scene cards, and Extended-Art cards. Every card has at least one of those, except for the Sagas, which exist only in regular frame foil and nonfoil. In the last slot in a Collector Booster, you can get any of these cards:

Type of Card (number of possible cards)RarityPercent chance for any card of that categoryPercent chance for a specific card of that category# of Collector Boosters needed to open for that card
Realms and Relics Surge Foil (30)Mythic0.8%0.026%3,846
Showcase Ring Treatment (14)Rare24.8%1.78%56.18
Showcase Ring Treatment (6)Mythic5.0%0.83%120
Borderless Lands (5)Rare9.9%1.98%50.5
Borderless Land (1)Mythic1.2%1.2%83.3
Borderless Scene Cards (21)Rare39.7%1.89%52.9
Borderless Scene Cards (9) Mythic8.7%0.97%103.45
Commander ‘Face’ Cards in FEA (8)Mythic9.9%1.23%80.8

Yes, you’re reading that right. Surge foil Box Toppers are going to be slightly more rare than Human Sol Rings. Given 3.3 million packs, there’s approximately 867 of each Surge Foil Box Topper. 

Of course, these aren’t serialized Surge Foils, and that’ll keep the prices lower. There’s also some less appealing choices in the list, such as a Thorn of Amethyst, that will mess with folks’ perception of what these prices should be. 

Here’s one thing that’s missing from that slot: Foil Extended-Art cards. Wizards hasn’t had a problem shoving all sorts of cards into one slot before, but this time, FEA cards from the main set and the Commander product aren’t going to be in the Collector Boosters. There’s slots for non-foil EA treatments, both main set and the Commander cards, but FEA got left out of these packs. 

Instead, they’ve been added to the Collector Booster Sample Packs, the two-card packs found inside of Commander precons. Here’s what’s officially in those: “a 2-card Collector Booster Sample Pack (contains 1 Traditional Foil or nonfoil special treatment card of rarity Rare or higher and 1 Traditional Foil special treatment Common or Uncommon card).” 

We know from the Collecting article that there are 28 rares and 9 mythics from the main set in the EA treatment. The Sample Packs have everything from the last slot in a CB, minus the Box Toppers and adding in those 13 FEA rares and 5 FEA mythics from the main set. There’s a stack of rares and mythics with no FEA version at all.

With all the options in a Sample Pack, here’s how the data breaks down:

Type of Card (number of possible cards)RarityPercent chance for any card of that categoryPercent chance for a specific card of that category# of Collector Booster Sample Packs needed to open for that card
Foil Extended Art from the Main Set (13):
Call of the Ring
Display of Power
Doors of Durin
Forge Anew
Horn of Gondor
Horn of the Mark
King of the Oathbreakers
Lotho, Corrupt Shirriff
Mithril Coat
Phial of Galadriel
Rangers of Ithilien
Sauron’s Ransom
Shelob, Child of Ungoliant
Foil Extended Art from the Main Set (5)
Andúril, Flame of the West
Arwen, Mortal Queen
Palantír of Orthanc
Radagast the Brown
The One Ring
Showcase Ring Treatment (14)Rare20.7%1.48%67.5
Showcase Ring Treatment (6)Mythic4.4%0.74%135
Borderless Lands (5)Rare7.4%1.48%67.5
Borderless Land (1)Mythic0.74%0.74%135
Borderless Scene Cards (21)Rare31.1%1.48%67.5
Borderless Scene Cards (9) Mythic6.67%0.74%135
Commander ‘Face’ Cards in FEA (8)Mythic5.9%0.74%135

We don’t have the same estimates on how many Commander decks get made as we do for the number of Collector Boosters printed, but it’s still an intimidatingly small ratio to get that FEA mythic. 

With all that said, let’s come up with some relative rarities for individual cards/treatments: 

Card/treatment/setApprox. number of CBs needed to find one copy
Elven Sol Ring (Serialized xxx/300)11,111
Dwarven Sol Ring (xxx/700)4,762
Human Sol Ring (xxx/900)3,704
Surge Foil The Party Tree (The Great Henge)3,846
Ring Frame Foil Tom Bombadil120
Borderless Scene Foil The One Ring 103.45

The biggest takeaway here is that Surge foils are crazy rare, and preorder prices bear this out. We should look for these to sell quickly, or at very high price points. 

Secondarily, we want to keep a close eye on the FEA cards from the main set that are only in the Sample Packs. Especially if there’s no other special version of the card, these foils are going to be opened quite infrequently. Prices might rise fast, and quantities will be low.

I hope all this math helps inform your buying, both of packs and of cards, and as always, if you have data you want to show me, please reach out on Twitter or our 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.