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Ultimate Masters Limited By the Numbers

Ultimate Masters Limited in Numbers

You might want to know what Ultimate Masters has in store for you because it’s been in stores for a while now. But if you plan to attend one of the upcoming GPs in Vancouver or Prague, then you really should know. I will be at MagicFest Prague, and I’ve already done a couple of Drafts in preparation, though certainly not enough to feel prepared.

Since it’s harder to come by booster packs than with regular sets, it’s also harder to gain meaningful experience. A little knowledge is a dangerous thing, as the saying goes. Basing assumptions on a small sample bears the risk of being misled. After all, reality is but a woefully imperfect approximation of mathematics.

That’s why I decided once again to look at some numbers, specifically multiples of: 10.61%, 4.02%, 1.77%, and 0.67%. These are the odds, in order, to find any individual common, uncommon, rare, and mythic rare in a fresh booster pack, including foils.

Note that the percentage for mythic rares probably isn’t exact. When Wizards published the card list for Ultimate Masters there was some debate over what the increased number of mythics meant. A regular set has 53 rares and 15 mythics, which works out to each rare being twice as common as each mythic, with roughly one mythic per eight packs. But this set surprised everyone with 20 mythics, and suddenly all bets were off. Either individual mythics were rarer than usual or mythics would show up at a higher frequency than usual …

After following much of the online discussion and talking to a few traders myself, I believe the average to come to one mythic in about eight packs. The above percentage reflects this conclusion, but the exact ratio remains unclear at the time of writing. At least, it can’t be far off.

What (Not) to Do with These Numbers

Taking into account the different frequencies at which cards of the various rarities show up, it is possible to work out the actual average values for a lot of things. For example, I could tell you that green offers both the largest creature selection as well as the largest creatures, while blue has the fewest and white the smallest. White offers the most flyers, although blue’s are bigger. White also has the toughest color requirements, while green and blue demand the most mana overall.

None of this tells us a lot about the reality of Ultimate Masters Limited though. This format is characterized, more than most, by theme decks. It isn’t so much that synergy trumps raw card quality and that you have to seek it out. Although this is both true as well. Rather, it seems as if you can’t pick up any five cards without finding some kind of synergy effects between them.

Of course, as another saying goes, some are more equal than others. It’s difficult to account for differences in power level, but it is possible to know how common a particular theme is. How many enablers and beneficiaries can you expect to find in a booster pack, and in which colors?

Note that I consider the expected value per pack to be the most meaningful metric. It is tempting to calculate how many copies of a certain card appear in your average 24 boosters. It’s 0.96 for uncommons and 2.55 for commons, meaning that on average each Draft table only gets about one Spider Spawning. Yet another famous quote: If your theme doesn’t exist at common, it’s not your theme.

But an average over multiple unconnected events can be misleading, or to assign blame where blame is due: humans are notoriously bad at them. It’s the same as with throwing dice. Having just rolled a six doesn’t make your next roll less likely to result in a six.

As an example, I once drafted a Tethmos High Priest and two Conviction early in pack 1, and then also found myself with a pair of Martyr of Sands after the first fifteen picks. A plan began to form, and so I wondered: How many High Priests do the remaining sixteen boosters contain? Well, the answer certainly isn’t to subtract one from the Draft table’s overall average. In fact, this isn’t even the correct question to ask. A much better way to think about it is to consider that each new pack has a 10.6% chance to include another Tethmos High Priest (and a 4% shot at Sigil of the New Dawn).

My Idiot Life Draft Deck

By the way, I was surprised with the effectiveness of the Martyr combo. As Conviction was usually in my hand when I activated Martyr of Sands, even the early iterations of the loop often netted 9 life, and things got pretty crazy later on. Several times I took my life total well into the three digits despite being attacked for double-digit damage each turn. My only regret is that I didn’t get to draft this deck on Arena, where furious clicking may have earned concessions rather than timeout losses.

But enough with the concrete examples. We’re here for the abstract numbers. Let the madness begin!

The Credit Discard Game

How many cards allow you to discard one of your cards? How many benefit explicitly from such a discard happening? You can find this many in a booster:

I tried to limit the numbers in the “madness+” column to things that require a discard effect for a bonus or for savings. There are others that might want to move to the graveyard without making a stop on the stack. They have their own category further down.

All colors except for white have at least one common with madness. Red leads the way with two commons and one uncommon, while green only offers Basking Rootwalla, which can even be used by nongreen decks. White remains completely unmad but features Spirit Cairn. Technically, Bridge from Below doesn’t need discard to have an effect, but it would be literal madness to run it in a deck without any. Consequently, it appears in the colorless row.

On the enabler side, I didn’t include Wandering Champion because wandering into the red zone while controlling, say, a red permanent seems like too much of a red flag. The Champion also doesn’t work with Circular Logic and Malevolent Whispers. Blue has the second highest number of discard outlets on paper, but note that the awkward Skywing Aven, Dreamscape Artist, and Magus of the Bazaar make up a little more than 0.16 cards per pack.

In black, Olivia’s Dragoons and Liliana of the Veil account for 0.113 cards per pack, while Ghoulsteed again requires some work. Red has 0.32 copies of easy to use discard outlets, split between Faithless Looting, Mad Prophet, and Sparkspitter—plus 0.04 Conflagrate and 0.018 Gamble. Green has the strongest enablers in Wild Mongrel and Fauna Shaman, but also the fewest next to white’s lonely and tearful Icatian Crier.

The red-and-blue options mostly require a lot of mana. Blast of Genius asks for 6, while Desolate Lighthouse wants you to tap four lands. If you’re looking to save mana on Reckless Wurm, don’t look here. Discarding Fiery Temper to either, on the other hand, is highly recommended.

What this analysis boils down to is that the dearth of reliable and repeatable discard options outside of red almost makes Grave Scrabbler a black-red card. You can probably get a deck in blue-red or red-green where up to half your nonlands play into a madness theme, but for the full madness experience you need to draft black-red.

My First B/R Madness Draft Deck

My Second B/R Madness Draft Deck

As you can see, I may be biased based on my limited experience with the set, though it is notable how both of these decks only include four to six spells that are unrelated to the madness theme. Before playing, I would have counted Magmaw as well, but Sanitarium Skeleton, Malevolent Whispers, Sparkspitter, and especially dancing Scrabblers provided enough free fuel that the connection in practice proved pretty solid.

We Can Be Heroes

This is straightforward. Play a creature with heroic and target it. How many cards in a booster qualify for such a game plan?

The recommendation that goes along with these numbers is straightforward too. In Draft, it’s usually best to prioritize the enablers and to pick the payoff later. In this case, you really need the payoff first because it’s trivial to get something to target your hero.

The red heroes don’t grow by themselves and there are too few of them in green. So if your game plan is heroic, your main color will almost always be white. This focus becomes even more acute if you add 0.11 copies of Skyspear Cavalry to the above, which is somewhat of an honorary member of the heroes club. Note that the second column here isn’t limited to power boosts…

Included are Repel the Darkness, Nightbird’s Clutches, and Fire // Ice. Not included are spells that are liable to get rid of your hero, despite the fact that I can imagine a situation where you would want to kill your Phalanx Leader. Indeed, this should be more likely than to spend 8 mana on Eldrazi Conscription. So you might as well ignore the blip in the colorless row, unless you somehow got way too many Hero of Iroas.

White has Conviction and blue has Defy Gravity for repeated targeting at a rate of about 0.11 each per pack. Red offers 0.23 targeted spells with flashback, while you can expect 0.04 copies of Travel Preparations and Wild Hunger from a booster.

Enchanted, I’m Sure

True heroes don’t care what weapons they have to use. But some cards in the set like to surround themselves with an aura of superiority, or multiples. This many of them and this many Auras appear in a booster:

Things don’t line up perfectly here, I’m afraid, but are riddled with exceptions. Technically, Lotus-Eye Mystics doesn’t care about the subtype. Then again, with the exception of Angelic Renewal, Auras are the most likely enchantments to be found in graveyards. Well, except for Undying Rage.

Likewise, the total number of white Auras per pack encompasses 0.11 Faith’s Fetters, which isn’t great with Whirlwind Adept, Iridescent Drake, Sovereigns of Lost Alara, or Daybreak Coronet. On the other hand, Fetters is great with Heliod’s Pilgrim, excellent when retrieved by Lotus-Eye Mystics, and better with Hero of Iroas. The Hero, in turn, doesn’t have any more affinity than Wingsteed Rider for Auras like Hyena Umbra, Unstable Mutation, or Spider Umbra.

Finally, I consider just one hexproof creature to fit well into this theme. Unless we’re talking Eldrazi Conscription or Daybreak Coronet, enchanting Slippery Bogle seems like a waste of a perfectly fine Aura. Sigarda, Host of Herons, in contrast, doesn’t need an add-on to be a monster. Only Whirlwind Adept finds itself in the sweet spot where Flight of Fancy and various Umbras combine to make something much greater than the sum of its parts.

Overall, this is but a minor subtheme, though comparing the available Auras in white and blue with the total targeted effects in these colors—see previous subsection—suggests that a white-blue heroic deck will rely on Auras for most of its targeting by default.

Instant Success

Another minor motif in the symphony of the set is instants and sorceries. Only three cards care about them being cast, while five benefit from finding some in your graveyard. Nevertheless, this can act as a deck’s main plan, for three reasons. One is the high power ceiling of Young Pyromancer, Thermo-Alchemist, Talrand, Sky Summoner, and Rise from the Tides. Another is the abundance of instants and sorceries, particularly in blue. And then there’s also way more card filtering in this theme.

When I calculated how many cards in a booster interact favorably with instants and sorceries, I decided to disregard the set’s two prowess creatures and the negligible benefits of black’s spell mastery. These are the results:

0.15 of these blue cards are Archaeomancer, Mystic Retrieval, and Snapcaster Mage, which benefit from lots of instants and sorceries just in so far as to have a better selection. But if you managed to get one of the Rise from the Tides that appear with a 4% chance in every booster, then the ability to get a sorcery back from the grave changes things dramatically. Mystic Retrieval in particular will allow you to make reckless use of blue’s self-mill. This, in turn, is very important because Treasure Cruise is common and because many decks want to keep the graveyard well stocked with some card type despite delving.

The 0.04 copies of Living Lore per pack can be another way to retrieve an important spell, but they can also be a massive beating in their own right. If you’ve never cashed in an 8/8 creature to go on a Cruise, you haven’t really lived, or at least haven’t lived the dream, or the lore.

My Favorite Draft Deck

This segue brings us, at long last, to the biggest theme in the set…

Self-Mill and Benefits

The graveyard is valuable farmland in this environment. Almost all colors have some cards that get into the zone. You can find this many of them in a booster:

I counted as self-mill everything that’s able to move cards from the top of the library to the graveyard. All of these cards happen to do this more or less for free, as a bonus tagged on to some other effect, although the quality of said effect varies.

There are 0.106 copies per pack of: Deranged Assistant, Sultai Skullkeeper, Crow of Dark Tidings, Satyr Wayfinder, and Golgari Brownscale. It’s debatable whether or not that last one should even count. Dredging Golgari Brownscale doesn’t accomplish much and comes at the cost of having Golgari Brownscale in your hand.

There are 0.04 copies per pack of: Forbidden Alchemy, Golgari Thug, Grave Strength, Reviving Vapors, and Dakmor Salvage. Once again, dredging is only a bonus if you want to draw the card, and Dakmor Salvage in particular needs to be hit by some other self-mill effect first to do any milling itself. Also, Grave Strength is a misnomer.

There are 0.018 copies per pack of: Tasigur, the Golden Fang, Golgari Grave-Troll, and Life from the Loam. Tasigur is included here for its activated ability and is included in the “benefits from others milled” category because of delve. All dredge cards are counted in the “benefits from being milled” column, and these two actually hit all three columns.

I won’t go through all of the benefits. Just know that some are very small like flashback, or require specific circumstances to be beneficial at all. For example, Marang River Prowler, Bridge from Below, and Verdant Eidolon. Lots of cards, like Resurrection, Archaeomancer, Pulse of Murasa, and Death Denied like to see more cards hitting the bin because they look to return the best or most. Finally, a few can totally warp and win a game. Examples of such: Vengevine ticks the “benefits from being milled” box,  Rise from the Tides and Laboratory Maniac benefit from others being milled, and Spider Spawning checks both marks.

Others

Reanimator is a problematic strategy because it’s a three-piece puzzle. You already know the numbers for self-mill and discard. Together, Miraculous Recovery, Resurrection, Reanimate, and Unburial Rites come to 0.2 copies per pack. The sum of Reya Dawnbringer, Angel of Despair, Artisan of Kozilek, Ulamog’s Crusher, and Platinum Emperion amounts to 0.21 cards per pack. Balefire Dragon, Penumbra Wurm, Walker of the Grove, and Woodfall Primus add another 0.17. Some of these elevate Apprentice Necromancer from a mere one-shot effect to something greater, but it’s all a little hard to pin down.

There’s a 4% chance to find Furnace Celebration in a booster. The word “sacrifice” appears on 1.44 cards per pack. 0.43 can sacrifice others repeatedly. If you’re looking for a two-card combo with Sigil of the New Dawn, the most creatures that sacrifice themselves—0.29 not counting Offalsnout—appear in black. Shirei, Shizo’s Caretaker forms a two-card combo with Fume Spitter and Martyr of Sands of which there are almost 0.11 each in a booster. Stitcher’s Apprentice works too, but is painfully slow.

I have fed Magmaw with Grave Scrabbler ten times in one game. I too have evoked Aethersnipe and reanimated it on the following turn. But my impression is that these things come up when they do. While it makes sense to stay on the lookout for opportunities during the Draft, I don’t think I can shed much light with my usual process. Also, I’m not being paid by the word.

I’m sure I missed something somewhere along the line, or got some rarity wrong. If you find a mistake, let the world know in the comments!

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