Numbers are a tricky thing. There is a reason that this topic, in some form or another, gets addressed again and again and again. Magic is a mutable game, and the rules of the game are such that elements of the game shift over time. We sometimes forget that the rules of old are not the rules of new.
Limited can sometimes remind us of this. There are definitely 16-land formats, 17-land formats, and 18-land formats. Clearly, these things are modified by the specifics of a particular deck or archetype, but there are definitely things about how you want to build a deck that are impacted specifically by the nature of that world. Currently, for example, Lorwyn seems to lean high in mana curves, pushing the 17 envelope into potentially 18-counts, whereas Invasion Block tended to be low on land, at 16, pushing to 15 (though with a metric ton of alternate mana).
One of the things that really helps us understand the way things change is to play other games, at least at some point. I cut my writing teeth online on USENET about a-majillion years ago, largely in two newsgroups, the Magic strategy newsgroup and the Vampire: the Eternal Struggle (nee Jyhad) newsgroup. Two results of that are very concrete: I ended up working at the Dojo and I ended up doing some design work for Vampire (the Ravnos from the set Final Nights were my design) and designing the foundation of the current tournament rules. One of the key lessons of working deeply in another game is that your knowledge of other systems can give you a different perspective in how games can work.
There are two massive differences between Vampire and Magic that actually can give you a useful frame of reference. One of the first differences is the method of drawing cards in the game (think of it as a game without a draw step, but with a Null Profusion in play on both sides). The second, though, informs my opinions in Magic greatly: there is no card limit in Vampire. Want to play 40 copies of a card? Go ahead. It better be the right card, though.
Another thing that furthered this experience was the lively card limit/no card limit debates in the early stages of the game, while the tournament rules were still largely in flux. One of the big differences in coming to the game of Magic being informed by this space is that I wasn’t as tied as many players are to fours. As you’d examine winning tournament decks in Vampire, you’d have people debate on the virtues of whether 7 copies or 8 copies were correct, or 4 or 6, or whether 15 was too many.
What is the relevance, then, of numbers?
It is simple. If we want to win in an event, we need our numbers to be correct. Sometimes having 59 cards correct in your deck, rather than 60 cards correct, can cost you a match, or a tournament.
One of the most interesting numbers in the game of Magic is one.
How can we know when a singleton in our deck is correct? That question is what this article address.
The Framework
I went much more deeply into an element of this topic earlier this year. One of the key points to remember in building any deck, whether it be a Sealed deck, Draft deck, or Constructed deck of any format, is that you’re working with a limited resource. While you build a deck, each and every single card in your deck has to justify itself. Patrick Chapin, by happenstance in our conversation or from forethought, introduced me to the idea of zero as the most common correct card count of a card in a deck. One of the things that comes to the fore of this, then, is the obvious need to examine a singleton in a deck.
It’s not just that a decklist with a singleton spell seems to stand out. I’m sure you’ve looked at a list and seen the conspicuous singleton in it and wondered why it wasn’t just chopped. It is, after all, only a single copy. Single copies, by their very nature, aren’t as likely to be drawn, so going from one copy to zero copies can, theoretically, increase your consistency. And, that’s good, right? Right?
Yes and no. Let’s go to it, from the obvious, to the not so obvious…
The obvious — the CL
Magic is a modified 4CL game. Four-card limit. One part of the modification is the part that allows us an unlimited number of copies of a card, so long as it is a basic land. The other part of that modification comes into play in Vintage, where some of the legal cards are restricted, and thus subject to a 1CL — one-card limit.
This is obvious, but it does bear stating. Remember, these cards are so powerful that these cards are far more demanding of taking a look at. But also, they are so powerful, they require far more consideration to cut. But cut, they may need to be. One of the hardest things about playing Vintage is the conflict between having focused lists, the large restricted list, and the limited real estate that all of the cards are competing for in your deck.
If you want a nice lesson in deck space management, dip your toes into Vintage. I expect that it will give you a lot of surprises.
Obvious, take two — the bullets (and friends)
The next most reason for a singleton is the presence of reasonable tutors in your deck. Take this list, from Max Bracht at Pro Tour Honolulu:
4 Drift of Phantasms
1 Maga, Traitor to Mortals
4 Sakura-Tribe Elder
1 Boomerang
1 Compulsive Research
4 Early Harvest
4 Heartbeat of Spring
1 Invoke the Firemind
4 Kodama’s Reach
4 Muddle the Mixture
1 Recollect
4 Remand
4 Sensei’s Divining Top
1 Weird Harvest
10 Forest
10 Island
1 Mountain
1 Swamp
That’s a lot of singletons. Maga, Boomerang, Compulsive Research, Invoke the Firemind, Recollect, Weird Harvest, Swamp, and Mountain. And each and every one of them is tutorable.
Take this list, one of my favorites ever, from the incredibly creative Ben Dempsey:
Temporary Solution — Ben Dempsey, Grand Prix: Boston
3 Exalted Angel
4 Gilded Drake
4 Meddling Mage
4 Silver Knight
3 Waterfront Bouncer
4 Brainstorm
1 Energy Flux
1 Engineered Explosives
4 Enlightened Tutor
1 Parallax Tide
3 Parallax Wave
4 Stifle
1 Worship
4 Adarkar Wastes
1 Ancient Den
4 Flooded Strand
6 Island
7 Plains
1 Seat of Synod
His targets: Energy Flux, Engineered Explosives, Parallax Tide, Worship, Ancient Den, and Seat of Synod.
Not every singleton in either of these decks is a bullet. The closest Bracht has to a “bullet” is Boomerang, and it is hardly worthy of the comparison. Instead, these singletons are eminently findable cards that can improve the performance of the deck, but not cards you actually hope to draw. You can keep high access to these cards that you might need, but avoid being bogged down by the card.
Compare this to the bullet, shorthand for silver bullet. These cards are just designed to take out an opponent. What does the poor Affinity deck do when you can consistently drop an Energy Flux in game 1? They’d better be able to race it incredibly well, or you’re doomed. Worship is similarly problematic for any poor Goblin deck when paired with a Silver Knight.
The key to including bullets and helpers is usually tested by need. Do you need the effect? We already know that it is unlikely that we don’t expect to simply draw a singleton, so the test of the card is in how it impacts a game. Take the one Flux; from a historical perspective, I can tell you that the cost of the card in the wrong matchup is real, but fairly small, but the impact of the card as a bullet target completely turned about that matchup from a loser to a winner. If there aren’t any Affinity decks in the field, it isn’t worth it. But if it a reasonable portion of the field, it really matters. Similarly, for other tutor targets, you have to decide whether access to an effect matters.
Tutor targets represent a very important part of deck construction, and deeply reward people that are imaginative (for finding a powerful target) or knowledgeable (for knowing their deck/the field enough to choose appropriate cards). If you are playing a deck with tutors, take great care to explore your options fully enough so that you can take the best advantage of your options.
Inevitability
Psychatog is the first deck that comes to mind when I think of inevitability. Inevitability might be the most remembered contribution of Zvi Mowshowitz to the game, but Psychatog is the deck that classically seemed to embody this concept. The Odyssey Block Psychatog decks all contained the ubiquitous Upheaval.
Many of these decks only ran a single copy, but not because they could tutor for it. Instead, the Psychatog deck knew that if the game went long, it would be found by then. The question of how long it takes depends upon a number of factors, largely the library manipulation present in the deck. In one, long ago article, I noted that in forty trials, the Psychatog deck averaged finding a random card in it by turn 6. The ability of a deck to find a card will vary from deck to deck, but this stat is still pretty illustrative about the impact of card drawing and other library manipulation in finding cards that are only found in limited numbers in a deck.
Inevitability has a lot more relevance when it is tied to cards that can deeply impact a game. Upheaval is so important because its existence in a deck has such a huge impact in the result of a matchup. There is a big difference between a deck that supports three or four copies of Upheaval and one, but there is an even larger difference between a deck that supports zero and one. In all of the non-zero cases, the deck can threaten to do something incredibly damning to the opponent if left unchecked. The more common “Upheaval” in Extended Psychatog these days seems to be Meloku. Meloku provides a dual role as kind of threat or a kind of answer for a long game that few other cards are even capable of producing.
For inevitability to matter, the card must greatly impact the way that the game is played. In my recent deck, Johnny Walker Red, the single copy of Furnace of Rath represents this kind of inevitability, but for a burn deck. If a game goes long, even if your opponent has been gaining life, even a lot of life, it often won’t matter. Generally the bar that must be met is profundity — is the impact of the card profound…
Analogs — As rulebreakers, subterfuge, and space-fillers
The concept of the analog is simple: is the card analogous, at least roughly, to other cards that exist in your deck. For some cards, determining analogy is trivial. It is clear that Fyndhorn Elf is not in any way distinguishable from Llanowar Elf, except in name. Even the distinction between Merfolk Looter and Thought Courier is essentially trivial. Slightly less trivial would be the difference between a Looter il-Kor and Merfolk Looter. Most common, though, is the analog of a card like Volcanic Hammer to Incinerate.
The essence of analogs is that they can function the same role in a deck as another card of a different name. A key use out of this is “cheating” card counts. If testing tells you that you want five copies of Incinerate, perhaps you need to find a “near” analog in the form of Rift Bolt #1, or Ghostly Flame #1 (or whatever card best suits your needs).
Subterfuge is a more interesting space, though. Clearly most cards are functionally similar, but have substantial differences. Take the Urza-Block Con-Troll deck that Brian Kowal and I designed back in the day: Miscalculation and Power Sink are not the same card. They function differently. Playing strange numbers (like a singleton Miscalculation) puts an opponent into a difficult place if they are gathering intelligence about your deck, whether before the match from hearsay, or during a match. One copy can look a hell of a lot like four copies if you don’t have an opponent’s decklist in your hand.
These processes are not unique to singletons, and are often used by cards where the counts are in twos or threes as well. It is worth remembering the option that these cards give you in singletons, though, especially as you get closer to trivially different cards. The subterfuge element becomes more worth considering. Are you better suited to running a 3/2 split in Merfolk Looter and Thought Courier, or is 4/1 better? What are you trying to make your opponent think?
The simplest reason to need to have an analog in your deck is to fill space. If you are running a “perfect 59”, and need a 60th card, sometimes you don’t want to increase your card count on a particular card to +1, and sometimes (in the case of a deck of 4-ofs) you can’t. Here, sometimes even the most imperfect analog will be sufficient, largely because of your confidence in the integrity of your card counts in the rest of your deck. Many of these filler cards are cards that have a “draw a card” clause on them, but other times, they are simply solid copies of a type of card in your deck. Another two-drop in an aggro deck. Another burn spell, like a singleton Forge[/author]“]Pulse of the [author name="Forge"]Forge[/author]. In most cases, these cards are generally just looking to further the typical performance of a deck.
Not every card is Ancestral Recall. Ancestral Recall probably has some level of diminishing return somewhere (you clearly wouldn’t want to play 60 of them in a 60 card deck), but regardless, that number is far above the typical 4CL, and worlds above the Restricted status that it lives at. Some cards, though, start giving you diminishing returns much, much earlier. Earlier, in fact, than a four-count.
The classic example of this are Legends. Take a look at this deck, my State Championship deck from a few years back:
Eminent Domain — by Adrian Sullivan and I@n DeGraff
3 Keiga, The Tide Star
3 Kokusho, The Evening Star
4 Icy Manipulator
4 Annex
4 Dream Leash
4 Wildfire
3 Spectral Searchlight
4 Dimir Signet
1 Island
2 Mountain
4 Dimir Aqueduct
4 Shivan Reef
4 Tendo Ice Bridge
2 Mikokoro, Center Of The Sea
1 Minamo, School At Water’s Edge
2 Miren, The Moaning Well
1 Oboro, Palace In The Clouds
1 Shinka, The Bloodsoaked Keep
1 Shizo, Death’s Storehouse
One of the most noteworthy things about this deck are its Legendary Lands. It is running eight Legendary Lands, and four of them are singletons.
Running single copies of Legendary Land is incredibly common. You’ll often see someone running a singleton Pendelhaven. There is some level of return from the card that is measurably better than another land, but it does have that little problem of being a Wasteland on any other copy of that land, whoever puts it into play. At what point is running extra Legendary copies of a card like putting a blank card into your deck?
This deck’s choice to run two copies of two key Legendary Lands in the deck is largely possible because of the presence of Wildfire in the deck. You can count on being able to sacrifice the card. If it weren’t for that factor of the deck, both of those cards would have most likely been singletons. The deck could not support a card that might be dead in multiples.
The classic example of this in non-Legendary contexts is in cards that do not actually have any function in multiples (or incredibly minimal function), other than insurance in case something goes away. I first learned this lesson at Grand Prix: Milwaukee, when my deck included in its sideboard 3 Price of Glory.
The first Price of Glory is absolutely incredible against a counterspell deck. The second? Not so much. While clearly, the card is a card that you want to see against them, if you get one out, you mostly don’t want to see another copy.
For a card to escape this problem, it has to be so damning on its own that it warrants extra copies. Cards like Worship, Choke, or City of Solitude are such complete hosers that it can be worth the extra copies that might be “dead” in multiples. Other cards often lack that virtue. Price of Glory was absolutely a card that I would be excited to bring a single copy of from the board against numerous matchup (with other analogs), but I will never again run multiple copies of it, unless somehow a deck exists that transforms it into a complete hoser.
The tie-ins
One of the things about all of these traits is that they are not necessarily mutually exclusive. A card can clearly fit into numerous of these categories, the most common of which is probably the tutor target that is also a card that fulfills inevitability. Conversely, it is also worth noting that fitting into a category or two is not sufficient justification for the inclusion of a card into a deck, though it is generally a necessary condition to warrant inclusion.
When you have a card that fulfills multiple conditions like that, it compounds the worth of a card in the deck. When we look at card lists and a card looks conspicuously out of place, one of the reasons it might look like it is because the number seems odd; by being able to recognize the traits that make a card potentially a good singleton, you can filter your perception so that actually bad singletons (or even simply potentially bad singletons) look conspicuous to you.
Take Grand Prix: Krakow, for example. I’m not sure whether or not Armin Birner’s deck is correct or not, but its choice of singletons look conspicuously suspicious to me, from a theoretical perspective. Conversely, Robert Jacko’s singleton Remove Soul seems like it might be correct, for a couple of reasons (analog for count, analog for subterfuge), though there are other reasons to be suspicious of it. Wafo-Tapa’s singleton Urza’s Factory makes perfect sense (inevitability, diminishing returns, tutorable), though the one Tolaria West seems conspicuous (is it a card count “cheat”…?) though there are potential justifications (diminishing returns).
Properly armed, you’ll be able to better examine lists for correctness. Remember, though, theory is no substitute for actually testing things out…
Until next time,