Magical Hack – The Rule of Fours

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Debates have flared recently as to how to “properly” design a deck, with the bold statement that the number four is the “correct” number for most developed decklists. Simple in concept, this belief is grounded upon the perception that an ideal deck is one that is able to play the same sort of game over and over again with little variation, and the best way to get the same game over and over again is to use the same cards over and over again.

Debates have flared recently as to how to “properly” design a deck, with the bold statement that the number four is the “correct” number for most developed decklists. Simple in concept, this belief is grounded upon the perception that an ideal deck is one that is able to play the same sort of game over and over again with little variation, and the best way to get the same game over and over again is to use the same cards over and over again. While this is certainly reasonable, this presumption that the best decks play all fours is naive: it has the ring of truthfulness in some cases, but does not account for other pressures besides just drawing “the best cards” more consistently by playing the most copies of them.

Magic is a game of rules. You can play one land a turn. You draw one card a turn. You untap your permanents once a turn, and can attack once a turn. Magic deckbuilding has its own rules, too… and just like these rules of the game in Magic, they can be altered by the cards present in your deck. DCI rules dictate that you can have no more than four copies of any one card in your deck, except for basic lands or other cards that specifically say you can play more than four copies of a card in your deck. This “rule of four”, then, is already by its own definition flawed: it does not account for the fact that you can play more than four copies of some cards, those being Island, Plains, Forest, Mountain, Swamp, and Relentless Rats. Vintage players would also note that four is not the correct number for every card in your deck; try playing a Vintage deck without the Restricted list and you’ll likely find your life made a lot harder. Worse yet, try playing Vintage with four copies of Black Lotus and Ancestral Recall… your deck will be amazing, but you won’t even get to sideboarding in round 1 before you’re likely to find yourself ejected from the tournament.

Outside of these rules that are generally external to the game, however, imposed as they are by the Duelists’ Convocation International and their standards for acceptable tournament play and varying from format to format, you will find that internal to the game itself as well there are “rules” that alter the Rule of Four. Fastbond and Exploration alter the “one land per turn” rule. Howling Mine alters the “one card per turn” rule. Seedborn Muse or Awakening alter the “one untap per turn” rule, while Relentless Assault and others might just alter the “one attack per turn” rule. Within the cards itself you’ll find little rules that alter that simple numbers game as to whether four copies of a card is the right number, and a failure to account for the needs of cards as they are put into your deck is a critical deckbuilding failure.

Magic card valuation, after all, changes in context: every card has an effect upon the “rules” of the game, and thus every card already chosen for the deck – or worse yet, expected to be in the opponent’s – puts weight upon the card-pool to value some higher and some lower than their unbiased value. Magic is a complicated game, full of complex strategic interactions on every level… and yet even a much simpler game, Fluxx, has an intrinsically obvious shift in card valuations as the “environment” changes. Play the “Play All” card and suddenly “Ten Cards In Hand” becomes an impossible Goal; play a single Keeper like “Cookies” down on the table and it increases the value to you of every Goal that includes Cookies as well as every Keeper that is paired with it as a Goal… Milk is high technology when you can have “Milk and Cookies”, both in the game and in your kitchen. Those innocent “Cookies” likewise alters the value of Goals requiring that keeper absent, such as “All You Need Is Love,” and this is just in the simple microcosm of a hundred or so card deck that is completely static in each and every single game. Magic’s rules are just as implicit… start your decklist with “4 Remand” and you implicitly write at least twelve and probably more than twelve Blue sources, be it the lowly basic Island (snow-covered or non) or the accelerating Izzet Signet.

As a basic unit of presumed truth, either the number four or the number zero is correct in a vacuum. If a card is good enough to include in your deck (read: greater than zero), it’s probably a good idea to at least consider playing four copies. But like any very basic unit, considering it to be an absolute is incorrect: in deckbuilding, card quantities are a non-absolute… even at the highest level of tournament play, some agree with this fundamental concept and play fours of their best cards, while the Japanese have a two of this and a three of that regardless of the “opinions” on that card of the rest of the world. Many a winning Japanese decklist has been criticized by Brian David-Marshall and Mike Flores on their Top8Magic.com podcasts. Even if the argument is somewhere between “four Remands is more correct than any other number besides zero” and “but this deck won a Grand Prix in Japan, it must be perfect,” a failure to understand the context in which that decision was made for each and every card numeration, four or otherwise, does a disservice to your own critical thinking skills. The concept that determines whether a deck’s card choices are correct or not ultimately come down to whether or not a deck can play the same game over and over and win that game. If that means choosing a number besides four through an active process of testing and analysis to determine the correct numbers for that place and at that time, we learn that the Rule of Fours is more of a guideline, really.

In modern parlance, the Rule of Fours isn’t even called the Rule of Fours anymore: the existence of tutors in a variety of formats has changed it effectively to the Rule of Fours and Ones. The best cards for your core strategy clearly earn “fours” if they are that good… four Force of Wills in your Vintage deck, four Remands in Izzetron, four Burning Wishes in Aggro Loam. However, when card selectivity is so powerful that you can afford to massively increase the power of your deck against portions of the metagame via the addition of one “silver bullet” to defeat that particular opponent’s strategy in one fell blow, then it becomes clear that there is room to give a chance to a number besides four: you can’t tutor for it if it’s not in your deck, so zero is the wrong number, but its usefulness in other matchups is so minimal that it might as well be blank… clearly not a four. A simple cost/benefit analysis, presuming multiple decks in the metagame against which each individual “bullet” only has one effective target, shows very effectively that the number one is the proper number… just enough copies to tutor for, not enough copies to gum up your average draws when the card is useless.

This is so intrinsically understood as the first rule that breaks the Rule of Fours, besides “you can play more than four copies of Island, Plains, Forest, Mountain, Swamp, and Relentless Rats,” that it has wormed its way into the standard conception of the “Rule of Fours” as a deckbuilding concept. However, it will often prove true that exactly the sorts of decks that can realistically play singleton copies and get a significant value for them due to tutoring effects are exactly the sorts of decks that will profit most from hybridized numbers on all of their cards, to draw an exact balance of cards both by choice and by probability over the course of a game. By making such a concession to the notion that four is the most right number, we see the first hint that maybe, just maybe, those “fours” need just as much forethought and justification as some other deck’s “twos.”

The purpose of this article, then, is to examine a variety of rules that impact upon the Rule of Fours, to learn when the needs of a deck happen to alter the otherwise presumed state of Schrodinger’s Card: Schrodinger’s Card has four copies / Schrodinger’s Card has zero copies. After all, there are a few numbers between zero and four, and as the addition of other cards changes the needs and goals of your deck then it should only be a fair presumption that the numbers one, two, and three might sometimes… only sometimes… have a correct application. We have already proven the point for the number one in at least some cases, like one Rebel Informer in an otherwise mono-White Rebel deck in Masques Block Constructed, or one Chain of Vapor in your average Vintage combo deck. We will eventually reach a point when just one copy of a card you cannot tutor for might also be correct, but we’ll work our way through the numbers as we get to it.

A long time ago in a metagame far, far away, the concept of a “mana curve” was born. When previously people had relied on generally good cards and the fact that compared to everyone else they weren’t awful at Magic, suddenly decks that started trying to do the same thing over and over again started to do well. Simple in concept, these decks relied not (necessarily) on having four of this or four of that but instead on having an arbitrarily large number of cards filling an identical role at an identical cost, providing a consistent effect thanks to the power of math and careful balancing instead of relying on drawing the right card as your two-drop. Considering that these decks were using math to warp their design to fill a very specific function, it became common to see that when picking from an otherwise identical pool of cards some slight favorites would appear… but otherwise you were aiming to fill the slot with the right number, which might not necessarily be a multiple of four.

Imagine that we wanted to play a beatdown deck, and we had the following options:

Watchwolf — GW, 3/3
Rolexwolf — GW, 3/3
Swatchwolf — GW, 3/3
Timexwolf — GW, 3/3

Presuming that these cards are identical, and presuming that these cards are good enough to make the main-deck, it is easy to think that it might be possible that you wouldn’t want sixteen copies of the card X-wolf in your deck. For mana curve reasons, sixteen two-mana 3/3s might not play as well as eleven two-mana 3/3s and some more space given to spells or creature drops at other places on the mana curve. Presuming that we had a known number of copies we wanted to play — eleven — would it be correct to play them as such:

4x Watchwolf
4x Rolexwolf
3x Swatchwolf
0x Timexwolf

Looking at other slight pressures, you’d probably come more often to see these as three cards with three copies each and a mere two copies of the fourth, which is functionally identical to that same decision but with four-ofs. Other cards that exist around these cards… say, Meddling Mage or Cabal Therapy… might make it beneficial to hybridize the names of your otherwise identical cards. Even absent any cards that have an effect by naming specific cards (and thus punishing you for multiples), certain psychological effects can be gained via simple diversity: if your opponent sees Watch, Rolex, and Swatch, but no Timex, he might reasonably presume that you are playing approximately a dozen timepiece-wolves and play accordingly with near-perfect information. However, if your opponent sees Watch, Rolex, Swatch, and Timex, he might instead draw the presumption that you are instead playing the full sixteen timepiece-wolves instead of the actual eleven you are playing, and operate instead with less perfect information. While psychological ploys have literally zero effect upon deckbuilding, when all things are otherwise identical, they do have to get at least nodding consideration as one possible reason you might choose numbers besides four when choosing between otherwise equal cards.

One problem with the Rule of Fours is that it presumes that four is the most correct number, because four is the highest number of a single card that can be played and thus the easiest number to choose in order to streamline a deck. However, mana curve theory presents a second axis on which you can streamline your deck, not just to draw the most repeatable game after game by playing four-ofs, but by playing the same sort of game over and over again by delicately balancing proportions using numbers greater than four. The only reason we play four-ofs is because for the most part we can’t play fives or sixes, and nines are right out. However, to fill a mana curve can see an exact simulation of having nine copies of something: which card it is you’re spending that two mana for on your second turn doesn’t really matter, so long as the impact is the same. Presume that it was determined that a Blue deck wanted exactly six and no more than six two-mana counterspells, enough to have one every time on turn 2 but not so many that you run into problems of them becoming dead cards later in the game. Three copies of Mana Leak and three copies of Remand might very well be the correct choice for that deck, with that card-pool… even if Remand is generally considered to be a four-of in similar decks.

Filling a mana curve works for both creatures and spells, but the concept is more commonly applied to creatures than anything else. Spending your early-game mana efficiently is very important, either for aggressive potential, setting up a combo kill, or responding to opposing threats in a reactive fashion to establish a stabilized board position. If the greater purpose in deckbuilding overall is agreed upon as “creating a deck that can play the same game over and over again, and win that game,” simple math can dictate how many copies of a certain effect at a required maximum cost are needed to consistently allow for early access to that effect. Let us say, for example, that you figure your Extended deck needs exactly seven two-mana or cheaper creature-kill spells to have the right “flow” of cards in the early game every time. Four copies of Smother should be an acceptable choice, and one that all sides can agree upon as “accurate,” while three copies of Terror might hit the rest of the design quota for proper functioning without hitting that magical number, four.

Even in the presumed case of the decks with fours and “only” fours, card choices vary from that ideal depending on exactly how many lands you require in your deck. A deck with 20 or 24 lands can have 9 or 10 cards present as four-ofs, but a deck that wants 23 or 25 lands will be hard-pressed to suddenly turn that odd number into a multiple of four… and yet, to function consistently the same way game after game, you need to shave off the 24th land or add the 25th to get the same effect. Manabases in total defy the Rule of Four, because more so than with spells even it becomes obvious that four is not always the right number. In a two-color deck with very specific color needs, you’ll of course want to indulge in sufficient dual lands to get you to the right blend of colored mana… but take away those dual lands and maybe you’ll find you want fourteen of one land and ten of another, as was frequently a question in Odyssey Block Constructed U/G decks.

Good mana comes at a price, as well, and how much you are willing to pay for it is presumably also a variable very dependent upon an individual deck based on what cards are currently available and their intrinsic prices upon your time and resources. Steam Vents will take either a bit of time or a bit of life, but playing four copies generally doesn’t hurt too much until you start putting it with a larger number of friends just like it that also ask for one turn’s respite or a free Shock to use it now, while the number of Izzet Boilerworks that is “right” to place in your deck could fall anywhere on the spectrum between zero and four depending on how your deck’s mana curve plays out and how much you need to use just the one card to produce two lands’ worth of mana.

And so, so far, we have three clear-cut exceptions to the Rule of Four: tutor targets, manabases, and curve-huggers. Tutor targets are excellent to have as a one-of, in the traditional sense of a “tutor target” where the card wins the game against the right opponent and is an absolute liability in your deck against the wrong one. Manabases have their own rules and finesses, and are delicately reliant upon the stresses your deck and the opposition places upon them… which can be made quite clear if you have to design a deck for current Standard while minimizing your vulnerability to Cryoclasm. You can easily have access to Blue and White mana but a minimum of actual Islands or Plains, but only if you design that aspect into your manabase. Manabases ask for a set number of slots depending on what else is present in your deck, and even among that number of slots doesn’t necessarily break cleanly down into fours and ones: U/R Tron decks prior to Tenth Edition did, sure, with four each of the Tron pieces, four each of its dual lands, et cetera… but look at a Solar Flare or Angelfire deck’s lands and you’ll see a delicately balanced set of ones, twos, threes, and fours… each of which can be easily defended as right, and the correct numeration of each can be highly crucial to victory. Likewise decks that want to hug a mana curve and need X cards of cost or utility Y in their deck and don’t particularly care if the numbers are pretty so long as they do the right job the most often… in maximizing their efficiency and thus the ability with which they play “the same game” over and over again, they are using numbers larger than mere fours to dictate how the game plays out time and time again.

When you get to the less clear-cut ways of looking at things, we start to look at the cards themselves to learn how they change the rules of deckbuilding. Some are simple: the Legends rule makes redundant copies of a card effectively useless, at least for a time, so one must balance the desire to draw the card “on time” against the danger of drawing the card in multiples at the wrong time. Umezawa’s Jitte, pointy stick of doom for a year and a half in Standard, in some iterations like Extended sees play as a three-of, simply because the second copy did little if your opponent wasn’t killing your Jitte or playing their own… a card that was accepted as literally amazing, and so good that it necessitated inclusion even in some pretty strange places. Some cards that alter the rules of deckbuilding are even less obvious than the Legend example… as we are beginning to learn from our good friend Tarmogoyf, who cares very much about how many card types fill the graveyard how quickly, and might ask for us to bias the types of spells we play in favor of a variety that feeds Tarmogoyf’s size more consistently from game to game.

The lesson of Tarmogoyf is not really a new one, though, so much as an old lesson stretched in a different direction. The Affinity mechanic clearly favored playing as many artifacts as necessary, up until the point where it no longer gave direct profits and nonartifact lands and spells could be considered for the remaining slots. So, too, do we understand Goblins as a tribe… Block Constructed, Standard, Extended, and Legacy have all been ruled at some point by that particular breed of Red creature, who for the most part likes his friends to look a lot like him. Instead of homogeneity, however, Tarmogoyf flourishes in a heterogeneous world… ideally, one where an artifact, enchantment, land, creature, instant, sorcery, Tribal and Planeswalker card can all be in the graveyard, which in most cases means having drawn at least one copy of each card of that type and having somehow disposed of it already. Thus instead of playing four Sorcery-speed burn spells and eight Instant-speed burn spells, as in an example presented two weeks ago when looking at Gaea’s Might Get There, Tarmogoyf would rather live in a world where you played six Instants and six Sorceries, even if the number six still isn’t a multiple of four.

Recent looks at a similar mode of thinking have pointed out that it is sometimes redundant to draw a second copy of a card that would compete with itself for the same resource; two Psychatogs working together don’t have exactly double the usefulness of one Psychatog working alone, after all, just exactly double the potential to survive a spot removal spell or attack successfully around a blocker. This is a somewhat new or novel theory, attempting to dictate a “rule” of deckbuilding placed down by the fact that the values of an individual card shift over the course of an individual game and very much rely upon the context of the moment, similar to our oversimplification of the situation by looking at Fluxx instead of Magic in earlier examples. It states simply enough that a card that will fight with itself for necessary resources… in Psychatog’s case, fuel to consume in order to grow in size… grows less valuable when drawn in multiples unless that resource similarly doubles, and the need for its unique effect is still present when that quantity doubles. Two Psychatogs clearly are less than double the effectiveness of an individual Psychatog, because they require the same fuel to grow them; two Saltfield Recluses in draft might be less than double the effectiveness of an individual Saltfield Recluse, if you don’t need more than the one activation each turn to get the best use out of your Saltfield Recluses.

This theory, I would say, is already well-known… as it is a natural extension of the mana curve theory that we’ve already agreed can have an impact upon the “rightness” of the Rule of Fours, just with a non-mana component to their costs. While Akroma, Angel of Wrath is openly accepted as amazing when she’s in play, few decks indeed will play four copies of Akroma with the intention of paying full retail price on her. Not “just” because her Legendary status precludes the second copy from being maximally effective, but simply due to the fact that eight mana is a lot of mana. Mana resources are obvious and easy to acknowledge… you can only develop so quickly, after all, and an expensive card that you don’t get to play because you lose the game before it can be deployed from the hand is an active liability: with a cheaper card, you might have survived and turned the tables to win the game. Stepping away from the Legendary finisher Akroma, look very simply at the five-mana spot and up in Constructed. Five mana spells can have a very big impact, as you get more bang for your proverbial buck… but as cards that take time before you can even cast one and only then begin to release the bottle-neck on your resources as expensive spells cluttered your hand, it is reasonable to think that the number of an individual card you want of that nature might be less than four.

On the one hand, you’ll have less time to effectively deploy the card before drawing multiples becomes an active liability, since you wait so much longer than with cheaper cards to begin playing out your expensive spells. On the other hand, you’ll have more draw phases in which to draw that card, meaning that a card you play four copies of as a two-drop and a card you play three copies of as a six-drop might both have the same exact probability of appearing on their fundamental turns, and thus quite possible to consider “correct” despite noncompliance with the Rule of Fours. Effectively, additional copies of cards that work off of these sorts of resources… either high mana cost, or less tangible resources like those that feed Psychatogs that swing for lethal… have diminishing returns compared to the original as more copies are drawn before their fuel can be readily provided. Be it in the early game where the mana costs of your Bogardan Hellkites and Angels of Despair are prohibitively far away from effective deployment, or two copies of a card that both use the same resource or provide the same utility that is not necessarily doubled just because you’ve drawn two of them, the number four is not necessarily the automatic “correct” number for maximizing the usefulness of the card drawn against the uselessness of additional copies drawn.

It may very well be correct… after all, four Psychatogs is often considered to be more correct than three Psychatogs. However, the number four is not correct because the Rule of Fours dictates that this is so; like a crutch, the Rule of Fours is only a good guideline for proper deck design up until the point where you should be walking on your own instead of hobbling. Neither number is more correct in the abstract; both require justification and careful thought to earn that defining characteristic of “correctness.”

Another angle of consideration is that card velocity has an immediate impact upon the virtual numbers of cards as you will actually draw them; fill a deck with cheap cantrips and suddenly your four-ofs are drawn like six-ofs, as might be considered the case with the deck of interest in last week’s Magical Hack. High card velocity can cause three-ofs to be drawn “like four-ofs” in other decks, and even justify two-ofs as just slightly harder to draw three-ofs from a deck without that level of card velocity. It is worth noting that this card velocity does help smooth the consistency of the game… but is still maximally efficient when applied to decks that are otherwise designed for maximum efficiency. Thus, while all of these other rules like the Legend Rule and Tarmogoyf spell-type heterogeneity still apply and both mana and non-mana costs have limiting effects on the utility of individual cards (and duplicates), just because you can choose a game-plan with carefully-balanced two-ofs and such does not mean that this plan will be better than a plan using both high card velocity and four-ofs.

Increased card velocity inflates the rate at which one will draw their individual cards, letting a four-of feel like a six-of… and is not, in and of itself, an excuse to try and have “more” four-ofs by starting to cram in three-ofs and two-ofs when you could play more fours that feel like sixes. Card velocity – by which we mean the act of playing cards that get more cards that play more cards, such as Sleight of Hand into Opt into Serum Visions – inflates the effective number of all cards drawn in the deck, because if you draw or look at fifteen cards in the span of time your opponent has looked at just ten, you’ll effectively draw much more consistently because you’ve seen more cards and been given the option of selectivity.

As a standard theory, the Rule of Fours is an excellent guideline: it reminds us that consistency is key, and that playing the maximum number of copies allowed by the rules of deck design is perhaps the simplest way to ensure you draw the same cards with which to play the same game over and over again. As holy gospel, however, the rule is flawed as it does not acknowledge its known (and ever-growing) exceptions, and remains inflexible in the face of different flavors of consistency and different costs that can be asked for as the game plays out.

Some go far enough to add a caveat to their Rule of Fours, to include the notion of tutoring for cards that cannot be found with a tutor if they are not present in your deck, bringing us to the 4/1 Dichotomy of Deck Design. I fear however that including this first caveat and no others is a disservice to the thinker whose mind is bent to the task of designing a deck. There are many more reasons to justify playing both more copies of a card than one and fewer copies of a card than four, and little reason to just throw most cards into a deck and presume that the best number for them is indeed the number four.

Others go further and attempt to point out that there are non-mana costs, opportunity costs, and other concerns that can go into the same conceptual plan of “playing the same game over and over again, and winning that game” than just playing the maximum number of a card allowed by the rules of deckbuilding. In the belief that the number four is not an automatic, but instead just another number available for use, careful consideration of the cards and their functions and costs requires thought and justification before considering any number to be correct, even the number four.

After all, the needs of the deck are paramount, not a pretty decklist full of fours and not having a flashy one-of just to thumb your nose at the conventions of others. After all, the simple rule of thumb that “four copies makes for the best consistency” is only useful until it is instead not, and both conscious thought (rather than a slavish dedication to dogma or principles) and active playtesting (because we do playtest, right?) might posit an alternative number as the “correct” solution. Decks will win consistently on both sides of the divide, some with pure fours and others with muddy ones and twos and threes along with their fours, because the goal is not merely to have the cleanest decklist but instead to have the decklist that is the best there is at what it does. Each will win not because their perspective on the applicability of the Rule of Fours is more correct than the opposite view but instead because their application of the rule and its limitations is more correct. Sometimes building a deck that consistently does the same thing over and over again uses straight fours… and sometimes, it emphatically does not.

A philosopher a few hundred years ago once said “Cogito ergo sum“; “I think, therefore I am”. A much more modern philosopher instead suggested that this relationship was stated backwards: I am, therefore I think. The use of the mind is a powerful thing, able to discern patterns and relationships through thought and reasoning that otherwise would remain unknown and unknowable. Thought and justification of one’s actions and one’s decisions is always preferable to one’s sad devotion to some ancient religion… be it the Force, or the belief that only the number four can be right… even if both thought and devotion would lead one to the exact same choices. Thinking is always better than not.

Study, and grow strong.

Sean McKeown
smckeown @ livejournal.com