Sullivan Library - Overcoming the 4-1 Dogma in Numbers
Writing about Magic is a very interesting thing. A lot of times a fantastic article idea will pop into your head, and there are a lot of things that can happen to keep it from reaching the "printed" page. Maybe you’ll be scooped (damn you, Richard Feldman!). Maybe your information will become largely irrelevant due to the rotation of sets or a new development on the tech front (oh, how often this has happened to a deck of mine). Perhaps you’ll be convinced to not write an article for tech concerns of your own (not wanting to say something because it might impact your own success at tournaments, or the success of your friends). And sometimes, articles just don’t want to be written. At least that’s how it is for me, sometimes.
Still, though, I keep a little notebook for article ideas. Sometimes it has the skeleton of an article, sometimes just the concept itself (I never wrote it, but my article about “How the Japanese Were Right!” was really good. Seriously. But, it would have been...), and sometimes thoughts about recent articles that simply need a response. Once you actually get into the writing swing, some really good articles can end up on the back burner just because there is something that is going on right now that needs your attention, especially when a particular new set comes out, or a deck list needs to be written about.
Two weeks ago, I mentioned how I disagreed with a number of writers about some things that are going on in Time Spiral Block, and that I’d be going into it in more detail “next week”. Well, I’d forgotten that Tenth Edition was on its way out, and so Ben Bleiweiss’s comments about the set were already in the pipe, pushing me back a bit. Then, the other day, I read Patrick Chapin’s article on a deck he’s terming ICE (Innovator Control), but what seemed to me a clear Baron descendent. I was going to call him up to talk to him about some suggestions for the deck, but he beat me to the punch and called me. We spent a long time talking about various ideas for the deck, but we ended up on a tangent about numbers that got me thinking about my old notebook full of article snippets, ideas, and skeletons.
It all started something like this:
“Come on, Adrian, some of those numbers of yours in decks are highly suspect!”
“Really? I’d be willing to defend very nearly every ‘strangely’ numbered decklist that I’ve played for at least the last six or seven years.”
“First of all, I’ve never played a tournament deck with Demolish. But, tell me, Patrick — are you one of those one / four dogmatists?”
“Oh, gosh no!”
The Dogma of the One/Four Crowd
There are a large number of important people in the Magic community that have proclaimed with booming voices of the superiority of decks that are built with the magic numbers of “One/Four”. That is to say, they advocate that the best decks are ones that have primarily four copies of a spell or one copy of a spell. The most visible proponent of this philosophy has got to be Randy Buehler, who can be heard making this proclamation from time to time in the video coverage of the Pro Tour.
The basic rationale for this is pretty simple. The best cards in your deck are very clearly cards that you should have four copies of, in general. Single copies of cards generally serve one of two purposes. Either they are cards there to be tutored, or they are cards that you’ll eventually run into if you go into an especially long game.
A classic example of a nearly picture perfect One/Four deck can be found in Buehler’s own “Buehler Blue”, a deck that he piloted to a 6-0 record in Standard at Worlds in 1999.
Decklists that run “strange” numbers (two or three) are usually viewed with extreme suspicion, especially as the two/three counts in a deck rise. It’s not that there aren’t occasions, they’ll say, that two or three of a card is correct, it’s just that the best decks will have few to none of those counts in a deck. This deck, for example, has only one card breaking the rule, the Masticore. There are some small exceptions they’ll make to the rule (usually on card counts of six or more — more on that later), but I’m sure that the sentiment has been parroted enough by this point, that regardless of who may or may not be the biggest advocates of this theory, you’re quite likely to have heard the concept mentioned.
It’s a shame that it is complete superstition.
Clearly the best deck at a tournament isn’t always the one that wins it. At the Pro Tour, there have been many, many times when people have argued that the best deck isn’t the one that gets the trophy at the end of the weekend, but some other deck, for whatever reason. Whether the winning deck is the best deck at an event like a Pro Tour is always something that people could argue about. It can even be argued that the winning deck at the Pro Tour could have been built better. But, these days, it simply can’t be said that the winning deck at a Pro Tour is actually bad. I invite players to try to find a bad deck winning a Pro Tour from any time after, say, Mike Long’s Paris win. I’m not saying that a winning deck couldn’t have been somehow better. I’m just saying you can’t find a list that is actually bad, on its face.
Let’s check out some recent winners:
Antoine Ruel, LA ’05: 6 non-4/1 spell counts (incidentally, beating Moreno’s
6 non-4/1 spell counts and 61 cards)
Gadiel Szleifer, Philly ’05: 4 non-4/1 spell counts
Pierre Canali, Columbus ’05: a more modest 3 non-4/1 spell counts
Mark Herberholz, Honolulu ’06: another 3 non-4/1 spell counts
Katsuhiro Mori, Japanese Nationals ’06: 8 non-4/1 spell counts
Paul Cheon, US Nationals ’06: 7 non-4/1 spell counts
Or, for real fun, check out the recent Top 8 of Pro-Tour: Yokohama 2007. Winner Wafo-Tapa runs 7, and what about the rest of them? 6, 2, 6, 5, 1, 5, and 5 non-4/1 spell counts. Clearly, players playing the most successful decks at the event used a wide variety of spell counts in their lists, likely because there are a wide variety of spell counts that are appropriate.
Can we put the 4/1 myth to rest? Can we just call it dead? Can we? I hope so.
How to go about thinking about numbers...
As Patrick and I got talking about dogmatic number counts, I defended his earlier accusation about wacko numbers. The thing is, there is something suspicious about 2s and 3s. And there is a reason that they are suspicious numbers.
First, though, let’s look at the number counts of cards in decks, from most common, to least common.
The most common “correct” number of card copies in a deck is...
As Patrick and I got going on card counts, he piped up and corrected us. “Zero is the most common correct number because most of the time, a card simply doesn’t belong in your deck.” Assuming you are playing, for example, the smallest currently played format, there are only 752 cards in the format (Time Spiral Block). Chances are you are playing zero copies of most of the cards in the block. Chances are even greater in a format like Vintage (8845 unique, legal cards). This may seem incredibly obvious, but it is important to point out that it is likely that the correct number of copies of a card in your deck is probably zero. This means that for a card to have a home in your deck, the burden of proof is on it. I’ll say it again, the burden of proof is on it.
This feature is also readily apparent as you work on a deck, particularly when a new set comes out. You try out the new card in the deck that you think is the correct card, and what you generally do is choose a card that already exists in the deck, change the card count from 4 to 0, and check out the new card. Often, the new card simply won’t work, and you don’t go from 4 to 3 to 2 to 1 to 0. Usually, you just drop the new card entirely.
The next most common “correct” number of card copies in a deck is...
Again, this may seem obvious, but it really bears stating. If a card is really, really good, and it has proven itself to be useful, it is really likely that you’ll probably be playing four of them. Oh, there are plenty of reasons that you might cut down a card’s count (more on that in a bit), but you’ll find it incredibly uncommon to see staples of a deck played in counts less than 4.
It’s simple, really. If it is a staple to our deck, we want to draw it. We’re only allowed 4 copies, and so that’s where we’ll stop. In other games, sometimes there is no maximum limit of cards that are allowed in a deck. Often you’ll find incredibly strange numbers of the cards that you really want to draw — seven in a fifty card deck, 19 in a sixty card deck. A card like Relentless Rats is a great example of how clearly we take for granted our 4s. In my old Wizards of the Coast column, I published a pair of Relentless Rats decks, but I honestly don’t know if either of them had the right number of Rats. Were 24 copies correct? 25? With enough experience in those other games or with a Relentless Rats deck, it can become possible to hone a decklist to the appropriate 12 or 14 or 17 or whatever number count that you might need, but generally in Magic, we have it easy. Our number is 4.
The next most common “correct” number of card copies in a deck is...
It depends, and often largely on the format that we’re talking about.
Clearly, in a format like Vintage, 1 is the next most common number, simply because of the number of restricted cards. Here, again, we’re butting up against a card limit. Typically, Magic’s card limit is 4, but in Vintage we have the extra card limit of 1 to contend with. Singleton and Highlander are also 1s, but that is a nature of the rules of that format.
But in other formats, 1 is the most common number when there are a sufficient number of good tutors for the existence of “silver bullets” to be appropriate. Silver bullets, for those of you not in the know are those cards that might not advance the specific strategy of your deck, but will tend to destroy a strategy that you might face. If there are enough good tutors, 1s can easily be fetched to tear apart an opposing deck, but sometimes you don’t even need there to be a sufficient number of tutors. In my old article “Building Singleton Psychatog” I found that using even the typical Psychatog decks, I could expect to find any individual card that existed in the deck before turn 6.
1s can also be common in format where we know that the format is largely going to go long. Let’s look at Paul Rietzl’s Grand Prix Anaheim Top 8 Psychatog list:
4 Accumulated Knowledge
4 Force Spike
3 Cunning Wish
3 Mana Leak
2 Fact or Fiction
1 Lonely Sandbar
4 Polluted Delta
4 Underground River
Paul knows that his deck is going to go to a long game, and in that long game he can essentially count on finding that Upheaval at some point. He might not need the Upheaval to win, but if he does, he’ll get there in the late, late game.
3s and 2s are far more complicated than 1s. There are plenty of reasons that you’ll need more than a singleton but you can’t pack a full set.
One of the most easily understood reason to drop to a 3 is because of the existence of Wishes. You can’t Wish for a card that is still in your deck, so if you’re going to be able to get the maximum use of a Wishable good card, dropping one to put it in your board is going to be a necessity.
The most common reason that you’d run 3s and 2s, though, is to manipulate the odds that you’ll draw a card. Essentially, you’re trying to help fix the timing of when you draw a card. If there is a card in your deck that you never want to see in your opening hand, running 4 of them is probably a mistake. Different people place different weight on exactly what time you’ll be seeing a card, on average, depending on the counts, but it is generally held that a 3-of is a card that you’re hoping to see early, but not in your opening hand, and a 2-of is a card you want to see at some point in every game, but not early. Both of those phrases (“early” and “at some point”) are both pretty vague, but the essence of them generally holds true.
A very common reason to play the 3s and 2s is to break the rule of 4. This has been covered many times before, but in essence, it is a way to run 5 or 6 or 7 copies of a card, simply by running some other version of the same cards. A Volcanic Hammer might not be an Incinerate, but it is often close enough that you can “count” them as the same card. Buehler’s single Miscalculation in his deck is essentially a 5th Mana Leak, or at least as close as he could get to one.
Probably the next most common reason to end up running less is the imposition of other “card limits”, and fulfills other needs that your deck has. Pretend, for example, that you’ve determined that your mana curve is such that you ought to be running 18 to 19 1-drops. Assuming that this is correct, for whatever reason, you’re going to have a situation where it is simply impossible to run 4 counts on all of your one-drop creatures. You’re going to have to make a decision about which creatures are simply the best and run 4-ofs of those creatures, while whichever creature is your “worst” will get the cut ever so slightly, and be dropped to a 3 or 2, depending.
This is one of those examples where the 4/1 purists get tetchy. They know that this is a reality in deckbuilding, and would argue that this is the perfect example of where deckbuilders go wrong. A list that should have a 4/2 split is played as a 3/3 split instead, creating two non-4 card counts instead of one. This kind of split is clearly the result of imprecise deckbuilding, they’ll say, and the thing is, often, they are right. But they aren’t necessarily right.
Sometimes what you aren’t simply bound by one need, but you’re bound by multiple needs. Let’s go back to that argument that Patrick Chapin put to me, that my count of 3 Avalanche Riders and 2 Lay Waste had to be a clear example of sloppy deckbuilding. Clearly if one was better, it should have been a 4/1 split.
I’ll tell you what I told Patrick. In the deck in question (Ponza, for Pro Tour New York ’99 — tied for Top 8, but no cigar...), I had 4 Wildfire, and I had determined that I needed more land destruction based on the metagame that I expected. All of the playtesting that I had done to that point suggested that I would need 5 more dedicated LD spells. On the other hand, I also had another requirement to fulfill. I was creature light, and needed a few more men. While playtesting made it seem very clear to me that the Lay Waste was the better card, I still needed more men than I was running, and so the Avalanche Riders pushed the creature count up to the 10 that I felt that I needed. In retrospect, after the event, I think that I should have only had 9 creatures, and the proper count should have been 2/3 instead of 3/2, but it still remains that the 3/2 split occurred in a fight between conflicting card space and multiple needs.
Our space in decks is a resource that we don’t want to push too terribly. There are only so many cards that we can reasonably fit into a deck before we begin to water it down. This kind of squeezing can sometimes happen simply because you have to accommodate a necessary amount of land. For most decks, for example, twenty lands are insufficient. Twenty-four might also be insufficient, but regardless, unless you’re running some multiple of four for your lands, you will have to squeeze out a spell, and probably a good spell, to accommodate your lands. The same can be true of nearly any very specific resource, whether it be creature kill, creatures, spells in a specific spot on the curve, or land. Proper playtesting can general find the sweet spot for any of these things, but it isn’t necessarily set in stone. The choice to include a particular card might decrease or increase your needs in other areas, simply by its interaction with the rest of the cards in your deck.
Card Count Analysis, at work...
Take the example of Buehler’s deck from Grand Prix: Lisbon, “The Forbidden Phoenix”.
Let’s look at the non-4s.
Obviously, Dismiss is one of those cards that Randy did not want to see in his opening hand. It’s inclusion, though, does allow him to up his counterspell count to a whopping 14. While personally, I’ve always believed Dismiss to be a pile of garbage, Randy clearly disagrees (note the 4 Dismiss in Buehler Blue).
The sole Mogg Fanatic is clearly a 5th Shock. Interestingly, though, it is also a 5th creature. While certainly not analogous to Shard Phoenix in how it performs, it does represent a creature that can block and attack. It is absolutely possible that the correct Shock count is 5, but it is also possible that the split might have been better as a 3/2 split, depending on the value of a 6th creature. My gut expects that 4/1 here is completely correct, but it might not be.
3 Capsize exemplifies perfectly another card that Randy doesn’t want to see in his opening hand, but it also is a card that he does want to start using quickly, so that he can “throw away” a Capsize by not buying it back without worrying. If his deck were such that it needed to Boomerang early, it would definitely be a 4, and if it never really expected to toss away a Capsize without buying it back, it would probably be a 2.
The 1 Scroll Rack represents both a pseudo-5th Intuition (they aren’t perfect enough analogs), but also a very late game means to survive if the fear of decking is a real possibility. In a deck like this, it is incredibly possible that your opponent will be able to hold you off via any number of means so that you could be in a position to be decked. 1 Scroll Rack ensures that you have insurance against that possibility.
1 Caldera Lake. Caldera Lake sucks. It’s a bad card. You probably don’t want to draw it. But by the same token, this is a deck that might regularly want access to UUUU, UUUUUU, RRR, RRRR, or RRRUUU. With very few options, the 1 Caldera Lake helps get a U and R count of 19 and 15, respectively.
A rational examination of a decklist should be able to puzzle out why numbers are what they are listed as. Many times, there will be a deck, even a good deck, that has really terrible numbers. Or maybe they are only seemingly terrible. Puzzling out which is which often requires an insight into why the particular numbers were chosen. Take this decklist, from the same Worlds that Randy Buehler took Buehler Blue.
Jakub Slemr, 6-0 in Standard at Worlds 1999
I have no idea about a lot of those numbers, and I designed the deck.
1 Bottle Gnome? Is the Bottle Gnome really a bullet? And if it is a bullet, where are the Tutors? Oh, I see. There is one Vampiric Tutor.
The problem here is that this decklist, which did incredibly well for the people who played it, was modified rather haphazardly. At some point a decision must have been made that the deck needed to have some more versatility, and so the Vampiric Tutor was added in (one copy?!), with a few bullets. This was accomplished by cutting a number of cards. One of the best cards in the deck was replaced in an attempt to “cheat a 5” by making a 3/2 split of Rats/Stupor. It all looks very “gut” to me.
Here is the original list, complete with the extra land that somehow got the axe:
Corrupter Black — Adrian Sullivan, World 1999 era Standard
Let’s analyze this, as we did Buehler, looking at the non-4s.
Let’s knock out the easy stuff first.
Land. The deck tested at needing about 23 Land + 4 Rituals. Phyrexian Tower was good enough to run as a card, but its Legendary status knocked it out of contention for a second copy, on the off chance that you screw yourself by double-drawing it. Volrath’s Stronghold was certainly powerful enough to consider playing a second copy, and the deck might have cut into its spells to fit it, but it simply wasn’t so good as to lose a spell. The 2 Spawning Pool provided for a reasonable special land without significantly cutting into the speed of the deck by coming into play tapped. 3, occasionally, made the deck chug too slowly.
The 3s. Each of Corpse Dance, Phyrexian Plaguelord, and Cursed Scroll were simply cards that you didn’t want to have in your opening hands in most matchups. You did want to be able to count on getting to them quickly, but certainly not in your opening hand.
That leaves the Gnomes. Here we have the classic example of semi-analogs. Each of the Gnomes fulfills a similarly role in conjunction with a Corpse Dance, effectively becoming a real problem when unanswered. But the deck definitely needs the life gain element of the Bottle Gnome/Corpse Dance. Clearly, it has to have at least two there. On the other hand, the deck also needs to be able to put pressure on the opponent, and perhaps kill more creatures. There are the Edicts, Kegs, and Scrolls (11 cards), but a little more could help. More importantly, the deck kills pretty slowly if all it has to go with are the 3 Plaguelord, 3 Scroll, 2 Pit, and Battle Gnomes (or Bottle Gnomes, if you prefer). A creature of a reasonable size has to be included, and yet, we still want to have synergy with Corpse Dance. Ticking Gnome is not a particularly exciting card, but it does fit the bill, by significantly increasing the potential of your clock, being a reasonable un-Corrupt-able creature, and having synergy with the Corpse Dance. You don’t really want to draw lots of Ticking Gnomes in general (that pesky Echo), but with the Tick and Battle Gnomes, you have a sufficient number of creatures to help hold the fort in the early game.
I always cringe when I think about what the Mogg Squad did with the deck (especially cutting a land — amusing that they complained about mana counts at that tourney), but I’m still pleased that the essence of the deck was able to help catapult two of those players into the Top 8 of that Worlds. The thing about bad numbers is that a deck can still be pretty good even if the numbers are off.
The Biggest Numbers Issue of Them All: 60/61
You should never have a 61-card deck. Never. It’s bad. Really, really bad. It is only the result of a lack of discipline. Or so goes the traditional wisdom.
In general, I agree with them. But it isn’t completely so rigid.
In a utopian world, we would almost certainly be building decks that were exactly 60 cards. Doing so increases the chances of drawing a particular card in our deck, which, since it has won its home in our deck, is a card that we theoretically want to see. Each card over 60 reduces our chances or drawing any individual card that we ought to want to have in our deck.
So why on earth would it ever be reasonable to have a 61 card deck? Isn’t it just foolishness?
There are a couple of reasons why building your deck as a 61-card deck might be correct, but essentially, they all boil down to the fact that it isn’t a perfect world, and sometimes you have to make concessions.
Let’s examine a hypothetical combo deck. Assume, for the sake of argument, that you’ve come to the conclusion that the deck absolutely requires 26 mana sources to function properly.
Unbeatable Combo Deck
4 Combo piece A
4 Combo piece B
4 Combo piece C
4 Tutor A
4 Tutor B
4 Force of Will
1 "Necessary" Answer A
1 "Necessary" Answer B
5 “Fast” Mana
22 “Normal” Mana
In this theoretical combo deck, we’re going to also assume that everyone and their brother, sister, step-child, and family dog knows about it. As a result, numerous cards have been introduced to the metagame that necessitate two “bullets” to be able to hope to go off versus resistance. Okay, fine, fine, fine.
But this deck is 61 cards. Something has to be cut, but what?
Over a large amount of time, perhaps the best card to cut could be discovered, but you’re uncertain which one it is, despite all of the testing that you, and perhaps even a team, are doing. You test and test and test, and you know that the deck is very powerful, but what on earth do you cut? One friend suggests only 3 Force of Will are necessary. Another suggests that 4 Fast Mana will do it. Another that a land can be cut, another that perhaps a Tutor. The problem is that the impact on card density in your deck in reducing a single one of these cards to make a 60-card deck is far greater than the impact on card density by having a 61-card deck.
Let’s examine that card density.
4 Copies/61 Cards - 6.557% density -- 4 Copies/60 Cards - 6.667% density
3 Copies/61 Card - 4.918% density -- 3 Copies/60 Cards - 5.000% density
2 Copies/61 Card - 3.279% density -- 2 Copies/60 Cards - 3.333% density
1 Copies/61 Card - 1.639% density -- 1 Copies/60 Cards - 1.667% density
So, if we move from 4 copies of a card in our 60 card deck (6.667% of our deck is that card) and we end up with a 61 card deck, our deck is only 6.557% that card — or 98.3% as full of the card as it used to be, but if we go to 3 copies of that particular card, we’re reducing that to 5% of the deck, a reduction of 75%.
Let’s look at how that works:
4/60 => 4/61 or 3/60 = 98.3% or 75%
3/60 => 3/61 or 2/60 = 98.4% or 66.7%
2/60 => 2/61 or 1/60 = 98.4% or 50%
1/60 => 1/61 or 0/60 = 98.4% or 0%
The 61-card deck reduces every card in your decks chance of showing up to only about 98.4% of what it used to be, but reducing the wrong card in your deck can have a devastating impact on the deck. It is even possible, in an incredibly tight deck, that 61 could theoretically be correct. (Though I will say that this is probably incredibly unlikely, and I can think of no deck that I would argue that this has been true for, historically).
The amount of playtesting that it takes to figure out which of the cards is the correct one to drop can sometimes be too much. Sometimes the actual bar is quite low (Billy Moreno’s deck from the Top 8 of Pro Tour, in retrospect, could easily have a card dropped, though many would argue which is correct), but it still might not be a bar that could be cleared by the resources of the player and deckbuilder. I’m going to guess that Moreno didn’t have the time to drop the correct card, but could have, with more resources.
In some cases, the bar is very, very high. If you’ve ever agonized about what card is the card that you should cut from a deck, and eventually just cut one, the impact is probably far greater than you realize. It’s probably far more effective to continue playtesting the deck as a 61-card deck until experience with the deck (and with the metagame) makes it clear that a particular card is the one that needs to go. That said, it is almost certainly much more correct to play with 61 cards than to cut the wrong card in some error in judgment.
I hope that this article has given you a good sense in how to think about interpreting deck numbers, and hopefully will help you when you’re honing your decks. Obviously, given enough time, you could theoretically figure out what the perfect numbers for a deck are for a given tournament, but sometimes you don’t have that time, and you have to wing it. With any luck, this will help you to better determine what your counts should be.