Deep Analysis - The Real Deal on 61+

I was a bit taken aback by Chapin’s article on Monday about his 66-card Teachings deck at Champs — but not for the reason most people were. Really, I was surprised to find I wasn’t the only one thinking about more than 60 for Teachings. As it just so happened, back in Time Spiral Block season, I legitimately considered beefing my Teachings deck up to seventy cards for similar reasons that led Patrick to play 66 at States.

As I knew it was a highly irregular idea, I only discussed it in earnest with notably open-minded deck designer Adrian Sullivan. After going back and forth about it for a bit, we eventually concluded that the costs outweighed the benefits, so I never played (in a tournament) or wrote about the 70-card Teachings list. However, the steps we took to realize this are both interesting and important; the costs outweighed the benefits this time, but it would be foolish to assume that will remain true in all cases.

There are plenty of dogmatists out there who will explain to you that decks must be 60 cards because It’s, Y’Know, The Best. However, I have never seen anyone put together any kind of – well, Deep Analysis, if you will – that acknowledges the reality that there are both upsides and downsides to running more than 60 cards. Being informed about the intricacies of this issue, rather than following a silly dogma, can lead you to do things like…oh, I don’t know, realizing that you can profitably add a 61st card to your deck just before Pro Tour: Los Angeles and then make the finals with it.

First Point: Ratios are Ratios

A number of people seem to be operating under the misconception that if your deck is larger, you will draw lands and spells in less-consistent proportions than you would in a 60-card stack. In fact, the ratio of lands and spells you draw actually depends in no way on the size of your deck, and only on… brace yourself… the ratio of lands to spells in your deck.

Barring library manipulation, a 60-card deck with 20 lands in it has the same chances of getting flooded or screwed as does a 600-card deck with 200 lands in it, or a 30-card deck with 10 lands in it. All three of those decks are 1/3 lands and 2/3 spells, so you can expect that if they are sufficiently randomized, all three will serve up the same mix of lands and spells in the long run.

Remember Battle of Wits decks? A lot of people wrote these off as “joke” decks, but they were consistent enough for Masahiko Morita and Akiro Asahara to make Top 8 of The 2005 Finals in Japan with stacks of over 240 cards. There’s a lot to be learned from these decks.

Take a look.

Battle of Wits

Akira Asahara

6th Place at Miscellaneous on 01-01-2006

Standard

Creatures (9)

Lands (93)

Spells (143)

Sideboard

Craziness, right? How in the world did he come up with that crazy mixture of lands, spells, and Signets? It looks like he just slammed together every Standard-legal card he could think of!

Asahara’s maindeck had 245 cards and 93 lands, meaning its manabase was 38% lands. A “normal” deck, on the other hand, with 23 lands out of 60 cards, has a manabase of… oh, that also works out to be 38% lands. Huh. Asahara also had 20 Signets and 4 Spectral Searchlights out of 245 cards, meaning that about 10% of the deck was artifact mana. A “normal” deck like this, on the other hand, with 6 Signets out of 60 cards would have had… hey, 10% artifact mana as well. Interesting.

It turns out those numbers aren’t as weird as they look. The land and Signet base is basically identical to that of Solar Flare, only enlarged from 60 to 245 cards.

Second Point: 4-of in 240 = 1-of in 60

In a lot of ways, a 240 card-deck operates like four 60-card decks stacked on top of one another. The main difference is that the maximum card count of four still applies to the stack as a whole, which has some obvious ramifications. While Asahara had 4 copies of Wrath of God in his deck, just like many Standard decks of the time, his concentration of Wraths was only 4 out of 245, or 1.6%. If you translate that ratio into a regular deck, you can see that in a 60-card deck, it would have been as though he were running Wrath as a one-of. Ouch.

Really, that’s the difference between a 240-card Battle deck and a 60-card deck: when you run a 4-of in the Battle deck, your chances of drawing it are roughly the same as your chances of drawing a 1-of in a 60-card deck. In that sense, Battle decks play out a lot like Jim Roy decks; even though they’re full of four-ofs, you can never really tell what to expect from the opponent’s hand. Even if you somehow work out that he’s got a 50% chance of having drawn one of his board sweepers, the question of whether that board sweeper is specifically Wrath, Final Judgment, Kagemaro, or Hideous Laughter can have a huge effect on your decision-making process. It adds a whole new level of complexity to your strategic choices, increasing the chance that you’ll mess up.

On the other hand, the deck is inherently underpowered compared to a 60-card deck with the same core card choices because the most powerful of those core cards will show up less often. Fortunately for Battle, there’s a certain five-mana enchantment that it can play as a core card that 60-card decks cannot, which is how Battle players justify diluting the rest of the deck’s best cards.

Third Point: 1-of in 240 = 0.25-of in 60

Asahara chose not to make use of this fact in his build of Battle, but it just so happens that you can pack four times the bullets into a 240-card deck for the same cost as you can a 60-card deck.

Consider the Genju of the Realm in Asahara’s board, a card intended to be fetched with Enduring Ideal and never, ever drawn. In a 60-card deck, playing a Situational Sally like this gives you a 1.7% concentration of do-nothings in your deck. Moving the other bullets in the board to the main (that is, Scour and Leave No Trace) would give you a full 5% concentration of Situational Sallies — far too high an incidence of do-nothings for the maindeck.

In a 240-card deck, though, Situational Sallies come at a “four for the price of one” discount. Asahara could have played Genju, Leave no Trace, and Scour in the maindeck, and would have had a lower chance of drawing any of them than if he had only added Genju to the maindeck of a 60-card deck. Both Asahara and Morita’s Top 8 lists jokingly included a Wandering Ones apiece just to underscore this; the odds of drawing a do-nothing one-of in a deck that large are laughably small.

Fourth Point: The Shrunken Sideboard

Your sideboard cards can – no, should – be incredibly potent. In the right matchup, Circle of Protection: Red can be utterly devastating, but you can’t really fit a playset into a sixty-card maindeck, because it’s a dead draw against any non-Red opponent. You can absolutely fit them into the board, though, and they will be one of your favorite cards to draw whenever you pair against Red. When you have a 60-card deck, boarding in a 4-of gives you a high concentration of that excellent card in your post-board games. When you’re Battle of Wits, though… not so much. Boarding in 4 CoP: Red in a 240-card deck is like boarding in the miser’s singleton CoP in a 60-card deck; yeah, you’ve got access to it, but good luck drawing the “one” copy.

The dilution of your sideboard slots is one of the least talked-about consequences of running more than 60 cards, but to me, it is the single biggest downside.

There is nothing I agonize about more before a tournament than my sideboard. Every slot is precious, and I am constantly wishing I had just one more slot to work with. Playing more than 60 cards works against this desire; to get the same effect as a sideboard that could only fit 1x Slay, Asahara has to cram four full copies of the card into his board. That’s more than a quarter of his total sideboard real estate gobbled up to add the equivalent of a 1-of in a 60-card deck. This problem is less exaggerated when you only go up to 61 or 62, but it is still there; you effectively decrease the number of devastating sideboard cards you can fit in the board when you game with more than sixty.

Somewhere Between 60 and 240

Now we come to my 70-card Teachings deck. I wanted to expand my deck size for many of the same reasons Patrick did. I wanted four Mystical Teachings in my deck to allow the maximum amount of chaining permitted by the DCI, but at the same time I did not want to draw them as often as I would if I played four out of sixty.

Teachings is a powerful late-game card, but an awfully expensive tutor for the early game. As Patrick noted, drawing two of them in the game’s early stages against beatdown can really gum up the works when all you want are efficient removal spells. With 4 copies, I was drawing multiple copies early on more than I liked, but when I went down to 3 copies, there were some games where I wouldn’t draw it at all — a big deal, considering how much of the deck’s desired late game revolves around Teachings — and I always wished I could find some middle ground. More importantly, with only three copies in the deck, my potential Teachings chain was not as long as it could have been.

In summary, I wanted to have a Teachings concentration somewhere above what 3 out of 60 works out to be (5% of the deck) but with access to 4 copies floating around in my deck. If I went from 3 Teachings and 60 cards to 4 Teachings and 60 cards, I’d have 1/3 more Teachings than I did before, taking me from 5% to 6.7%. To stay at a 5% concentration while playing 4 copies of Teachings, I’d have to go up to an 80-card maindeck, but I had found the 3 out of 60 concentration to be a bit too low anyway. Playing 4 Teachings in a 70-card maindeck gave me a 5.7% concentration of Teachings, which was almost exactly the same as running “3.5 copies” of Teachings in a 60-card deck.

The other big reason I wanted to go up to 70 cards was the bullets. I wanted access to all kinds of things in my maindeck – obviously Haunting Hymn and Pact of Negation, but also Slaughter Pact, Venser, Pull from Eternity, Strangling Soot, Spell Burst… the list went on and on. Like Chapin, I found myself wanting to play 2-3 more bullets than I could fit in a 60-card maindeck without cutting important spells.

I was happy with my 27 lands out of 60 cards, and wanted to preserve that concentration (45%), which meant that in my new 70-card deck, I would need 31.5 lands. Hmm. That math didn’t quite work out, so I tabled the question of 31 or 32 lands for later.

Wanting to add 2-3 more bullets while having an end goal of 70 cards worked out really well for me. Obviously if I added only bullets and land, I’d be doing more harm to myself than just exceeding the 60-card minimum – I’d be increasing my concentration of bullets, and therefore increasing my incidence of clunky draws. That wasn’t what I was after at all!

The solution I came up with was Foresee. Check this out:

+4 Foresee
+2 bullets
+4 lands

Going from 27 lands out of 60 cards (45%) to 31 out of 70 (44%) meant I was taking a slight hit in my land concentration, in a deck where – if anything – I wanted more than 27 lands. However, I was also adding 4 Foresee to my list. As long as I could make it to the four-mana mark, I’d have Foresee to help me get to the 6- and 8-mana marks, so it was like I was running “more” lands by decreasing my overall land count by 1% and adding 4 Foresee. (Admittedly, this didn’t quite make sense; if anything, I’d want more than 27 lands out of 60 cards in order to make sure I got to the 4-mana mark in the first place.)

This would have worked much better if I’d had something like Ponder to work with. There’s a lot of value in increasing the concentration of early-game library manipulation cantrips for a control deck, as they serve up mana in the early game and help guard against late-game dead draws, all the while digging you closer to the cards that you wish you could play more than four of.

The Drawbacks

4 Damnations out of 70 works out to be about the same concentration as 3.5 Damnations out of 60. That’s the quickest summary I can give of why I abandoned the idea. The card is so powerful and crucial to the deck’s success, that no amount of additional bullets are worth decreasing its concentration in the deck.

It wasn’t just the Damnations, of course. It sucks to lose 12.5% of my Damnations by going from 4 to 3.5 effective copies, but it’s not the end of the world. However, I was also losing 12.5% of my Careful Considerations, 12.5% of my River of Tears, 12.5% of my Tolaria Wests… you get the idea.

In a nutshell, the drawback to playing 70 instead of 60 is this: you lose 12.5% of your best cards.

Now, in all fairness, card drawing and library manipulation do help mitigate this. Remember that while I’ve diluted the concentration of busted cards in my deck, I’ve also increased the concentration of Foresees that dig me around the situational cards and help me find my best cards again.

It’s a bit counterintuitive to think that adding even more cards to the deck is going to make you draw your bombs even more, but cards like Foresee and Ponder really do fight against the dilution of the deck. If you think about it, the exact situation where adding a 61st card like Bottle Gnomes to your deck is a problem is when it’s sitting on top of the card you wanted. Let’s assume, for a second, that you really want to draw Mystical Teachings and that the top of your library looks like this.

Bottle Gnomes
Land
Mystical Teachings

Unfortunately, it will take you three draw to end up with a Teachings in hand. In a 60-card deck without Gnomes, the top would have looked like the following instead.

Land
Mystical Teachings

Here, you would have had Teachings a full turn earlier, after only two draw steps. It’s when those 61st cards get in the way of your four-of bombs that they hurt you. Now consider this stack.

Ponder
Bottle Gnomes
Land
Mystical Teachings

On your first draw step, you hit Ponder and cast it, reorganizing the stack so that Teachings is on top and Gnomes and the land are below it. If you have the mana, you can cast Teachings right now, in which case you actually got to your bomb card even faster with your 70-card setup than you would have with a 60-card version! If you don’t have the mana, you can still cast the Teachings next turn, which is the same turn you would have been able to cast it in a 60-card deck.

Of course, this isn’t the whole story. Teachings works well with this example because when you cast it, you shuffle away the offensive Gnomes. If Damnation was the card you were looking for, you’d still be stuck topdecking the Gnomes in a turn or two. There’s also the fact that Ponder costs mana. Only one mana, sure – and you can usually find an extra point lying around somewhere in the early turns – but when you really can’t spare it, the presence of the Bottle Gnomes will hurt you as much as ever.

Now here’s something interesting. After I wrote this, it occurred to me that I was kind of advocating a slippery slope. After all, if going from 66 to 70-72 to make room for Ponder (plus another land or two) makes sense, why stop there? Why not add as many Ponder effects as are legal? And why not go from 60 to 66ish in order to fit Ponders into an otherwise correctly balanced deck?

Over the course of trying to come up with an explanation for why it was a bad idea to go from 60 to 66 just for the sake of adding Ponder, I realized that… well, it actually might be correct in some decks.

Some decks.

Here’s the situation I came up with. Let’s use Zac Hill’s U/B non-Teachings Control for reference.

U/B Non-Teachings Control

Zac Hill

Test deck on 11-04-2007

Standard

Creatures (14)

Lands (25)

Spells (21)

Sideboard

Let’s assume Zac has done a good job balancing this deck’s ratios. He explicitly wants 4 out of 60 Damnations, 3 out of 60 Coldsteel Hearts, 2 out of 60 Vensers, etc. However, he frequently has access to a spare Blue mana, and could put Ponder to really good use smoothing out his draws.

Consider these two alternative turn 1 scenarios.

Scenario 1: I play Snow-Covered Island and Ponder. Ponder sets up my draws for the next couple turns. Maybe I now have a Coldsteel Heart to play on turn 2, where I would have otherwise topdecked it turn 3. Awesome.

Scenario 2: I play Snow-Covered Island and pass.

In general, I’d almost always rather play Ponder than nothing at all (assuming I have spare mana, which this deck often will), implying that it is desirable to have Ponder in the deck.

So how do I fit it?

Traditionally, I have two options. I can either give up and do without the benefits Ponder could bring to the deck, or I can cut some cards to make room. The problem with doing without it is that I’m missing out on some early-game consistency bonuses I could be enjoying, and the problem with cutting cards is that doing so will disrupt the deck’s existing, correct ratios.

More specifically, the problem is that I can’t just shave off a fraction of each of the existing cards. The smallest amount of trimming I can do to help fit some Ponders is to cut one full card, and that’s a big change in ratios. For example, I might try this.

+4 Ponder
-1 Makeshift Mannequin
-1 Mulldrifter
-2 Snow-Covered Island

That changes my ratios as follows.

Ponders go from 0 / 60 to 4 / 60, or 0% to 6.7%
Makeshift Mannequins go from 3 / 60 to 2 / 60, or 5% to 3.3%
Mulldrifters go from 4 / 60 to 3 / 60, or 6.7% to 5%
Snow-Covered Islands go from 6 / 60 to 4 / 60, or 10% to 6.7%

According to the Alan Comer Rule of cantrips (you can cut a land for every two cheap cantrips you add), it’s okay to cut the two Islands because I’m adding four cantrips, but I’m cutting the number of Makeshift Mannequins in the deck by a full third, and Ponder is by no means going to draw me into a third more of them to compensate.

Fewer Mulldrifters also makes Makeshift Mannequin worse, fewer Snow-Covered Islands make Scrying Sheets (and to a lesser degree, Mouth of Ronom) worse, and fewer first-turn Blue sources make Ponder worse. It’s entirely possible that after some testing you might conclude that Ponder is awesome enough that it’s worth it to accept these trade-offs, but if – as we’re assuming – the deck was properly balanced to begin with, then the ratios are now incorrect.

Because Ponder is a cantrip that doesn’t let you selectively “throw cards away” (like, say, Sleight of Hand or Serum Visions – the shuffling just isn’t the same in this case), the addition of the cantrip has also effectively increased the ratios of everything else in the deck. I’ll probably pumped about drawing more Damnations per tournament than I was before I added Ponder, but more Coldsteel Hearts? More Vensers? There’s a reason Zac wasn’t playing those as four-ofs to begin with.

Assuming this deck’s ratios were correct coming in, there’s just no way I can add Ponders and stay at 60 while maintaining those correct ratios. The only way to keep the ratios (very close to) intact is to go up to 65 cards or so. Add four Ponders and a Snow-Covered Island. If I do this, I miss out on the higher incidence of Damnation draws, but my concentrations all shrink by the same amount. The amount of Vensers in the deck relative to the amount of Mannequins, Mulldrifters, etc. will all remain almost exactly the same as they were in the 60-card version, because all I’ve added to the deck is a cantrip – that is, a card that turns into the card below it.

The only reason the ratios will be different at all is the addition of the one Snow-Covered Island that I might draw instead of a business spell (for better or for worse, mind you; I might want a land), the fact that sometimes I’ll choose to shuffle with Ponder, and the fact that I’ve decreased my chances of hitting a Snow card with Scrying Sheets. Minor quibbles aside, the 65-card setup will allow me to reap the benefits of free Sage Owl effects that help me make my land drops on time.

Again, is this necessarily a reason to jump from 60 to 65 every time? Clearly not. For one, I think that in the case of this particular deck, the benefit of increasing the Damnation and Shriekmaw concentrations (by simple virtue of adding cantrips) outweighs the cost of having to mess up the deck’s ratios. I doubt Zac would contest the claim that he didn’t get this list’s ratios exactly right, nor the idea that a better version of the deck might exist that has Ponder in it somewhere.

The fact is that certain ratios are impossible to arrive at when you are always dividing by sixty. Granted, I have yet to find the list where ratios are so important that it’s worth decreasing the concentrations of the best cards in your deck to get there, but that hardly implies that such a list will never exist. I would expect that it would happen in a deck where there are lots of comparable effects at the deck’s highest-power-level slots. A W/B/U control deck sporting both Damnation and Wrath as its most powerful cards, for example, is probably okay with decreasing its concentration of Wrath effects for the sake of some added benefit (like Ponder) if it wasn’t playing 4 of each Wrath equivalent in the first place. (See also: last year’s Solar Flare decks.)

In other words, keep all this in mind when you’re working on a deck that does not have a big gap in power level between most of its cards, and don’t let any dogmatic jokers tell you that you’re a lunatic if you consider more than 60.

The Last-Minute 61st

Finally, we come to an interesting corner case: Billy Moreno’s 61st card at Pro Tour: Los Angeles. Billy had been testing his deck for a very long time, and just before the tournament, apparently realized there was going to be more graveyard hate than he had expected. He suddenly found himself wanting another Cycling land in his deck to help guard against things like Coffin Purge nailing his dredgers. (The more cyclers he had access to, the more easily he could defend against these cards by cycling in response to dredge the key card safely back to his hand.)

However, Billy didn’t want to mess up his manabase by cutting some card he’d been testing with for ages to make room for the Lonely Sandbar he wanted to add. So what did he do? He just added in the Sandbar as a 61st card. This is a surprisingly reasonable position if you consider the Ponder arguments I discussed earlier. If you add something like Bottle Gnomes to your deck as the 61st card, you may wish you hadn’t if you really want a Circular Logic and end up with the following top-of-library stack.

Bottle Gnomes
Circular Logic

However, if your 61st card is Lonely Sandbar…

Lonely Sandbar
Circular Logic.

Curses! I really wanted a Circular Logic here, but all I have is this worthless Lonely Sandbar. Guess I can’t counter anything this turn… wait, what? What in tarnation is Cy-cling?

In his Day 1 report, Billy maintains that it was mathematically the right choice at the time to play the 61st card, but also implies that the situations for which he included it (Coffin Purge, etc.) did not come up as much during the tournament as he had predicted. Obviously if he had known that was going to happen going in, he says, he would have stayed at 60, but given the information available to him at the time, he says — and I believe him — that 61 was the way to run it.

The Wrap-Up

It’s frustrating to know that, even as I write this, there are a significant number of readers who will not take what I have to say to heart because the only example I could find of a “correct” 61+ deck was Moreno’s, and only then because of a technicality. It’s a tragically common defect in many players’ logic circuits that they cannot comprehend the notion that just because something has never happened before, it might still happen someday.

Granted, there’s a historically low chance that 61+ is correct; if you choose to run more than 60, you had better think and think and think and no, seriously, really really think about it first. But if you take that historically low chance of correctness and casually round it down to zero chance of success, you will miss out on the opportunity to be one of the few who stumbles upon a correct list of 61 or more, and your deck will miss out on a chance to improve.

Regardless, the real value in an article like this is the concepts that are discussed. Even if you never play a deck of 61 or more in your life, I hope you’ve gotten something out of the process of taking apart something as fundamental to decks as the number of cards to put in them. It’s not something that gets a lot of discussion, but questioning the basics like this is a great way to improve your understanding of deckbuilding and Magic as a whole.

Thanks for reading.

Richard Feldman
Team :S
[email protected]