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In Development – The Twenty-Three Percent Solution

I was talking earlier this week with a friend about Bayesian reasoning. Put very briefly, Bayesian reasoning is a method in which you use evidence to generate the probability that something is true. In bioinformatics research, we can use these reasoning methods to look at what we know about something – say, a gene – and guess what it’s likely to be doing.

In a sense, this is what you do when you glance at a new deck list and immediately assign it a role. “Oh, right, this is an aggro deck.” What you’re really doing there is reviewing the cards, taking what you know about their traits, and then picking the likeliest classification for the deck as a result. You might not even be looking at all the cards when you do this – maybe you just saw [card]Stromkirk Noble[/card] and said “Yup, aggro” and moved on.

You’ve probably made the same judgment about Solar Flare. “Yup, control.” And that seems accurate to me.

But…what defines it as a control deck? What defines it as an effective control deck? And is there a way to enhance that effectiveness to suit the current metagame?

That’s what I’m going to take a look at this week.

What it means to be “control”

So what is a control deck?

Questions like these tend to have intuitive answers that focus on feel more than on a functional, “how it plays” definition. For example, we intuit that control decks are slow and grinding, and that they tend to linger in the White-Blue-Black color wedge. And that’s usually true…but it doesn’t mean that every White-Blue-Black deck is a control deck, for example.

Control means being in everyone’s business

At least for today’s discussion, I’m going to suggest that a control deck focuses primarily on cards and plays that intersect with its opponent’s lines of attack.

I’m told it’s bad to use that much jargon.

In case you haven’t kept up with my oeuvre, when I talk about lines of attack I mean different mechanisms a deck has available to win games or mess up opposing game plans. For example, a typical Red deck can win by attacking or by throwing burn at your face. These are two separate lines of attack, and they do not completely overlap – so even if you removed the ability to attack entirely, the deck could still just burn you out. Similarly, a mono-black Infect deck has several lines of attack including, well, attacking, proliferating, removal, and discard.

Consider Martin Juza’s Township Tokens deck from GP Hiroshima:

Township Tokens (as played by Martin Juza)

[deck]8 Forest
4 Gavony Township
4 Plains
4 Razorverge Thicket
4 Sunpetal Grove
4 Avacyn’s Pilgrim
4 Birds of Paradise
2 Blade Splicer
2 Geist-Honored Monk
4 Hero of Bladehold
2 Mikaeus, the Lunarch
4 Mirran Crusader
2 Mortarpod
3 Oblivion Ring
3 Overrun
3 Elspeth Tirel
3 Garruk Relentless
Sideboard:
2 Celestial Purge
1 Elesh Norn, Grand Cenobite
1 Fiend Hunter
1 Garruk Relentless
1 Garruk, Primal Hunter
2 Naturalize
1 Oblivion Ring
2 Sword of Feast and Famine
2 Sword of War and Peace
2 Thrun, the Last Troll[/deck]

Juza’s main deck has 27 cards that serve the “kill you with dudes” line of attack. It has only 11 cards that serve to disrupt the “kill you with dudes” line of attack – and that number drops to 8 if we don’t decide to count [card elspeth tirel]Elspeth[/card] (who has some limitations on her dude-killing abilities). Juza’s main deck has essentially no cards to deal with an opponent’s burn-based line of attack, or a discard-based one. In most cases, the deck is just hoping to get there first.

Thus, aggro.

In contrast, consider Akira Asahara’s take on Solar Flare from the same GP:

Solar Flare (as played by Akira Asahara)

[deck]4 Darkslick Shores
1 Drowned Catacomb
2 Ghost Quarter
3 Glacial Fortress
3 Island
4 Isolated Chapel
3 Plains
4 Seachrome Coast
3 Swamp
3 Consecrated Sphinx
3 Snapcaster Mage
1 Sun Titan
3 Day of Judgment
4 Dissipate
3 Doom Blade
4 Forbidden Alchemy
4 Mana Leak
3 Oblivion Ring
3 Think Twice
1 Unburial Rites
2 Liliana of the Veil
Sideboard:
1 Day of Judgment
1 Gideon Jura
2 Jace, Memory Adept
3 Mirran Crusader
1 Negate
2 Nephalia Drownyard
1 Nihil Spellbomb
2 Ratchet Bomb
1 Timely Reinforcements
1 Wurmcoil Engine[/deck]

Asahara’s main deck features just 7 cards dedicated to the “kill you with dudes” line of attack. On the other hand, it has 19 cards in the main deck that intersect with that same line of attack. Thus, control.

Naturally, there isn’t a bright, dividing line between aggro and control – I’ve just picked examples that rest reasonably far away from each other on both sides of that conceptual divide. Realistically, we’re just talking about the degree to which a deck has control features.

You’re only as controlling as your next matchup

If being a “control” deck is about running cards that intersect with your opponent’s lines of attack, it follows that the deck’s current worth as a control deck fluctuates based on what your opponent is playing.

That’s why we have the saying that there are “no wrong threats, only wrong answers.” If you’re only packing cards that don’t intersect with your opponent’s lines of attack, then you suddenly aren’t a control deck.

So with that in mind, we could do a simple tally of cards in our deck that apply to intersecting with each of the archetypes we expect to face.

Consider how Akira Asahara’s main deck stacks up against a number of major opponents:

Note that I’m not counting creatures as “intersecting” an aggro game plan here just by dint of existing. Sure, a [card]Consecrated Sphinx[/card] is a big body that can block, but it doesn’t explicitly do more than that to mess with your opponent’s long-term plan of trampling you to death with a [card kessig wolf run]Wolf-Run[/card]-fueled [card]Inkmoth Nexus[/card].

If we add in Asahara’s sideboard cards, his tallies look like this:

Again, this reflects my personal judgment on what’s useful in each case. The [card]Mirran Crusader[/card]s, for example, might help you win games against Wolf Run decks – it’s always handy to just walk by all those potential blockers. But they don’t need to help you disrupt the typical “Nexus, Wolf Run, kill you” plan the deck is on. So “good against deck X” is not the same as “controlling against deck X.”

This is what we’d expect out of a control deck or any deck after sideboarding, really. Sideboarding lets you bring in cards that have the express goal of intersecting with your opponent’s lines of attack.

But it also highlights the control deck’s dilemma – what happens when you draw the wrong answers?

There’s a way dedicated control decks deal with this, of course.

Indexing your assets

Let’s look at the other spells in Asahara’s deck – those cards that don’t have a job to do in intersecting an opponent’s lines of attack.

[deck]3 Consecrated Sphinx
3 Snapcaster Mage
1 Sun Titan
4 Forbidden Alchemy
3 Think Twice
1 Unburial Rites
Sideboard:
2 Jace, Memory Adept
3 Mirran Crusader
2 Nephalia Drownyard[/deck]

Some of these are your finishers. [card]Consecrated Sphinx[/card], [card]Sun Titan[/card], [card]Mirran Crusader[/card], and [card]Nephalia Drownyard[/card] all handle that job. [card]Unburial Rites[/card] is also a sort of “pseudo-finisher,” giving you a double rebuy on your other finishers. Some of our “intersection” cards were also finishers, of course – [card]Wurmcoil Engine[/card] ends games just fine, whether or not life gain works to disrupt your opponent’s plan.

If we cut out the finishers, that leaves us with:

3 [card]Snapcaster Mage[/card] 4 [card]Forbidden Alchemy[/card] 3 [card]Think Twice[/card] Sideboard:
2 [card]Jace, Memory Adept[/card]

…and they all have something in common.

They give us more access to our cards. Some of them do it in the most obvious way, by drawing us more cards. Others let us dig through our deck, giving us the combined advantage of card drawing and card selection.

Two big ways to index

As we just touched on, the most obvious way to have more access to your cards is to simply draw more cards. Cards that exist solely to draw cards act, essentially, to make your deck smaller. Consider the most basic option in Standard in this category, [card]Gitaxian Probe[/card].

In addition to the very useful benefit of seeing your opponent’s hand, [card]Gitaxian Probe[/card] effectively says “pay 2 life or a blue every so often to run one fewer card in your deck.” There are other features here, of course, since Probe is a spell. It can be countered, and it adds to storm count, although that latter one won’t matter here. But if [card]Gitaxian Probe[/card] resolves, your deck simply “becomes more compact” as a result.

We’ll look at the math on this in just a bit.

The other way to index is via filtering. [card]Forbidden Alchemy[/card] is a solid example of a filter, letting you review the next four cards in your deck and keep your favorite. In one sense, this also “compacts” your deck by letting you review a bigger slice of it. However, it’s not as clean a compacting of your deck as simply drawing a bunch of cards, since Alchemy requires you throw some of your cards away while you make your deck smaller. Other filtering cards simply don’t compact your deck, as they feed the cards you don’t keep back into it.

The numbers behind our indexing

So how good are these indexing options? Is a [card]Think Twice[/card] better than a [card]Divination[/card], or not?

To start considering this question, let’s take a look at what we gain when we deploy these spells. In the following table, I’ve grouped the cards by how far they dig you into your deck. Then, I’ve listed the likelihood that you’ll hit the target you’re looking for if it’s a three-outer (gotta get that Day of Judgment!) or a six-outer (gotta hit removal!) and you’re casting the spell in question on your fifth turn on the play.

So, to be clear, this means that if I am digging for one of my three copies of [card]Day of Judgment[/card] on turn five, a [card]Gitaxian Probe[/card] will get me there 6% of the time. In contrast, [card]Forbidden Alchemy[/card] will get me there 23% of the time…except now I’ve spent three mana and I’m likely not able to cast Day the same turn.

Rather than be coy, let me cut to one of my big punchlines right here.

Ponder is a beast.

More specifically, [card]Ponder[/card] is a beast when it comes to hunting for that one card you desperately need. It is perhaps unsurprising that it got hit by a ban in Modern. For a solitary blue mana, Ponder gives you basically the same digging power as [card]Forbidden Alchemy[/card], and nearly twice the power of a twice-cast [card]Think Twice[/card].

More on that in a bit, though.

First, let’s look at one other math case – Jace. What [card jace, memory adept]Jace, M.A.[/card] do for me in terms of getting me to the cards I need? In the following table, we’re looking at the cumulative chance of hitting the card you need depending on what turn it is, starting with your first “draw a card” with Jace, and then including his ability and your card for the turn in each of the following turns.

That’s the power of progressive card advantage, also known as “drawing two cards per turn.” The same math applies for [card]Dark Confidant[/card], by the way (albeit with the threat of your confidant killing you off with an ill-timed [card]Inkwell Leviathan[/card]).

Sure, but what should I play?

So how do we wrap these numbers into deciding which indexing cards to actually use in our control decks?

Obviously, this is a big cost-benefit consideration. [card]Divination[/card] gives us that 12% shot at our three-outer for a cost of three mana…as a Sorcery. Instead, we can spend five mana, spread over two instances, to get that same 12% shot via [card]Think Twice[/card]…as an Instant.

That Instant-versus-Sorcery consideration alone is enough to drive me to pick [card]Think Twice[/card] over [card]Divination[/card] in a Solar Flare build, even though it costs two more mana overall. Add to this the fact that we still get to use the “second half” of [card]Think Twice[/card] even if we churn it into our graveyard via [card]Forbidden Alchemy[/card], and I’d say that [card]Think Twice[/card] is a clear winner over [card]Divination[/card]…at least in Solar Flare.

But…

The main reason we care about [card]Think Twice[/card] being usable as an Instant is that we would like to leave mana open for [card]Mana Leak[/card], [card]Dissipate[/card], [card]Go for the Throat[/card], [card]Doom Blade[/card], [card]Dismember[/card], and other Instants that help curb our opponent’s early tempo.

Let’s repeat the important part in isolation just to make sure it’s clear. We want to leave mana open.

[card]Ponder[/card] costs one blue.

In most cases, from turn three onward, you can leave [card]Mana Leak[/card] mana up while casting [card]Ponder[/card], and from turn four onward you can have [card]Dissipate[/card] mana up while doing the same thing. For the relatively innocuous cost of investing one mana up front rather than keeping all of your mana up, you upgrade from a 12% shot at your outs to a 23% shot at them.

Naturally, [card]Ponder[/card] lacks the intrinsic flashback qualities of [card]Think Twice[/card], so if you churn one into your graveyard as part of resolving a [card]Forbidden Alchemy[/card], you don’t get to use it…unless you do so with [card]Snapcaster Mage[/card]. Three mana for a 2/1 body and those great odds to get the card you need seems pretty good, right?

For this reason, I’ve been using [card]Ponder[/card] instead of Think Twice in my Solar Flare builds, and have been completely satisfied with the results.

Among the remaining indexing cards, [card]Forbidden Alchemy[/card] is the clear winner, especially since it (1) fuels [card]Unburial Rites[/card] and (2) has flashback itself, for the long game.

As a consequence of these considerations, my “indexing package” for a Solar Flare deck looks like this:

4 [card]Ponder[/card] 3 [card]Snapcaster Mage[/card] 4 [card]Forbidden Alchemy[/card]

That gives me eight cards that give me 23% or more to hit critical answers in my deck, buoyed by three other cards that let me efficiently rebuy those answer, doubling up the value of having hit them in the first place.

It would certainly be possible to run even more indexing cards, but at some point your deck’s tempo begins to suffer due to the deck consisting of more gap filling than actual action. That, however, is a topic for another day.

Reduction to practice

One of my major themes of late – both in Magic and everywhere else – has been “reduction to practice.” In other words, if we start with “card advantage wins games” as a concept, we’d do well to figure out how it does that, and what the best execution of that plan is.

Thus, for our contemporary take on Solar Flare, the answer to the “how?” question is that card advantage and indexing give us more access to the correct answer to the threat we’re facing right now, letting us diversify our answers to cover more of the field. I’m suggesting that the “best execution” involves Forbidden Alchemy, Snapcaster Mage, and Ponder, rather than Think Twice or other, lesser options.

What do you think? What’s the crucial glue holding your control deck together?

Discussion

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