The Snowball Effect: Viewing Advantage In Magic, Part 2

Two-time Grand Prix Top 8 competitor AJ Sacher explains the snowball effect, a very important piece of game theory he mentioned in his last article, with helpful current examples.

The snowball effect is a very important piece of game theory. I mentioned it briefly in my last article since it pertained to keyword abilities and mechanics. I’ll be exploring and explaining that concept a little further here. Before continuing, I suggest reading my original article on the subject. Please ignore the now-outdated examples as well as the heavy-handed, recurring, and obscure reference that seemed to go over everyone’s heads.

For those too lazy to read an entire article in order to read an article (and who can blame them?), here is a quick review of the principles of the snowball effect in Magic:

  • If a game is exactly even, the first person to gain a small edge is more likely to be able to parlay that into a larger and more significant advantage.
  • If you are ahead on cards, it becomes easier to generate more card advantage (you have more opportunities for pieces of additional card advantage).
  • If you are ahead on board, it becomes easier to generate more board advantage (the pressure you have on your opponent can force them into unfavorable positions). This generally holds truer in Limited than Constructed.
  • If both players break even for a turn, whoever was ahead before is the one who profits.
  • Because of all of this, it is easier to extend an existing advantage than it is to come back from behind.

Someone who will remain nameless but has some more-than-decent chops at the game and may or may not have been completely awake and sober at the time and may even have been misunderstood by me anyway once said something that ended up inspiring the predecessor to this piece however many years ago. It was in a Team Draft match in a hotel room the night before a tournament. I mulliganed to four, and as I was shuffling we discussed that no matter how implausible it seemed winning from four cards did happen. We traded stories of winning from or losing to triple mulligans for a bit. Then he said, "It’s like when you win a game with three spells still in your hand; you could have won that game from four," or something to that effect.

This rang false to me, but I didn’t quite have the language or mental construct to parse why exactly. I argued it for a bit before giving up.

The next morning in between rounds and on until well after the day’s competition had completed, I was thinking and scribbling in my notebook about what this meant and how to explain it. I had some notes on total card percentages at the different points in the game, but that only served to further the argument that my theory was true yet not necessarily explain it. (My theory being that the cards at the end of the game are not worth as much as cards at the start, something that I knew to be true but wanted to explore.)

The total card percentage idea ended up being useful in other areas of theory, but the explanation that best fit was the snowball effect. If each card theoretically parlays itself into some type of advantage, which it should or you wouldn’t be playing it, then it follows that the more you have, the more you’ll be able to invest, and the higher rate of return you’ll see.

By definition, the most critical juncture for these snowball-oriented subgames is the early game. This has to be true, as that is when the positional struggles are taking place to get that slight edge that can later be pushed into significant advantage. It’s about setting up that tipping point.

This is why mulligans are so detrimental. The first mulligan has a statistically significant impact on a player’s win rate [in that game], and the second has even harsher repercussions.

Let’s step outside of Magic for a moment.

Imagine starting a game of StarCraft or StarCraft II with one less worker than your opponent. Even though it is only one worker—just 50 measly minerals, which is nothing in the grand scheme of things—the fact that your opponent gets to mine a little more early on makes it easier for them to produce more workers faster, meaning they’ll be able to make more unit producing structures and subsequently units more quickly and in greater numbers. This is the snowball effect in action and a large part of the theory behind worker-harass tactics.

Imagine starting a game of chess with one less piece than your opponent. Even if it’s only a pawn—just one point of material—the fact that your opponent has more options and already a more fortified position makes it easier for them to develop more safely and strike at your weak point[s] with tactics that may not even be available to you. This is why material is considered so important in chess—because once you drop just a little bit, if not properly compensated by other means, it can rapidly snowball and end up costing you even more material and eventually the game.

Two. Two examples is enough. If neither of these resonated with you, come up with any other game and I’m sure you’ll be able to illustrate this concept for yourself (and post them in the comments or tweet them to me because I want to see what you can come up with!). While those are good examples of mulligans and how they pertain to the snowball effect, there is one more I want to throw out there that illustrates the later stages of the snowball rolling and gaining mass and speed:

In StarCraft II, if two small and simple armies battled, the results may surprise you. Take an army of ten Marines versus an army of eleven Marines. Intuitively you would think the latter army would win by one unit, when in reality that army wins by about three or four units. This goes to show how thin the tipping point can be and how quickly it spirals out of control for the player who finds him or herself behind.

I really do hope you guys come up with your own examples, as I’d love to hear them. How does the snowball effect work in football? Or first-person shooters? Fighting games? Go? I actually know Kaijudo has a pretty cool mechanic for combating the snowball effect and helping a player who is behind come back where in Magic terms if you hit a player that player gets to draw a card (and sometimes miracle off of it!). This is the opposite of the Pokemon TCG, which is the worst culprit of snowballing I’ve ever seen since not only do you get to draw a card for killing an opposing Pokemon but it also likely sets them back a handful of land-drop equivalents!

It’s about investment. Liquid versus stale resources. In order to develop your card economy, you need those initial cards to parlay them into either an advantageous position, a material advantage, or both. Or some other sort of dynamic advantage like a foothold in an important subgame, but that’s more content for another time.

Alright, I need to get out of the abstract. I know how many people have little appreciation for such things and much prefer concrete examples and more easily applicable lessons. There are five types of cards in regards to the snowball effect. In regards to having an advantage that grows from an initial tipping point, there are:

1. Cards that begin a snowball rolling, or "starters"
2. Cards that keep a snowball rolling, or "enablers"
3. Cards that utilize big snowballs, or "toppers"

Then the other side of the principle that works in the world of "everything is a Time Walk" and states that if all else is otherwise equal and if nothing happens then the player who was ahead is the one who profits. In regards to this idea, there are also:

4. Cards that give you an advantage to maintain
5. Cards that help you maintain that advantage

To steal a paragraph from myself:

Obviously there is a ton of overlap and some ambiguity about specific roles depending on certain deck or draw dynamics, but you know what I mean. Viewing cards in different terms is a refreshing way to switch things up to try and learn more, and I recommend trying to think of cards in these terms for a few drafts and see how it impacts your evaluations.

Full disclosure: these classifications and identifications are much more prevalent in Limited than Constructed. The mechanics that push you one way or another are more common, and Constructed tends to be more subgame oriented than this can really account for. That being said, the archetypes are more clear-cut and the card choices are more purposeful, so Constructed tends to be more illustrative of these concepts even if they may be slightly less relevant.

Time to look at some Standard lists from the recent-enough StarCityGames.com Invitational in Indianapolis in terms of their snowballability. This is to teach how these decks operate in terms of this theory as well as showcase some of the different types of snowballs that exist. We’ll be looking at Snowball Aggro, Traditional Control, and The Rock. We’re going to start with the breakout deck from Pro Tour Dublin in Mono-Blue Devotion. This is one of the more snowball-oriented decks I’ve ever seen, so it seems like a good enough place to start, don’t you think? I mean, Cloudfin Raptor is a snowball all by itself!

The main snowball here is about getting a huge board presence and then converting it into either a win through damage or an overwhelming advantage through drawing a ton of cards. The starters are the one- and two-drops that get you on board and build your devotion. The step up to the enablers is somewhat murkier thanks to the low curve of the deck and the nature of the snowball being created, but they include the heavier drops, twos and threes, that continue to establish your board presence and devotion. Jace, Architect of Thought as a card drawer; Thassa, God of the Sea’s upkeep scry; and even the incidental Bident and Nightveil Specter bonus cards also help keep the ball rolling towards the end goal. That end goal being the toppers—the catapults used to hurl these snowballs at the opponent.

Master of Waves is a harsh topper that scales to the size of the snowball you’ve created. Bident of Thassa is the other side of the coin, allowing you to convert a big snowball into a full tank of gas which you then deploy to finish the opponent off. In actuality, Bident often plays the role of an enabler, being cast on turn 4 as you get in for a hit with one or two creatures and start generating the resources needed to get to the tipping point. Finally, the body on Thassa, God of the Sea herself is quite good at closing out games and is turned on by the snowball rolling done to build up devotion.

As for advantage generators and equalization cards, while they are still going to exist and apply, the more aggressive your deck is, the less impactful these principles are going to be. With that little rule of thumb in mind, any time you have an evasive creature attacking, both players taking a turn breaking even is going to profit you. This is the principle behind Aggro-Control decks, aka CounterSlivers. Another key way of generating such an advantage is planeswalkers, of which this deck has Jace, Architect of Thought. Every turn that Jace is in play all else equal is going to be more profit for its controller. It’s that simple.

As for equalization cards, blockers and Rapid Hybridization do what they can in this category. Cyclonic Rift does a pretty good impression of a removal spell a lot of the time as well. Post-board is when it is taken a step further, as the ultimate equalizers (read: pseudo Time Walk) in Magic history have to be counterspells. Not only are they the epitome of a one-for-one, but they do so preemptively (the creature doesn’t get to enter or leave the battlefield, the planeswalker doesn’t get to activate, etc.) and flexibly (a hard counter can take care of anything except a land, whereas something like Doom Blade has a narrower range of threats it can neutralize).

Speaking of counterspells, let’s move on and look at a control deck through the snowball effect’s lens:

Your traditional control deck snowballs in a slightly different way, building to a position of true favor. The simplified way to state this is that you start with one-for-ones to not fall behind and develop into the midgame of two-for-ones to be able to continue making land drops while also staying on top of the one-for-ones until reaching an endgame where you bury the opponent in an avalanche of card advantage triggered by a big Sphinx’s Revelation. This sort of phasality allows for a clear distinction of where the game stands and is what causes that "slipping out of your fingers" feeling that you get when losing to one of these strategies.

The reason this is important is because it helps recognize something that not all players seem to grasp—the big Sphinx’s Revelation being cast is not a standalone event that changes a losing game into a winning one. As much as non-Rev players would like to believe this to be the case, it is rarely an "easy button" that happened separate from the rest of the game. The control player got to a point in the game where they:

1. Weren’t dead.
2. Weren’t devastatingly behind to the point of not being able to take the turn off of defending themselves in order to cast their Rev.
3. Had made all (or most) of their land drops up to that point.
4. Had a Sphinx’s Revelation in hand.

That didn’t happen by accident.

The deck thrives in those middling turns, chaining Divinations (cheap enough to get out quickly or do two things in a turn) and Jace, Architect of Thought -2 activations (some of the time you get two cards, plus either you get a second activation or they have to invest some sort of resource into preventing any additional value) or even miniature Sphinx’s Revelations (the instant speed of which can often slow an opponent down a bit and gives you a little bonus life to work with as well).

If you’ve ever seen a player chaining ever-growing Revelations, then you understand how unrelentingly it can bury its opponent.

Esper is also good at having both players break even for a turn, or "equalizing" with their cheap and effective one-for-one removal and countermagic. As for making that advantageous, this happens almost incidentally for the Sphinx’s Revelation deck, as every turn that passes is [likely] one step closer to that deck being the victor. The reasons for this are two-fold. The first is simply that it is another card deeper into your deck to get to Sphinx’s Revelation and another land drop to fuel it.

The second and more subtle reason is that [most] cards in [most] opposing decks are going to [on average] be worth less than each corresponding card from the control deck. This is because those decks are [usually] filled with cards whose value is in their board presence (something that isn’t as impactful in a topdecking stage of the game against a deck like Esper) or are otherwise equalizable by a Dissolve or Detention Sphere. Meanwhile, the Esper deck has a significant portion of their library that yields additional cards. That is why these decks are so hard to beat in topdeck mode even if you can catch them without a Sphinx’s Revelation catapult at the ready.

There really are two types of snowball fights: ones that start in the early game and evolve throughout and ones that start from an even game state, aka topdeck wars. Esper excels at both but does so from a very reactive angle.

The extreme of the latter side of the spectrum is The Rock. Traditionally, these decks thrive on creating and maintaining a barren game state dearth of resources for both players with a slight edge (often one with incremental value) and riding that out. Quintessential pieces of this deck include a surplus of one-for-ones in the form of discard and removal and then the aforementioned advantage engine to pull ahead and close out the game.

The example of this type of strategy in today’s Standard is Mono-Black Devotion. All of the telltale signs are there: Thoughtseizes, a bunch of spot removal, and some super-grindy win conditions.

Unlike when we went over the board-oriented aggressive snowball of Mono-Blue Devotion, this deck doesn’t come out of the gates with the intention of steamrolling the opponent. It certainly has snowbally cards (namely Pack Rat) as well as cards that act as toppers (Gary, the Traveling Insurance Salesman). However, the number of hyperefficient one-for-ones is outrageous, and every other card in the deck is focused on profiting off of otherwise breakeven turns.

The best card at exactly this is the deck’s signature card, Underworld Connections. It turns out that one-for-ones are pretty good when you’re drawing twice as many cards a turn as your opponent. Nightveil Specter is another good example of this principle. Desecration Demon is a slightly more dynamic card but does play this role fairly often with its "incremental advantage" being bludgeoning the opponent over the head for a giant chunk of their life total. DeseDaddy also plays the role of brick wall or forceful one-for-one and more. He wears many hats.

This may be the most useful/helpful part of the whole article. A lot of people have asked me about how to beat Mono-Black Devotion, suggesting cards like spot removal for Desecration Demon, life gain to outrun Gray Merchants, or other some other type of symptom-treating approach. There are two ways to effectively neuter this type of strategy:

1. Attack their ability to profit from breakeven turns.
2. Attack their ability to create breakeven turns.

The way in which you attack their ability to profit from breakeven turns is to answer the piece of the puzzle that is allowing them to pull ahead. Desecration Demon may be the one that takes your life total to zero, but Underworld Connections is the card that won them the game. If you are able to cut off this engine effectively and play in a more balanced topdeck-war scenario, you’re likely to come out on top. The deck is not designed to have to play a "fair" game, as it is essentially made up of mana, one-for-ones, these engine cards, and cards that scale.

There are a couple of ways to attack their ability to create breakeven turns. First, you can make their one-for-ones ineffectual. Something like using shroud or protection-from-black creatures (or no creatures at all!) to blank spot removal. Or using cards like Voice of Resurgence to value town their attempts at one-for-oneing you down into the ground as they are wont to do.

Another strategy is to have your cards parlay themselves directly. The simplest example is that they can’t create a breakeven turn with you if you have your own Underworld Connections. If you are able to play and activate a planeswalker [for value] and force them to spend a full Hero’s Downfall on it, then this was not a breakeven turn—you come out on top. That is, you come out on top very slightly assuming they don’t have an active Connections or other engine and only if the effect you got was valuable enough to warrant the hit to mana efficiency you’re very likely taking on the exchange. What does this all mean? Well, while Divinations do help keep your head above water, they are just treading that water; you have to be building towards something of your own. That’s an important distinction that needs to be addressed in our own games.

I was going to talk about how it applies to Limited, but this article is already running a tad on the long side, so I’ll let you guys and gals figure out how to apply the principles discussed in Theros. Alright, I can’t help myself; here are some quick notes. Ordeals might as well be called snowballs. Heroic creatures—especially the ones that pump—also follow the theory quite closely. It’s very easy to press an advantage in Theros due to the myriad of combat tricks in the format, not to mention the blocking deterrents (including all of the bestow cards) and of course the outright evasion.

I strongly suggest looking for spots where the snowball effect may be at play in your own games while observing others or even watching coverage. Learning to identify these positions will help you realize specifically what matters at a given point in time, which you can then focus on. And focusing only on what matters is kind of important in Magic (or so I’ve heard). Exploiting these scenarios by having a better understanding of the subgame at hand will result in a lot more favorable positions.