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Back to Basics #3: Counting Card Advantage

Magic has a small number of fundamental rules: One land per turn, one attack phase per turn, a certain maximum power-to-mana ratio for creatures, and one card drawn per turn. Breaking this last rule – one card per turn – is one of the most basic yet most powerful strategies in the game.

There hasn’t been much in Type I circles lately, except everyone is still trying to gauge how lethal Growing ‘Tog is. I have more changes to”The Deck” myself. I swapped Fire / Ice for a second maindeck Swords to Plowshares, but have other things to playtest e-mailed from other Paragons, like replacing Misdirection for the present metagame.


My summer job has thrown a monkeywrench into my playtest time, though, since I’m home only during evenings, which is after 8:00 a.m. for most American players. I’m a proud intern of a cozy local firm, the Abello, Concepcion, Regala & Cruz Law Offices. It may be a coincidence, but that was where my Dad started out thirty years ago, and all my bosses now are his old co-workers.


I guess I’m beginning to feel like a real lawyer. First of all, they let us take two-hour lunch breaks if we want to. Second, that’s now the time it takes me to drive home through two cities worth of traffic from Metro Manila’s commercial district.


An embarrassing typo…

Jeff Stones from San Diego wrote in last week’s article. The formula for Psychatog is really”1.5X + 0.5Y +1″ where X is your cards in hand and Y is your cards in graveyard. The one published last week omitted the 1.5, and it was a typo, albeit an embarrassing one. (Since he’ll insert something here, sorry, but Ferrett missed it too.) (As usual, I take full responsibility – The Ferrett)


Counting Card Advantage

Last week’s article was a tad advanced, and I’m encouraged to follow it up with a basic article. If you didn’t have a comprehensive, up-to-date understanding of the Type I metagame, last week’s article wouldn’t have made sense. If you’re new to intermediate concepts such as card advantage, it would have made even less sense. That’s what we’ll try to fix today.


By the end of this article, a beginning player should, hopefully, understand why Gush nets a one-card increase, and why other factors theoretically balance this one-card gain out.


I’ll start by sharing one of the first questions I e-mailed”Sensei” Frank Kusumoto back when Mirage had just come out (I think I was just fifteen back then): Why was Vampiric Tutor not used in the Type II Necrodecks of the day?


I don’t have the original e-mail, but the Sensei explained that Vampiric Tutor normally nets you a one-card loss. With Necropotence, one life equals one card, so the life loss from Vampiric Tutor means a three-card loss all in all. You have to get something that regains this loss of cards with interest to make the investment worth it, theoretically something like Ivory Tower.


If you understand how the Sensei computed the card loss involved, then you know how to gauge the card advantage any single spell or play produces.


Defining The Buzzword

Unlike”mana curve” and”tempo,””card advantage” is fortunately one of the more straightforward fundamentals of this game.


Magic has a small number of fundamental rules: One land per turn, one attack phase per turn, a certain maximum power-to-mana ratio for creatures, and one card drawn per turn. Some of the best cards in the game are simply great because they break at least one of these fundamental rules. Mox Sapphire and friends allow you to effectively play more than one land in one turn, and that’s also why Fastbond is restricted. Phyrexian Dreadnought (played via Illusionary Mask), Psychatog, and Quirion Dryad are among the strongest creatures in the game because their power-to-mana ratios break the envelope. Everything from Ancestral Recall to Necropotence allow you to draw more than one card per turn.


Breaking this last rule – one card per turn – is one of the most basic yet most powerful strategies in the game. Obviously, if you have more cards in your hand, you can do more nasty things to your opponent. The most basic explanation is that since you can only draw one card per turn, drawing extra cards is almost equivalent to taking extra turns. Imagine yourself playing chess, and you could suddenly take five or ten turns for every turn your opponent takes.


Outmaneuvering him into a checkmate would be inevitable.


This is the simplest illustration of card advantage.


Bean Counting

Counting card advantage isn’t so different from managerial accounting. You begin with resources or assets such as your hand, your library size and your life total, and you gauge swings in the game by the net changes in each resource. To compute card advantage, thus, you just have to take a couple of”before and after” snapshots of your hand size.


Take this simplest case: Ancestral Recall.


When it goes on the stack, you have one less blue mana and one less card in hand. When it resolves, you add three cards to your hand. If we tabulate this:


-1 card (Ancestral Recall goes from the hand to graveyard)

+3 cards (Three cards move from the library to the hand)


Thus, Ancestral Recall produces a net gain of two cards.


This computation method, next, easily shows why Necropotence is the most powerful card ever printed, even more so than Ancestral. If Necropotence is in play, you gain the ability to convert life points into cards. Now, life is one of those resources that normally doesn’t affect the game. That is, you can tap the same mana and cast the same spells regardless of whether you are at one life or twenty. This means that your first nineteen life points are actually irrelevant; all that matters is the imminence of losing the twentieth.


Taking this idea, we get:


-1 card (Necropotence moves from the hand to the board, but has no effect on the board)

+19 cards (You may theoretically trade your first nineteen life points for nineteen cards)


With a theoretical net gain of eighteen cards – and an actual gain against many decks – you can see why this single spell beats even Ancestral Recall. You also see why a player with a deck incapable of dealing damage has to Disenchant a Necropotence that hit the board. The Necro player will still get to refill his hand, but it’s better to take your chances with that than let him milk all nineteen out of the Skull.


Now, this may look obvious to you, but it’s really not based on what I see in my e-mail and in Type I forums. The most common examples are Vampiric Tutor, Mystical Tutor, and Enlightened Tutors. To too many beginners, these should instantly be played in every deck that can use them, since they’re cheap tutors. But let’s tabulate their effect on the game:


-1 card (Vampiric Tutor moves from the hand to the graveyard)

+0 card (A card is moved from the library to the top of the same library)


Thus, the Mirage tutors have an inherent card disadvantage, and the card you put on top of your library has to offset this disadvantage with interest to be worth it.


The same example illustrates why the tutors that put cards directly into your hand are the more powerful ones, such as Demonic Tutor, Merchant Scroll, and Cunning Wish. Our computations also show why Demonic Consultation is arguably the best of them all:


-1 card (Demonic Consultation moves from the hand to the graveyard)

+1 card (A card moves from the library to the hand)


A card of your choice moves to your hand at no card disadvantage, at instant speed, and for just one mana. Many are scared by the drawback of removing cards from the library – but much like life, cards in library are a resource that won’t affect the game until they’re actually drawn, and library size is irrelevant unless you have no more cards left to draw. In other words, the cards you remove could just as easily have been at the bottom of your library, and they won’t matter if you can win quickly thanks to pinpoint tutoring.


Advanced Bean Counting, The Opponent, And Card Disadvantage

Saying that card advantage is all about drawing more cards doesn’t give the complete picture. In a more complete sense, it’s about having more than your opponent.


This simple concept is actually what underlies every discard deck you know of. Take the computation for Hymn to Tourach, for the black player and for his opponent:


-1 card (Hymn to Tourach moves from the hand to the graveyard)

-2 cards (Opponent moves two cards moves from his hand to his graveyard)


-1 minus -2 ends up as +1. Playing thus Hymn to Tourach produces a one card net gain. Although this seems small, the disruption of the early, random discard amplifies it, making Hymn an important Type I spell. The same computation also shows why Hypnotic Specter and Mind Twist are good; they actually produce card advantage, albeit in reverse, or through negative card advantage.


Finally, the same computation shows why something like Specter’s Wail stinks:


-1 card (Specter’s Wail moves from the hand to the graveyard)

-1 card (Opponent moves a card from his hand to his graveyard)


The card advantage computation ends up with zero, meaning an even trade, but remember that the black player has to spend a turn and two mana to make the even trade, which is why he really comes out behind.


You might also say the same about Duress – but remember that Duress aims to disrupt by taking a better card with it, breaking the symmetry of the trade (compare this to an eighth-pick Hill Giant forcibly trading for a first-pick bomb rare in Limited).


Taking your opponent’s hand size into account can be more complicated than when playing a Mind Twist. Take, for example, a symmetric card such as Howling Mine:


-1 card (Howling Mine moves from the hand to the board, but has no effect on the board)

+X cards (Player draws X additional cards over X turns)


+X cards (Opponent draws X additional cards over X turns)


Although you’re drawing cards, you’re not gaining any advantage because your opponent is drawing the same amount – and even gets to draw before you do. Moreover, you actually lose a card by playing the Mine in the first place, making it a dead slot in your deck more often than not. It worked in very specific decks where the opponent’s extra cards could be neutralized, such as with Stasis or a Black Vise or three (and Stasis has gained more and better nonsymmetrical tools, and Black Vise has long since been restricted). Generally, however, the subtle disadvantage on that first turn will come back to bit you.


Again, this isn’t as simple as it looks because of the number of people who still post decks with Arcane Denial:


-1 card (Arcane Denial moves from the hand to the graveyard)

+1 card (A card moves from the library to the hand next upkeep)


+2 cards (Two cards move from the opponent’s library to his hand next upkeep)


0 minus +2 is -2, and you can see that casting Arcane Denial is the equivalent of your opponent casting Ancestral Recall on himself.


(When Alliances first came out in Manila, some players would tell me it was a great new cheap counter. They rationalized its use, saying that you would both draw two cards on your turn, since you’d draw an additional card normally. They also said the opponent might draw two lands anyway. Read my lips: This is stupidity. The numbers don’t lie.)


Putting It Together: Interactions

So far, we’ve been gauging the card advantage produced by individual cards. Good decks, though, are made good by the synergy of their components. One interesting example is Quiet Speculation, something Eric“Danger” Taylor opined was broken via AIM shortly before Judgment was released. Here’s how he reasoned it:


-1 card (Quiet Speculation moves from the hand to the graveyard)

+2 cards (first Deep Analysis moves two cards from the library to the hand)

+2 cards (second Deep Analysis moves two cards from the library to the hand)

+2 cards (third Deep Analysis moves two cards from the library to the hand)


Thus, it potentially produces a five-card net gain, albeit you also have to factor in the eight mana and nine life needed.


The more complex computations, though, are those made after the stack clears. Take this simple example: How much do you gain by using Force of Will on an opponent’s Ancestral Recall?


You might do it this way:


Player

-1 card (Force of Will moves from the hand to the graveyard)

-1 card (A blue card leaves the hand and is removed from the game)


Opponent


-1 card (Ancestral Recall moves from the hand to the graveyard)


This is obviously wrong because it concludes that the play leaves the player with a one-card loss, implying that using Force is a bad play.


What you have to do, however, is compare the above result to the scenario had the player not countered:


Player

-0 card (Force of Will stays in hand)


Opponent

-1 card (Ancestral Recall moves from the hand to the graveyard)


+3 cards (Three cards move from the opponent’s library to his hand)


Obviously, the player is better off countering because the opponent ending up with a two-card net gain is bad.


Note from this example that no matter what one does, the opponent will bury Ancestral Recall anyway, making it irrelevant to gauge the benefits of countering. It should be removed from the computation.


Further, one entry was simply missing from the first table, namely something else the opponent lost in the exchange:


Player

-1 card (Force of Will moves from the hand to the graveyard)

-1 card (A blue card leaves the hand and is removed from the game)


Opponent

-3 cards (Opponent no longer moves three cards from his library to his hand)


Thus, countering with Force of Will actually saves you one card – which makes sense since that’s the difference between you being one card behind and the opponent being two cards ahead (consider that every card he gains is one card you lose). Moreover, it also explains why a player may not be willing to pitch Mana Drain to Force of Will against Ancestral Recall; keeping the two counters may be better than losing them to end up with just a one-card gain.


(The same modification tells you why it is obviously bad to pitch Ancestral Recall to Force of Will.)


To extend the exercise, what happens when you counter Ancestral Recall with Misdirection?


Player

-1 card (Force of Will moves from the hand to the graveyard)

-1 card (A blue card leaves the hand and is removed from the game)

+3 cards (Ancestral Recall moves three cards from the library to the hand)


Opponent

-3 cards (Opponent no longer moves three cards from his library to his hand)


You get a devastating four-card net gain (from a six-card gross gain), which explains why a good player is cautious against an opponent with even just one Mis-D in his deck.


(You might be confused why we removed the opponent’s expended spell from these computations. The initial computations were for net card advantage produced by individual cards, or what a player gains by playing that card. There is a choice between letting it sit in hand for a zero-card gain, or playing it. In this section, we are computing for the change in card advantage caused by taking a certain action, and we begin with the opponent’s spell already on the stack. He will lose that spell no matter what you do, so it does not change the card advantage you get by reacting to it. Note that we also excluded the opponent’s spell in the earlier computation for Arcane Denial.)


Rounding It Out

In addition to counting hand sizes, you have to take the permanents on the board into account, since the hand and the board are the two places where cards affect or potentially affect the game. Thus, a spell that destroys multiple permanents produces card advantage, even though your hand is actually reduced by one card.


For example, take a Stompy player with a Ghazban Ogre, an Elvish Lyrist and a Quirion Ranger in play. If a”The Deck” player then casts a sideboarded Pyroclasm, he loses one card – but the Stompy player loses three permanents, which is practically like casting Ancestral Recall.


An offshoot of this extended card advantage concept is virtual card advantage, or making cards in hand that have yet to be played useless. If you play a Null Rod against an opponent with a Mox Sapphire, a Black Lotus, and a Mana Crypt, for example, you effectively destroy three permanents (at least until your opponent can destroy the Null Rod). However, you also make any mana artifacts the opponent has in hand useless. Over time, you actually gain more card advantage because he actually loses a draw each time he topdecks a mana artifact. Moat and other cards work similarly.


Finally, card advantage isn’t generated solely by spells and effects that read”draw.” You can have reusable effects that approximate draw effects. Cursed Scroll is a very good example, being a reusable Shock. It doesn’t draw anything, but if it can kill three creatures, it’s as good as an Ancestral Recall in terms of card advantage.


Pop Quiz

To see if you’ve understood what we discussed, try this short test:


#1: Roy plays a Serra Angel. He then enchants it with Spirit Link, then with Inviolability, then with Empyreal Armor. His opponent, Quillian, responds to the Empyreal Armor with Swords to Plowshares. Compute the card advantage or disadvantage Quillian gained with that play. Comment on whether creature enchantments are good or bad, as a general rule.


#2: Roy plays a first-turn Swamp, followed by a Dark Ritual and a Hymn to Tourach, with no one-mana spells in his hand. Quillian has a Force of Will in his hand. Assuming he has at least one blue card, should he counter?


#3: Roy plays a first-turn Swamp and Mox Jet, followed by a Hymn to Tourach. Quillian taps the Island he played on his turn and casts Disrupt. Compute the card advantage or disadvantage generated by that play.


#4: Compute the card advantage generated when you cast and resolve Wheel of Fortune.


#5: Roy plays his first spell of the game, a Masticore, with only a Badlands left in his hand (assume he got hit by Mind Twist or something). Quillian has a lone Swords to Plowshares in his hand. Assuming no other cards are relevant in this game, how can Quillian play to generate card advantage?


#6: Roy is playing Stompy, and has a Forest, a Ghazban Ogre, a Rogue Elephant, and a Quirion Ranger in play. He has an Elvish Spirit Guide removed from the game, a Forest in the graveyard, and two cards in hand. Quillian has a single Tundra in play and seven cards in hand. If one of them is Mystical Tutor and another is a land, should he fetch and play Balance on his next turn?


STOP! Do not scroll down any further until you have finished answering the quiz.


Answers

#1: Quillian gains a three-card advantage in the exchange, and the example illustrates why creature enchantments are generally bad.


-1 card (Swords to Plowshares moves from the hand to the graveyard)


-1 card (Serra Angel leaves the board and is removed from the game)

-1 card (Spirit Link moves from the board to the graveyard)

-1 card (Inviolability moves from the board to the graveyard)

-1 card (Empyreal Armor moves from the hand to the graveyard)


#2: This is a case where common sense actually helps more than our computations. What happens is that you have the option to lose two cards at random, or lose two cards and one life. It’s a lousy choice, but Forcing it gives you the option of choosing which two cards you lose, so you counter only if you have a better card to protect.


If you try to compute it, you’ll end up thinking it’s an even trade because you lose two cards to prevent a two-card loss – but common sense tells you that doesn’t make any sense. Moreover, you might make the mistake of thinking that countering is good because had him lose one extra card, the Dark Ritual. However, the card advantage involved in the Hymn play actually doesn’t depend on how the Hymn itself is played. Whether or not you counter, the Dark Ritual was already used, and is thus irrelevant (“sunk” in accounting parlance).


It’s a different story, however, if you have a Black Lotus on the board as your only mana source and want to counter with Mana Drain. Here, you will lose two cards if you choose to counter.


#3: You save yourself two cards.


-1 card (Disrupt moves from the hand to the graveyard)

+1 card (A card is moved from the library to the hand)

+2 card (You no longer have to move two cards from the hand to the graveyard)


Another way of looking at it is that you have the same hand size if you counter, but lose two cards if you don’t, and the difference is two.


#4: Y – X – 1, where X is the number of cards left in your hand and Y is the number of cards in your opponent’s hand. Thus, Wheel of Fortune generates card advantage if your opponent has more cards than you do right before you cast it.


-1 card (Wheel of Fortune moves from the hand to the graveyard)

X cards (X cards move from the hand to the graveyard)

+7 cards (7 cards move from the library to the hand)


-Y cards (Opponent moves Y cards from his hand to his graveyard)

+7 cards (Opponent moves 7 cards from his library to his hand)


#5: Since you’re still at twenty life, wait before killing the Masticore. You gain a maximum of five cards this way (the opponent can let Masticore go or some other circumstance can force you to use the Swords earlier).


-1 card (Swords to Plowshares moves from the hand to the graveyard)


-1 card (Masticore upkeep during the first attack)

-1 card (Masticore upkeep during the second attack)

-1 card (Masticore upkeep during the third attack)

-1 card (Masticore upkeep during the fourth attack)

-1 card (Masticore upkeep during the last attack, where you cast Swords)

-1 card (Opponent moves Masticore from the board to the graveyard)


#6: Quillian chooses whether or not to cast Balance at the point where he has two land in play and five other cards in hand. Roy has three creatures and one Forest on the board, and two cards in hand. Thus, Quillian will lose two cards if he casts Balance.


-1 card (Balance moves from the hand to the graveyard)

-1 card (a land moves from the board to the graveyard)

-3 cards (three cards move from the hand to the graveyard)


-3 cards (Opponent moves three creatures from the board to his graveyard)


The question, however, didn’t ask about the card advantage involved, but simply whether Quillian should cast the Balance. It really depends on what else he has in hand, but the moment he is in danger of hitting zero life next turn, he is forced to cast the Balance regardless of any card disadvantage. It’s better to have a bad chance at recovering than face an inevitable beatdown.


Obviously, having your entire library in your hand is useless if you’re going to lose anyway. Remember, card advantage is a powerful concept, but it’s not a victory condition.


Going Back To Gush

After all this, I’m sure you can compute for yourself that Gush replaces itself with two cards for a one-card net gain. Further, this one card gain is offset by the loss of two lands in play. Since you can only play one land per turn, this is like losing part of two turns, and offsets the part of the turn you get by drawing an extra card.


You might ask about Psychatog, however. You often see players dumping their entire hands into Mr. Teeth, and they don’t gain new cards in hand or new permanents. Is that a stupid play because it does not generate card advantage?


No, it doesn’t generate card advantage. On the other hand, it disposes of the opponent, so it must be a good play.


Again, all the card advantage in the world doesn’t matter if you’re going to lose anyway. Card advantage is a powerful concept, but you have to remember that it’s only a means to an end.


What if, for example, your opponent plays an Illusionary Mask then a Phyrexian Dreadnought, and you have a Mystical Tutor in hand and a Swords to Plowshares in your library. Should you fetch it, assuming you’re down to twelve life?


Yes. You will lose a card by using the tutor – but unless you have some other way to deal with the Dreadnought, a one-card loss is better than losing.


Don’t mechanically substitute your understanding of basic concepts for winning!


Oscar Tan

rakso on #BDChat on EFNet

University of the Philippines, College of Law

Forum Administrator, Star City Games

Featured Writer, Star City Games

Author of the Control Player’s Bible

Maintainer, Beyond Dominia (R.I.P.)

Proud member of the Casual Player’s Alliance