Details of Card Advantage: Theorizing With Doobie

To start from the beginning, Card Advantage was an idea born out of the fact that Magic: the Gathering is at heart a resource battle, and that the initial resources are cards. Thus it was from here that it seemed easy to take the first step toward the foundation of the theory: whoever had the most resources (or then specifically the most cards), would or should win. With this general starting idea, we have something that is both simple and useful. However, as we later found out, this was not always completely correct in the way things were defined.

Anyone who has been reading Star City of late would have been hard pressed to have missed the recent spate of articles dealing with card advantage. To start with, after reading Geordie Tate’s initial article, I only had enough interest to wish him well on the endeavor, as it’s my belief that any time such ideas are presented it is good for the Magic community. As things progressed, and I kept an eye on the forums and the responses there, I began to realize that there were some things about card advantage that were not being addressed by even some of those authors who have done the most writing on the subject. Basically, I became interested in some things apparent to me that they either did not know or realize, or were not expressing. The foundations of these discussions are based on the limits of what the theory could and could not do, and also why so many of the specific arguments were happening without much progress towards resolving them.

I began to suspect that rarely, if ever, have the problem areas for the whole of card advantage ideas themselves been defined very well, even if a lot of excellent work was done on filling in these problematic areas with certain specific solutions relative to the card advantage idea. It seems rather odd that solutions would appear without having the limits and problem areas really well defined, yet it appears that this is what has happened.

I say this only insofar as I know things. It is possible much of what follows will be a reiteration of things that I am unaware of, and if that is so, I think a reiteration should still be worthwhile. Basically the crux of what I think I see is that, for some time, while various authors have been trying to come up with more holistic theories of card advantage, they had not delved deeply into what specifically was causing the problems, breakdowns, and often differences of opinion regarding the matter. The end was that these things were leading to some rather fervent arguments about the ideas being tossed about in such places as the Star City forums, with regards to where Geordie’s original article on the subject had started.

So as I felt I had something to add I sat myself in front of the old keyboard here, and am going to let my thoughts be known. This should be considered a bit of a personal addendum to the recent articles put forth by Geordie.

To start from the beginning, Card Advantage was an idea born out of the fact that Magic: the Gathering is at heart a resource battle, and that the initial resources are cards. Thus it was from here that it seemed easy to take the first step toward the foundation of the theory: whoever had the most resources (or then specifically the most cards), would or should win. With this general starting idea, we have something that is both simple and useful. However, as we later found out, this was not always completely correct in the way things were defined.

As with most theories, what is most interesting and useful is taking such a simple base idea and moving towards more specific examples and also to finding where the theory is applicable and useful and also when and where it breaks down. It was through these exercises that authors came up with ideas allied to card advantage like tempo, virtual card advantage, and card quality.

With this article, I am going to try and show that many of the specific arguments that have been made with regard to Geordie’s initial article are in fact meaningless, because of the problematic nature of the more specific uses of card advantage ideas with regard to the general theory, and a lack of understanding as to the limits of the theory regarding those specifics.

In short, in becoming more specific, or in trying to be used in a certain way (namely as a predictive tool), any card advantage theory makes concessions. Because these concessions are necessary, how they are made is simply a matter of convention created by whoever is creating the theory. For a long time, the concessions have been made in one way. What Geordie has done is to make those concessions in a different way, and because it is simply a concession, it makes it a hard point to find a conclusive line of thought that will end the arguments once and for all.

Toward Time Dependent Variable Value

Geordie initially gave us what he called Pure Card Advantage or PCA. Pure Card Advantage was only interested in counting actual cards. This should be a very easy idea, and is a starting point arrived at by the card advantage basic concept. Nothing could be simpler than to count the actual cards.

What progressed from there, was a problem where specific examples problems came up for argument. The problems themselves were related to the specific concessions in the theories, placed with a lack of context and the inability of those in the argument to realize why this was, namely that these theories generally start with a disregard for changes in card value when they change zones.

One of the basic problems has long been the disregard for the effects of moving from the game as a whole (and how the basic idea of card advantage works), towards what happens when you actually get into a game, and the cards themselves change zones. The changing of zones triggers a change in value for the cards played. This is one of the ideas that I have rarely, if ever, seen directly addressed, but has only been somewhat approached through the allied theories. Even as I define this situation, it is intuitively well known by many players.

To advance towards explaining why this was, and the general nature of the very big concessions that card advantage has generally had to make, I’m going to have to regress a bit, and outlay some of the nature of the problems in another way.

When card advantage ideas moved beyond the simple resource idea, they initially made a leap to an idea that one card had a static value or

Card = 1

This is a very straightforward step, and was about all that could be done, but this idea is at the root of the major concession these theories make. As an example, the beginning game state for a game of Magic is that both players hold in their hands seven cards, and that there is a deck of some number of cards that the players draw from. From here, one would count the cards in each hand, each card being equal to one, and then resolve the difference with the game start point yielding a difference in cards of zero. From here one of the players, lets call them player A, would draw a card, and in doing so change the game state. They would move a card from the library zone to their hand, itself a uniquely governed zone.

Now if we took a count, we’d find one player to have eight cards in hand and the other to have seven. We could assign the difference a value of +1 to the player with eight cards. In progressing further, player A could then play a land, lets say an Island. In doing so, the total card count has not changed, however very many other things have. Player A has opened another zone of play, usually referred to as the board, where the value of cards played is not static, but variable.

The play zone, or board, is where the vast majority of action takes place. Another zone that is now also open to play is the stack, where once again, cards have variable value. I cannot stress enough that the value of cards played onto the board or stack is rarely static. Most players intuitively know this, yet too often this idea is simply left as an afterthought when discussing card advantage, and takes a backseat to the formulating idea that a card = 1.

The land that has been played has now gone from a brown backed Magic card in a player’s hand, to an Island on the board. What this does, is create a gap between our idea that any card = 1, and that the values between hand and board can ever be equalized or considered equal. Cards in hand always have a potential value, related to the other zones of play, and that potential value is the one that creates this and other gaps.

[This potential value is something that Zvi and I have settled on calling”Card Impact,” since it differs from Card Quality (which is a comparison of cards outside the game state). Expect this concept to be further fleshed out in the weeks to come. – Knut]

Let me get to a more specific example that I think will illustrate this further.

As player A progresses, they tap their Island for mana and cast Ancestral Recall, placing it on the stack. The other player, player B can do nothing to disrupt the play, and player A draws three cards and then places Ancestral Recall into the graveyard, opening another zone of play. They now have nine cards in their hand, one tapped island in play, and an Ancestral Recall in their graveyard. That is eleven total cards, in comparison to just seven for Player B, and Player A is now up two cards in hand, one on the board, and one in the graveyard.

My point here is that Ancestral Recall has moved from a brown-backed card in hand, that card = 1 thing, to the following. Nine brown-backed cards in hand and an Ancestral Recall in the graveyard. The most common idea of basic card advantage theories would now be to give Ancestral Recall a value of +2 for the two brown-backed cards that it has added into the player’s hand. If we stop the game here and look at the card advantage situation, the idea is often offered that this was a”good play” by returning roundabout to our beginning concept that having more resources will lead to victory.

We must ask ourselves if this is true? Is it?

Card Advantage and Victory Progression

This reveals the other great gap in card advantage ideas, which is that they are very often only indirectly related to winning an actual game of magic.

First of all player A has made no actual move toward winning the game in any sense that we can define outside of card advantage. They have made player B lose no life, Player A has not played an”I win” card, and each player in any normal game would have many more cards in their library before they would be forced to draw and could not. Most of the time, in most Card Advantage ideas, both the life resource and the library are excluded from consideration, which cause a series of problems, as these are the most common resources that lead to actual victories.

This all forces us back to point where the specifics of plays involving zone changes cause a world of problems for final numerical evaluation by any Card Advantage idea, because the values of cards and pieces of cardboard (again that card =1 idea), and the card’s potential in the other games zones (and against other resources) cannot be rectified. Our Ancestral Recall has gone from that single brown-backed card in the hand to three other brown-backed cards of differing future potential, and also put itself into the graveyard, both creating it and enlarging it, where its quite possible that it could be used again.

It has also shrunk the library, which could be seen as moving the opponent closer to one of the victory conditions – that is being forced to draw from an empty library – but which is an idea almost never discussed. Rarely is an opponent decked in a game of Magic. Most games end in the complete loss of life resources, so that worrying about”decking” when drawing cards is almost negligible. What it does do, however, is illustrate again one of the gaps in the theory.

One of the best ways to break any card advantage idea, is to set up a situation whereby one player has no cards in their library, but has a position of card advantage that will not lead to a life resource victory before they draw out. It may be generally agreeable to say that”all games are won through card advantage,” but sometimes that only occurs after the fact.

When at the point that the player with advantage can’t reduce his opponent to zero life before he’s forced to draw and cannot (thus losing the game), the whole game swings. The player who was before (by all measure) in the card advantage lurch, has just won a victory from his opponent’s exhausted library. We can say that they have”virtually” rendered they’re opponent’s whole deck moot, but again this was only after the fact, and what has been the focus during most of the card advantage era was that predicted win before the draw step.

A Return to Time Dependent Variable Value (Or Card Impact)

That the potential of cards is variable has long been known. This is basically why the advancement of magic theory, which started with card advantage* was forced to branch off into other ideas with titles such as tempo, virtual card advantage, and card quality – a direct admission as to the nature of such variable value dependant on zones – to try and rectify the basic problems revolving around the themes that I have been discussing. Still, I found it amazing that there could be such vehement arguments about the nature of such things as tokens, and whether they were a card or not in the zone of play, because while one might assign them a value of one (stemming from the idea of the brown-backed card in hand), their real value would always be variable and dependant on the game state, a game state that changes over time, and which can change the values of the cards in the different play zones.

Whether you count a token (or even a creature or other permanent) either way, is simply a concession to the potential of the card in time. If you would like to count it as a card, what you are really saying is that it has potential to interact with other cards, the concession is that if the token is measured as card =1, its future interaction is being predicted to occur on a one for one basis. It is just as legitimate to say it has zero value until it has actually interacted with another card or cards. This says nothing of other resources.

This is the major concession present in all of these theories.

One must also realize that cards have dependant value, based on the phase of the current turn. One example would be that walls can only block during your opponent’s attack phase, and in most other cases are effectively useless and have zero value at any other time during the turn. Sorceries, since they can only be cast during a player’s main phase, are useless during an opponent’s turn, and could easily be considered virtually dead during this time. There are many ideas that branch off from this idea as well and one can see that by using this time dependant evaluation method, that instants generally carry a much greater chance to be useful throughout more of the game.

More on Tokens

Beast Attack is an instant that makes a 4/4 token. This is fairly unique. As I pointed out above, instants generally have greater time dependant value, because they can be cast at any time. Beast Attack offers a look into something else. While one might like think of Beast Attack as being useful through the full game turn, in reality (in most cases), it is only useful during the attack phase either as an attacker – to potentially reduce an opponent’s life resource – or to block an opposing attacking creature. Again, while Lightning Bolt is similarly an instant, it has full utility through the turn to attack the opposing life resource or attempt to destroy a creature.

The other reason why Beast Attack is a sticky problem, is because it offers potential – to create a 4/4 token – while it resides in the graveyard, a game zone that doesn’t normally offer potential to cards.

The root of the arguments on the nature of tokens specifically was simply about potential. One side of the argument was Geordie’s, where he gave tokens no value until they interacted with another card. This was one way to resolve the token problem. The other resolution, of course, was to have the token count as a card. The difference here is really about the resolution of potential, and what meaning it has to give a token value before it interacts with some other resource. One can give it a value of”1″ but this is making a concession that it’s future interaction is going to be on a one for one basis. There is, however, no way to really know this is going to be true in advance.

There are several reasons for all of these differences of opinion. One is that Magic is a game of planning, and as such we’d like to use all of the tools that we can muster for planning our win. Card advantage ideas are near perfect when you can use them to reverse analyze a game of Magic or look at a specific game state, and in this I am referring to every possible card’s potential and not a singular card played into a vacuum.

They generally are much worse at prediction. This root of this lies mostly in things that I have outlined above, which boil down to the concessions made with regard to changes in potential, based on zone of play movement and what is usually an ever-changing game state (which often has the ability to change the value of cards over time). They would generally like to count cards in hand that have variable potential as equal to those in other zones, and this is always going to cause various problems without an easy resolution.

If Magic were a game of perfect information (like chess), specific examples of card advantage analysis would carry a lot more weight. One of the traps of specific examples is that they neglect the idea that in certain match-ups you can expect certain plays from your opponent, and that while analysis may give you the proper play in terms of at the moment card advantage, you may know that that specific play would only lead to an opponent’s next play swinging the card advantage idea away from you. Currently, if one thinks of the Standard match-ups between Affinity and W/x control decks, one often finds that the whole of the match-up revolves around the gigantic swing that a resolved Akroma’s Vengeance brings. It’s not hard to think of a situation where tapping out to cast a Future Sight or Rush of Knowledge might bring you a moment of tremendous advantage, all the while it will be ripped away on your opponent’s next turn, when the Vengeance decimates your whole board.

To get back to Geordie’s ideas of Pure Card Advantage, which in trying to count only pieces of cardboard, makes the concession it is going to fail in many ways outside of that specific task. It will not assign any variable value to cards, thus avoiding virtual card advantage, and it won’t regard tokens as cards, ignoring their potential until it is actually used in interacting with some other resource. As such, PCA has limits based on the concessions made which Geordie has repeatedly admitted to.

This was a problem for some, which Geordie in part brought upon himself by using Beast Attack as an example, a card that changes the nature of the graveyard zone, and which as a topic Geordie did not touch on. I am here to say that any card advantage idea is going to make concessions and have limits. To close the specific problems for Geordie’s PCA ideas, it is simply necessary to count every real card and to ignore potential.** From what I’ve seen, much of Geordie’s take, which was somewhat new and has brought to the fore many of these issues, is to ignore potential until the moment when the cards interact actually arrives, that is, he would like to makes less concessions about a card’s future value, yet we found out that this can hardly be avoided.

In what has fascinated many, the leap in Geordie’s second article, was to link virtual card advantage again to the potential of cards in hand. In this case, cards that have only potential in time to answer threats are virtually dead until they actually answer them. This is somewhat interesting, and I think has been somewhat counterintuitive, because we all generally focus on the potential of cards in hand over their actual value. Again this goes back to the brown-backed card in hand = 1 idea, where you are continually looking forward to counting the card in another zone of play, whether or not you can get that card to bring effect in any other zone.

This was generally handled before by ideas of tempo, which resolved parts of the problems in moving cards between the zones. I’m just pointing out again that the zones of play, and potential changes in moving cards between them over time, make a total card advantage assessment prior to the fact problematic. It’s been problematic for a long time, and it makes card advantage theories of limited value as a predictive tool. These problems are all related to what I’ve come to call Time Dependant Variable Value (Card Impact) and also the ideas of Card Advantage related to true Victory Progression.

I hope in pointing out these problems that this will bring some understanding to these issues.


* And also with the Mana Curve

** Should we even look at the state where Beast Attack is flashed back removing the cardboard from the game and leaving two 4/4 tokens behind? You’ve opened a new zone and cast a card twice.