Lately the topic du jour for Magic articles seems to be theory - especially Card Advantage and Tempo. While I have not the long-standing reputation of a Tan or Tait, I do have something of value to add. As Ted Knutson mentioned in his article, much of what is being said right now has been gone over many times in the past; rather than Standing on the Shoulders of Giants, we've been reinventing the wheel. As such, some of what I'm going to write has been said before in some way or another, but hopefully my version will say it more clearly. And in one article, rather that ten (God, I hope not ten).

In science, a law is a statement of fact, such as"what comes up must come down." A theory is an attempt to explain that fact, for instance"there's an attractive force that all masses exert on each other." Now, you might think from this definition that the best theories are those that come closest to the truth in explaining something's cause. However, many (if not most) scientists think otherwise. They are the Positivists, and their philosophy is that the best theory is the one that makes the most accurate predictions in the greatest number of cases. When you're talking about a card game, this is especially true; you use the theory that gives the best predictions of who will win.

Much of the focus in theoretical physics these days is on finding one theory that explains all the phenomena that we observe in the universe. For example, most people know that electricity and magnetism are really the same force. Physicists think that all the forces, i.e. gravity, electromagnetism, the strong and weak nuclear forces, etc., are all different aspects of one single force. The idea is that in the moments just after the Big Bang, when their was a very high concentration of energy (such a huge amount that the atoms were unable to hold themselves together), there was no difference between the forces. Only after this energy dissipated did the forces as we know them begin to appear.

The best way I've heard of explaining this is by comparing the universe to a roulette wheel and the universe's forces to a roulette ball. The wheel has thirty-eight slots. If you observed the wheel only at rest (low energy), you might think there were thirty-eight different types of"ball." See the wheel spinning (high energy), and it becomes clear that there is only one type of"ball." The theory that accurately describes the behavior of this single, unified force, called the"Grand Unified Theory" or the"Theory of Everything," is the Holy Grail of modern physics. This article is about finding the Theory of Everything in Magic.

More than a few attempts have been made to unify Tempo and Card Advantage. Most of them are needlessly complicated and generally unhelpful. These theories state things like,"when I play a land, I get +1 CA for each spell in my hand that I can now cast." Another example in this vein is:"My opponent is at five life with an empty board, three cards in hand and four Swamps. I cast Blistering Firecat and attack, getting +1 CA for each card in his hand that won't deal with the Firecat." This defies common sense, as the number of cards in your hand has not changed at all.

What rally happened in these examples is that a player has gained or lost options. Garry Kasparov, the chess master who plays those well publicized matches against IBM's various supercomputers, understood this concept very well. He lost his first game, but gained this insight: the computer's power laid in its ability to consider each and every single option it had for each move, and the likely effects of each move, in mere seconds. The result of this was that in a given situation, the computer saw (and effectively had) more viable options than Kasparov did, and was more likely to have the best move. In their next meeting, Kasparov changed his strategy dramatically. His pieces spread across the board so that he controlled more and more area, and the astronomical number of options that the computer was able to consider was gradually reduced until the computer's advantage was nullified.

Magic is much like this. A sure indicator that someone is winning a game is that the other person starts chump blocking. Would you block a 2/2 with your 1/2 at twenty life? I would hope not. Would you block the 2/2 at two life? Yes, because if you don't, you will die. It is your only option. When a person's best option is essentially"sacrifice a creature: gain two life," and the other player's best option is"attack with no risk of anything bad happening: opponent sacrifices a creature," you're looking at a win for the attacking player. When his opponent runs out of ways to avoid taking damage (when they have no options), he will win.

This is the basis of option theory: whoever runs out of options first loses. The concept of an option is closely related to that of an"answer." Any option that permanently neutralizes a threat is an answer, whether that be playing a 3/3 to stop the 2/2 in the above example or killing it with Shock. This concept is similar to Geordie Tait's Virtual Card Advantage theory, so you might find it helpful to read about read about that.

In my physics class, we learned that the formula for computing the distance an object has traveled is x = x₀ + v_it + 1/2at², where x = total distance, x₀ = the distance already traveled, v_i = the object's initial velocity, a = the object's acceleration, and t = the time the object has traveled at the given acceleration and initial velocity.

This equation applies to any object, so long as it's acceleration is constant. However, if an object is not accelerating at all (a = 0), we can just use the equation x = vt. Personally, I'd rather just forget about the extra variables if at all possible.

In Magic, there are two universally recognized measures of who's"winning," or at least who came out ahead in a given exchange of plays. These are Card Advantage and Tempo. In my book, card advantage is simply the difference between the number of cards I have, and the number my opponent has. No, tokens aren't cards. Yes, I count a card with flashback in the graveyard as a card in hand. But the finer points of card advantage have been beaten to death, and I'm not going to get too far into them here. This is because I believe that many of the squabbles over card advantage result from trying to apply it to situations where it doesn't make sense to apply it at all.

Tempo is not quite as simple; it has many aspects. If you have an unblockable 1/1 in play and are at twenty life and your opponent has five 2/2s but one life, some people would say that you 1/1 gives you +5 to your card advantage. I don't buy it - the cards are still there, but they're useless because of time. Sure you're opponent can kill you in two turns, but you can kill him in one. If your opponent has a Boomerang, he can win by buying himself two turns at the cost of -1 to his card advantage.

Now if a player is beating down with a Call of the Herd Token, he's dealing in Tempo, not Card Advantage. He's got his opponent on a clock, but his opponent can use bounce or an Astral Slide effect (a normally temporary solution) to deal with the token permanently, buying himself time. In effect, the token was beating on borrowed time. (That sounds so wrong.)

Interestingly, tempo is easier to explain in the late game, but is more important in the early game. Imagine an ideal situation where each player has a card in their opening hand at each casting cost value 1-6, but only one land. All else being equal, the player who draws the most land will be the winner. If one player plays something on each turn, and the other player doesn't, the first player is at a huge advantage. Now, notice that the effect of missing a land drop in this situation is basically equivalent to what would happen if one of the player's creatures or lands was Boomeranged. So that's tempo, briefly:"clocks" and"board position." Card advantage is a measure of the resources potentially available for you to use, tempo is a measure of how long you have to use them.

If you can adequately describe a situation purely in terms of card advantage or tempo, then by all means do so; use x = vt when you can. I define the middle game as beginning when each player has out enough mana sources to cast any spell in his respective deck. After that point, tempo becomes a very minor factor for purposes of calculating options. However, there are times when card advantage and tempo intermingle, and it becomes difficult to consider one without the other. There is no realistic way to use some proportion or equation to compare the two. As Oscar Tan has written, it's kind of silly to try to turn card advantage and tempo into a singular"baby-food-mush" unit. Rather than arbitrarily smushing Tempo and Card advantage together, like most unifying theories, Option Theory encompasses them under one umbrella. Option theory => Card Advantage + Tempo, not Card Advantage + Tempo => baby-food-mush.

Oscar Tan has several objections to Option Theory. Firstly, he contests that trying to unite tempo and card advantage under a single value, such as one extra land drop = 2 cards, is impractical, and I couldn't agree more. Secondly, he says that Option theory is flawed because it fails to adequately explain aggressive strategies. To paraphrase,"there's only one way to play a Goblin Piledriver - it doesn't give you more options." I disagree. While you don't gain options by playing Goblin Piledriver (gain two options[to attack or not to attack] lose two options [to cast or not to cast the Piledriver] net gain=0), your opponent loses many options because you've put them on a clock. [Assuming there are other cards in your hand, you have personal options with the Piledriver as well, usually dealing with maximizing the damage you can do in a minimum amount of time. - Knut] Tan also believes that Option Theory is flawed because it assumes, for instance, that Spite & Malice is better that both Terror and Counterspell individually. Writes Oscar:

Options have a price, and many of them are lousy bargains. For example, what happens if you replace a Diabolic Edict or Counterspell in your deck with Spite / Malice? Sure, that slot now gives you double the options, but you also have to spend double the mana.

Spite/Malice may give you two options on one card, but in practice, a card like Counterspell will give you more options for a longer period of time. Its lower mana cost makes Counterspell more versatile than Spite & Malice in the late game, because you will have more mana open to cast two Counterspells if you need to, and also in the early game because Counterspell starts working two turns sooner. This specific type of example is really just a misapplication of Option Theory (Naturalize is a better card than Shatter, but whether or not it's better than Creeping Mold is subjective; Option Theory is not as much about card evaluation as about making play decisions), but the dilemma is real: Option Theory does have the potential to get rather mixed up with itself. To eliminate this problem, I propose an amendment to Option Theory that many of you may find familiar:

"Focus only on what matters."

Yes, my friends, that's the voice of Jon Finkel you're hearing, echoing down the halls of yore (whatever those are) to Magic Players everywhere. Sure, he wasn't talking about Option Theory specifically, but it still applies. Does it matter that Spite/Malice gives you added flexibility? No. In actual play, i.e."what matters," it doesn't perform. This is why playtesting is so important. In"Counting Shadow Pieces," Tan gives the hypothetical problem, should a player Force of Will a turn 1 Dark Ritual? Oscar says yes. However, here is what he says about why:

Note, you don't know exactly"how much" you're ahead. That is, you don't know if Force of Will on a turn 1 Dark Ritual is five points ahead, ten points ahead, or 3.1412 points ahead.

This is basically true, but option theory can put a rough number on what happened.

Let's say that The Ferrett's hand is Dark Ritual, Hypnotic Specter, Swamp, and four Twiddle and that Knut has four Island, Force of Will, and two Twiddle.

Ferrett plays a Swamp. (Options +2 - he can now cast Dark Ritual and therefore Hypnotic Specter this turn)

Ferrett casts Dark Ritual (Options -1, trying to realize the option of casting the Specter this turn)

Knut counters it with Force of Will by pitching his Twiddle, denying Ferrett the opportunity to gain a large advantage in options through discard from the Specter or otherwise. (Options -1 card advantage/future option -1 for Knut, putting him at 0 options remaining this turn, and options -1 for the Ferrett putting him also at 0 options. Neither player can do anything else this turn.)

Knut has traded his options to cast Force of Will and later on Twiddle to cancel out two of Ferrett's options this turn, as well as preserve his potential options in future turns. If Knut thinks his Twiddle will be useless, this is a no-brainer. It's still a good decision, because if he had let Hypnotic Specter be cast, he would have been in serious option disadvantage trouble (that's a very technical term, I know).

Note that Knut wouldn't know what to do about the Ritual if he hadn't practiced against Ferrett's deck. If Knut knows from experience that decks like the Ferrett's tend to cast either Necropotence, Hypnotic Specter, or even another Dark Ritual (any of which will create a huge option advantage for the Ferrett) when they cast a turn 1 Dark Ritual, then he will know to counter it. Dark Ritual in itself poses no threat. Because each decision in Magic depends so much on context, applying Option Theory requires some conjecture and some foreknowledge of what you're getting into. In some situations, the exact number of options a player has is obvious, such as when an opponent is reduced to zero cards in hand and an empty board. Often times, the total number of options is so high that calculating it is impractical.

The game of Magic has an aspect that exacerbates this problem with Option Theory: incomplete information. To get an exact number of options gained or lost, you need to know exactly what cards your opponent has. This can often be partially remedied by considering only the options that matter. Sure, I could tap all my mana sources and take burn for fourteen, but I'd never consider it. Sure he could be playing Goblin Sky Raider, but it's much more likely that he's got a Goblin Warchief at the three mana slot instead (unless he's Chris Romeo).

Humans have an advantage over computers in this department. We don't consider the blatantly stupid options, while computers do. To get better, we need to train ourselves to improve at recognizing the best option in a situation, even if it isn't readily apparent. Even still, there can be an unmanageably high number of options. You don't know what your opponent has, so you need to calculate all the possible options that they could have. In the mid-game especially, where you have access to lots of mana, this number can get very big very quickly:

(Total # of possible options) = ( number of cards in hand)*(number of cards that each card in hand could possibly be)*(number of orders in which the cards could be played)...

Now, this kind of calculation is not practical. But we don't have to do it. In any given format and situation, the number of options gained by adding a card is a set, calculable, definite value. Going from zero cards in hand to one gains you a certain number of options. Going from one card to two gains you a different set number of options. Going from 254 to 255 gains you yet another set number of new options. Rather than calculate the exact number of options that each jump gains you, it is enough to know that you gain options at a definite rate. We can use a scale where we set a value, one"unit" for instance, that corresponds to each jump in the number of available options. Comparing the number of jumps is just as useful as comparing the total combined value of the jumps.

"Wait right there," you're thinking,"If I draw a card, I get +1 unit...if my opponent discards two cards I get +2 units...this is supposed to be an article on option theory, not card advantage! What are you trying to pull?!"

Card advantage, in the context of option theory, is a measure of probable options. If they cast Inspiration, they get +1CA. Even if they only drew two"dead" cards, you don't know that. Even if their draw is indeed"dead," they still did gain one option: the option to bluff.

The next step in developing Option Theory is a system for counting options for purposes of making decisions. I've scratched the surface of the issue here, but there's still work to be done, especially regarding options that are on the board rather than in the hand. Restricting options in combat comes to mind. I do hope that I have demonstrated here that such a system is very feasible. It may be that many of the ideas necessary already exist under the guise of some"card advantage" system or another. I'd like to reiterate here that Card Advantage is not"dead" under Option Theory, just seen as part of a larger picture. Focus only on which aspect of the game matters. If a situation can be adequately described in terms of Card Advantage alone, that's good. In the opening and in the end game, as in this article's examples, option theory tends to be more applicable.

A Quick Review:
A theory is nothing more than a convenient analogy. The theory that is the most useful in making predictions is the best theory.

Option Theory incorporates the limiting factors of Tempo with the potential power of Card Advantage.

Option Theory is quantifiable.

Focus on what matters. Sometimes Card Advantage is all that matters; sometimes Tempo is all that matters.

I'd like to take this opportunity to thank Israel Marques and Jun-Wei Hew for their writings on Option Theory. I'd also like to thank Oscar Tan for pointing me to them. Thanks to Oscar Tan and Geordie Tait for making me think more about Card Advantage than I ever would have otherwise and for their contributions to the Magic community in general. I don't know if you can get better at Magic by simply reading articles. After writing this (my first), I can say for sure that writing articles can make you a better Magic player; explaining things on paper forces you to rethink your assumptions and deepens your understanding of the game.

Somewhat Unrelated Note:
I started working on this article right in the middle of the Tan-Tait Card Advantage war. I started it in school one day, tried to bring home what I had typed in rich text format, only to have my version of Word refuse to open it. Not even"salvage text from file" worked. So I started up about where I thought I had left off (in notepad, to avoid any software conflicts whatsoever), got about halfway through where I wanted to go, and saved. A few days later, I put in an afternoon's work and finished. Then the power went out for five seconds or so, and I lost it all. Doh. About a week passed. I copied the beginning of the article from a hard copy into Word, and moved the rest of the text that I had written with one big Copy-Paste. I re-finished the article in Word, except for the proofreading and linking.

That brings me up to today when Zvi Mowshowitz published a premium article on Brainburst called"Advantage: The Grand Unified Theory." I haven't read it because I don't have a premium membership, but I'm assuming that it is very similar to and much better than mine. I decided to submit this anyway, because while I can't compete in terms of quality with Zvi, my article is free to read. Hopefully it will still be of some use. Let this be a lesson to anyone who thinks they want to write an article: (1) Don't use Notepad, it won't recover your work after a crash; (2) save your articles as you write. Class dismissed.

--Grant Babcock

[The way Option Theory is expressed in this article is essentially a broader scope of the Card Impact concept discussed here. At its heart, Card Impact is a conceptualization of how cards (and plays) affect the amount of options available for both you and your opponent. Zvi's article series (which isn't anywhere close to being fully published) examines a lot of other items as well, but the two theories are easily merged. - Knut]