This week I want to take a small step back and look at the unifying principles of Magic. Understanding these principles, and how the various conceptual elements of Magic interact, is useful as a framework for not only improving technical play, but understanding both the synergies and tensions within any given deck. This framework is essentially "The Grand Unified Theory of Magic." For those of you who are familiar with physics, this is similar to the Grand Unified Theory in physics, in that the attempt is to unify all our disparate heuristic concepts into one theory.

There has already been some work done in this department, specifically by AJ Sacher and Patrick Chapin. Sacher’s take is a theory called Stock Mana, which you can read about here and here. Chapin wrote an article called "The Theory of Everything" which is here. Chapin's article contains his opinions on Stock Mana and I agree with him for the most part, so I will not re-hash those ideas here. These concepts serve as the background for the developments I intend to make.

Magic has once critical conceptual element – it is a game of resource utilization. Because this is Magic's identity at its core, the player who better utilizes their total resources over the course of the game is going to have a significant advantage, frequently leading to victory.

So what are the resources that Magic players have access to? There are three of them.

1. Mana
2. Life Total
3. Cards, specifically, cards in library.

This is my first great departure from Chapin and Sacher. Cards in hand are not a resource. They are simply an extension of cards in your library. The real resource you are drawing on is the pool of potential cards you are able to use over the course of the game, in other words, the cards you put in your deck. This is why knowing your exact decklist is important. If you have 4 Tectonic Edge in your deck and you have already used 2, you only have 2 more available to you. This pool is the real resource. Cards in your hand are simply a representation of which elements of that resource you have available to you at the current moment. The other two resources, mana and life total, are fairly self explanatory.

This naturally leads to the next question – how do you evaluate resource utilization? Stock mana is an attempt to do this, but I think there is a similar, but superior angle to approach this problem. What matters is not the individual utilization of each player's resources, but the relative difference between their resource utilization. In other words, in terms of mana, what matters is not that you curve out, but that you curve out better than your opponent.

Thus, I propose a metric called Marginal Mana, which builds on Sacher's idea of Stock Mana. The basic principle is to calculate the Stock Mana for both sides, then modify it. After that, the modified numbers of each side are compared, and the difference between the two is Marginal Mana. One player will be up Marginal Mana. This player is the person who has the instantaneous advantage (which is subject to change).

Stock Mana is wonderful as the basis for plays that affect the board because it deals very well with the resource of Mana, but there are needed modifications to the theory. The first is the incorporation of life total, which will allow us to discuss the concept of Tempo and the Philosophy of Fire. It also needs to be integrated a bit better with the principle of card advantage, and thus the resource of cards. Here are some basic principles that are applied to Marginal Mana calculations in addition to Stock Mana.

1. The value of a card (barring exceptions like Panglacial Wurm, Narcomoeba) in your library is zero, generally speaking. There are situations where your library becomes relevant, but in most games of Magic decking is not a concern. When it is, individual cards in your library obviously affect Marginal Mana.
2. The value of a card, independent of its effect (aka the cardboard), in play or in your hand is 2. This only applies to cards that you can use (spells that can be cast or lands that can be laid). Cards that you cannot use are worth nothing at that particular moment. This value is chosen because the baseline cycling cost is 2, and cycling simply replaces the card in your hand with a different card in your hand, and thus should be value neutral.
3. The value of each life point is 2^6-(x/2) where x is the life point in question (more on this later).
4. Any card that goes from your graveyard, exile, or library into play or your hand is worth +2 Marginal Mana.
5. Tokens are treated as normal creatures as long as they are in play, and are therefore worth +2 Marginal Mana when they are created.

Thus the goal of each player is to maximize their Marginal Mana. It is important to note that this system assumes you have perfect information. The general principles and guidelines can be used to make educated guesses in actual games, but you will never know what the actual maximum Marginal Mana play is unless you have perfect information. This mirrors the way that you have to guess what the "correct" play is in any given situation.

Here is a simple example of Marginal Mana in action.

It is the start of the game.

Player B plays Mountain (+0), and plays Lightning Bolt targeting player B. Player A suffers a 2 point reduction in Marginal Mana (-2 from expending the card, 3 damage is worth ). Player B suffers a 2^-4 + 2^-3.5 + 2^-3 reduction in Marginal Mana. This is minimal gain.

Let's compare this play to T1 Goblin Guide. Goblin Guide is a 2/2 haste, and thus is worth mana, making your gain +3 Marginal Mana. You attack with it and your opponent reveals a land, drawing them a card (-2 Marginal Mana). You deal two damage (+2^-4 + 2^-3.5). Thus, even if your Goblin Guide "hits" on turn 1 you've gained a bit more than 1 mana. This gain becomes larger when you factor in the fact that your opponent might well have 8 cards in hand at the end of his turn, forcing him to discard a card, thus giving you back 2 Marginal Mana (because he discarded a card). This means that Goblin Guide, even when it hits a land, is usually worth a bit more than on turn 1.

The reasons why I selected 2^6-(x/2) as the equation for life total are two-fold – exponential modeling and simplicity. Chapin stated in his article that each successive life point is worth more than the one that precedes it, which is true. Your 19th life point is worth more than your 20th, and this proceeds down to your 1st life point, which has effectively infinite value. This fact meant that any model that attempts to showcase the value of each individual life point must be an exponential function. The second criteria I used was simplicity. The function itself would be fairly pointless if it were a page long, and thus I chose a simple baseline exponential function (y = 2^x) and tweaked it until it had the properties necessary. I believe this function is sufficiently large close to 1 to represent the fact that those last few life points are very valuable. For those of you who disagree, perhaps you should use 2^8-(x/2), which was another function I considered. As a whole, this function is not perfect, but I feel it is serviceable.

This also serves to illustrate why Lightning Bolt on turn 1 is a bad play, but Lightning Bolt can be such a strong card in aggressive strategies. Taking the first three life points is a minimal gain in Marginal Mana, but by using Bolt to take, for example, someone's 4th, 5th, and 6th life points, you get a large amount of Marginal Mana. This function also illustrates something control players learned long ago – that sometimes it is correct to take damage in exchange for information. While the value of information is intangible, taking damage when your life total is sufficiently high is only a small decrease in Marginal Mana, and thus could well be worth the information you gain.

My selection of Life Total and Mana as resources is, I believe, understandable to most. But my selection of cards in library as the third resource requires some explanation. The reason I selected cards in library as the resource is because the item Magic players bring to battle is a deck of cards. They don't bring seven card hands, they bring a constructed group of forty or sixty cards (depending on the format). In general, a player only has access to the cards in his/her deck. The complication is the six Wishes, but those will not be dealt with here.

In reality, a player's hand is, conceptually, part of their deck. The opponent must do something to have access to both pieces of information. The only difference between the cards in a player's hand and the cards in their deck is that a player can play the cards in their hand and cannot play those in their deck (except Panglacial Wurm). This difference is strictly one of accessibility.

A useful analogy is to think of cards like money. Cards in your deck are like money in the bank, whereas cards in your hand are like cash. One is more readily accessible than the other, but they are both money. Thus cards in your hand and cards in your library are the same resource. Cards in your library encompasses cards in your hand, and is thus the resource used in Marginal Mana.

The bonus of this valuation is that it makes the power of card drawing conceptually easier to understand. What does card drawing do? It is like an ATM card, giving you the most readily accessible form of the resource. By drawing cards and putting them into your hand, what you gain, beyond more cards to use, is accessibility.

By combining all three resources into a single metric, Marginal Mana, it becomes easier to understand the interchangeability of resources in Magic. This is one of the most distinctive features in the game, and understanding the fluidity of the resources within the game, and thus the game itself, is useful.

Essentially, I created Marginal Mana as a reasonable metric on which to evaluate a player's overall resource utilization compared to that of his or her opponent, since resource optimization is, what I feel, Magic game-play is all about.

Let's do an extended thought experiment, as an illustration of how Marginal Mana works. We will, once again, turn to a classic aggro vs. control match-up – Wafo-Tapa's UW Control versus Mori's mono-red.

The combatants:

"Wafo-Tapa's UW Control"

• Creatures (6)
• 2 Sun Titan
• 4 Wall of Omens

• Spells (28)
• 2 Oblivion Ring
• 1 Cancel
• 2 Condemn
• 2 Deprive
• 2 Essence Scatter
• 2 Jace's Ingenuity
• 4 Mana Leak
• 2 Path to Exile
• 2 Elspeth, Knight-Errant
• 1 Gideon Jura
• 3 Jace Beleren
• 3 Jace, the Mind Sculptor
• 2 Day of Judgment

• Lands (26)
• 5 Island
• 4 Plains
• 4 Celestial Colonnade
• 4 Glacial Fortress
• 1 Scalding Tarn
• 4 Sejiri Refuge
• 4 Tectonic Edge

Buy This Deck Export text format

"Mori's Mono-Red"

• Creatures (18)
• 4 Goblin Guide
• 4 Hellspark Elemental
• 2 Kargan Dragonlord
• 4 Ball Lightning
• 4 Hells Thunder

• Spells (17)
• 4 Lightning Bolt
• 3 Burst Lightning
• 4 Searing Blaze
• 1 Staggershock
• 2 Quenchable Fire
• 3 Earthquake

• Lands (25)
• 15 Mountain
• 4 Teetering Peaks
• 4 Scalding Tarn
• 2 Arid Mesa

Buy This Deck Export text format

Mono-red wins the die roll and keeps Goblin Guide, Hellspark Elemental, Ball Lightning, Lightning Bolt, Mountain, Teetering Peaks, Mountain.

UW keeps Celestial Colonnade, Glacial Fortress, Island, Plains, Mana Leak, Wall of Omens, Jace, the Mind Sculptor.

Mono-red plays Mountain, and now can play either Goblin Guide or Lightning Bolt. At this juncture, Goblin Guide clearly represents the larger Marginal Mana gain, and thus mono-red plays Goblin Guide and attacks. Goblin Guide reveals Glacial Fortress and UW takes 2. The Goblin Guide is worth 2R, the 2 points of damage worth 0.15, and the Glacial Fortress -2. Thus Mono-red has gained 1.15 Marginal Mana, but this is effectively 3.15, since mono-red is very likely to recover the loss from Glacial Fortress, since it is probable that UW discards.

Now we add hands to the picture. On it's next turn, mono red will have a hand that is worth at least 6 mana (it can play one of its two lands, then Elemental or Bolt), meaning that it is effectively up 11.15 Marginal Mana on UW at this juncture. Of course, this is going to change as UW plays out its cards.

UW draws Condemn and plays Plains. It then proceeds to discard and pitches Celestial Colonnade. UW has a current hand that is worth 2 mana (the Condemn it can cast), and next turn has a potential hand worth 6 mana as well (one land plus Mana Leak and Wall of Omens). Thus UW has recovered 8 of that Marginal Mana advantage, and is only down 3.15.

Mono-red untaps and draws Mountain. It plays Mountain and then plays Hellspark Elemental (clearly the largest Marginal Mana gain again). It attacks with both its creatures. UW plays Condemn on Hellspark Elemental and Mono-red gains 1 life. Goblin Guide reveals Sun Titan.

Let's examine the Marginal Mana situation again. Both players have lost a card, so that is neutral. Mono-red has gained 1 life while UW has suffered 2 damage. This represents a 0.34 Marginal Mana gain for mono-red. Now let's examine Mono-red's hand. Next turn there is another land drop in addition to Ball Lightning or Lightning Bolt, so Mono-red's hand is now worth 6 (the same as last turn). Thus Mono-red is now up 3.49 Marginal Mana.

UW untaps and draws Sun Titan. It then plays Glacial Fortress. UW's options are now to drop Wall of Omens or to hold up Mana Leak. Wall of Omens is worth ~1.5 mana for the 0/4 and 2 mana for the card. Mana Leak is worth whatever card it stops from the opposition. These two plays have to be examined separately.

Let's start with Mana Leak. The two worst cards for UW at this juncture are Ball Lightning and Hell's Thunder. Hell's Thunder would be a net 1.2 mana gain for mono-red whereas Ball Lightning would be a net 3.6 mana gain for mono-red (the 15th and 16th life points don't count, since UW would suffer that damage from a Goblin Guide attack anyway).

Wall of Omens represents an immediate 3.5 mana gain, and then represents an additional gain of at least 2, probably 4 life. At this juncture, 2 life is worth 0.6 mana and 4 life is worth 1.8. Given that the worst case scenario is similar to the best case for Mana Leak, UW plays Wall of Omens and draws Island.

Next turn, UW has access to one land drop and Mana Leak, thus making the value of its hand 4. This is a net loss of 2, but UW has made up ground in the overall Marginal Mana count due to Wall of Omens. It is now down only 2 Marginal Mana.

Mono-red untaps and draws Searing Blaze. Mono red now has a number of options:

1. Teetering Peaks + attack, then pass.
2. Mountain, attack, with the intention of playing Bolt or Blaze.
3. Mountain, Ball Lightning, attack.

Let's examine these plays individually again.

Playing Teetering Peaks makes the Goblin Guide a 4/2. If UW blocks, the Marginal Mana gain is either 0 if Goblin Guide hits or 2 of it misses. This seems underwhelming.

The second play is to play Mountain and attack. In this line, UW suffers 5 or 6 damage, dropping to 10 or 11 (a 2.81 Marginal Mana gain). Mono-red also loses two cards, so that is -4. This is a net loss in Marginal mana, even if Goblin Guide misses.

The third play is to play Ball Lightning, leading to the loss of a card but UW suffering a minimum of 4 or 6 points of damage. Four points at this juncture is worth a net of 1.8 (both players lose a card), and six points is worth a net of 2.2 (life is worth 4.2, but mono-red loses a card and UW doesn't). This play is roughly mana neutral if Goblin Guide hits.

As you can see, the mono-red deck is already losing traction. UW is slowly recovering the disadvantage that it was placed in early in the game, but the mono-red deck is not dead in the water yet. The Searing Blaze play is potentially viable due to further draws. By dealing UW 5 damage now mono-red makes the next 3-point chuck of UW's life worth about 6 Marginal Mana, not a cost to be scoffed at. Considering it is still holding a Ball Lightning, this might very well be worth it. Also, this makes Searing Blaze a live card, since UW is not exactly creature heavy.

However, since mono-red just saw a Sun Titan out of UW, it knows that it will be able to play its Searing Blaze for value later in the game, making that concern not valid. Therefore, Ball Lightning is clearly the strongest play. Mono-red drops Ball Lightning and UW blocks it. Goblin Guide reveals Path to Exile. UW drops to 12. Mono-red has gained 1.8 Marginal Mana via this play. Its hand still has a land, Blaze, and Bolt, so the hand is still worth 6 (since the Blaze is still live because UW has Sun Titan). Mono-red's total Marginal Mana advantage is 3.79.

UW untaps and draws Path to Exile. It drops and Island and passes, having access to Path and Mana Leak. At this juncture UW's hand is worth 8 (land drop, Path, Mana Leak, Mind Sculptor), meaning that it has picked up some ground in that department. UW drops mono-red's advantage to 1.79 immediately, and likely less since it has two instants available to trade with mono-red's threats. Given that UW has significantly more cards in hand, this will become relevant, especially as it approaches the 6 mana necessary for Sun Titan.

Mono-red untaps and draws Burst Lightning. It plays Teetering Peaks on Goblin Guide and attacks. Goblin Guide reveals Tectonic Edge and UW plays Path to Exile on Goblin Guide. Mono-red has gained a land (2 Marginal Mana) out of the exchange, but has lots ground. UW has also gained a land, so that is neutral, but Mono-red has lost a creature worth 2R whereas UW has just lost a card. Mono-red's advantage is now 0.79 Marginal Mana.

UW untaps and draws Elspeth. It plays an Island and can now play Jace or Elspeth or leave up Mana Leak. Once again, Mana Leak is worth the opponent's strongest play, which at this point is probably a burn spell. At this juncture 3 points of life is worth 6 mana to it. This means that Elspeth or Jace has to generate more than 6 Marginal Mana over the course of the game to be worth playing at this juncture. This seems likely, since planeswalkers have loyalty and mono-red's only way of killing them is with damage, so they will effectively gain life.

However, this is not the only consideration. Given the current position, it is likely that mono-red has burn, which means that Mana Leak could very well protect later life points. Life Points 6, 7, and 8 are worth a grand total of 17.65 Marginal Mana to UW, which means that using a Mana Leak to protect those life points would be very valuable.

The decision comes down to how much damage the UW player feels he is likely to take at this juncture. In order to be dead, the Mono-red player would have to have a haste creature, along with a land (specifically Teetering Peaks if the creature is not Ball Lightning), Lightning Bolt, and Searing Blaze. Given that mono-red has four cards in hand, this exact combination seems unlikely. UW drops Elspeth and makes a token.

At this juncture UW has gained 3 Marginal Mana off of Elspeth (1/1 token), while maintaining a hand that is still worth 8. Elspeth promises to either gain 5 life or make a token next turn, making the investment worth it. UW is now advantaged in Marginal Mana by 2.21, although this is precarious, since mono-red has open mana and UW has none.

Mono-red now has a number of options. It can throw both the Bolt and the Burst at UW, dealing 5 points of damage to UW and leaving it with 6. The Searing Blaze is now eternally live due to Elspeth, which represents 3 more, leaving UW with just 3 precious points of life to work with. However, mono-red can wait to kick the Burst Lightning, and therefore get two extra points out of it. Mono-red plays Bolt at end of turn, ripping off 3 life points and the 6 point Marginal Mana advantage that goes with it. The UW player is worried.

Mono-red untaps and draws… Hell's Thunder! The game is over - Mono-red plays Hell's Thunder, Teetering Peaks, and Searing Blaze, crashing across for the last 9 points of damage.

This game is an excellent example of what I feel Marginal Mana is capable of. Marginal Mana tracks very well the ebb and flow of the game, with critical cards (for example the burn spells at the end) being worth a large change in Marginal Mana. The system is designed as a metric to help players understand the fluidity present within the game of Magic, while also presenting an effective means to evaluate various resource trades, which occur constantly during game-play. I believe the system accomplishes this reasonably well.

My desire is to build an understanding of Magic from the ground up, and thus I feel it is correct to start with the fundamental aspect of Magic – resource utilization. This is the principle that Marginal Mana is built on. The problem I came across was tempo, and how to have a metric that tracks the ebb and flow of the game with reasonable accuracy. I believe Marginal Mana solves this problem through the application of an exponential function to life total. The strength of burn spells can be clearly seen in the example I presented above. Lightning Bolt and Searing Blaze are both worth a large amount of Marginal Mana in that game due to the specific life points they take and thus the time they are played. Now that we've covered the outline I will develop individual aspects of this theory more in the next few weeks. The preceding two articles I wrote on mana curves and mana acceleration are designed to fit into this framework as well.

Next week – Understanding card advantage, in both the abstract sense and within the framework of Marginal Mana.

Chingsung Chang

Conelead almost everywhere and on MTGO

Khan32k5@gmail.com