Zvi Mowshowitz
3/1/2004
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Life

Life is the resource whose importance varies most in the game. Cards can be irrelevant, but more often than not they are critical and most of the rest of the time the battle can be viewed as some form of virtual or effective card war. Tempo can be irrelevant, but that is almost always because neither side has any, while mana is the same case in reverse: It becomes meaningless when both sides have too much. Like mana, life points have a critical point: The big difference is between Not Enough Life, Enough Life and Lots 'o Life. When both players have more than enough life points life often becomes all but irrelevant until something changes that. One and four life points are very different numbers, but it can be much harder to tell the difference between twenty and twenty-five. It is also common for one player's life total to be moot or almost moot.

This is all true because life doesn't do anything at all until that moment that it does everything. As long as you're alive your life total has no direct impact on the game. When a player starts getting close to death it has a dramatic effect on the game and so does paying life to get something in exchange, but the primary reason to pay attention to life is that when a player drops to zero life points he is dead and nothing else matters. Being dead does not have any effect on tempo or card advantage (in any form) or anything else. It wins you the game. Nothing more, nothing less. This system allows Magic to grant players an early advantage and not automatically shut the player who falls behind out of the game.

Life can also on occasion be nothing but a chore, or even completely irrelevant. A Millstone deck only cares about its opponents' life total if a Greed or similar card hits the table. A deck like TurboLand plans to kill with damage but also doesn't care in the slightest unless there is danger that the round clock will run out and the combination will need to be secured in extra turns. With almost any other scenario you can do infinite damage to your opponent. In these extremes, life totals are irrelevant. It doesn't take anything that extreme to make one life total irrelevant. All it takes is for one deck to win by means other than damage even if the deck kills with damage, shutting the opponent out of the game first and dealing the damage afterwards. At that point it doesn't matter that I did you in with a big creature rather than a Millstone. One total can also be irrelevant if the decision in the game will happen in a fight over the other life total, whose owner will be able to turn the game around afterwards. These are all related: Your life total only matters when you are at risk of dying without having then gone far below zero, although this can be long term as well as short term, or when are using it as a resource.

That means that all life points are not created equal. The last one is worth infinite resources, and assuming that damage in the matchup would be dealt a point at a time each one after that is worth less. Life only helps if having that point makes it less likely that you will hit zero or gives you a point you can profitably spend, so against an opponent whose deck is full of three point Bolts and no other damage only factors of three and those two points spare from your starting twenty matter. Against Draco-Explosion there's a huge difference between sixteen and seventeen but sixteen and nine are virtually the same number. The value of reducing someone's life total to a number greater than zero is to enhance the value of future life reduction, eventually to a win, thus making your cards and threats more powerful and preventing your opponent from sacrificing life points either by soaking up damage or by paying life. Each point of damage is valued only to the extent that it puts the next point at the head of the line, turning Bunch 'o Life into Enough into Not Enough.

There is therefore a distinction between plans that try to win by directly attacking their opponents' life total, those that attack it by generating effects that do continuous damage such as attacking creatures while the game is still up in the air and those that don't intend to launch an attack until the game is over. In the first case life can directly be considered the primary resource of the game, in the second tempo becomes the primary resource and in the third the resource is usually cards.

In terms of relating life points to cards, even up to something like virtual effective card economy measured in a power-based card impact scale, there is obviously no direct relation or formula that will work, although there are special cases where you can do exactly that and describe the game in this fashion.

Of Course, You Realize This Means War: Life as the Primary Resource

To see how in some games one players' life points are the only important resource and are easily translatable to cards I will look at the simple case: Burn (Red) versus Draw-Go (Blue). This is a classic battle in Magic but it is even more of a classic for theorists because it is so pure. To make it even more pure, assume for now that the burn deck runs no creatures at all. Burn is attempting to kill Draw-Go while Draw-Go is just trying to survive. Eventually the blue player will be able to turn the game around and win, but that will take a long time and he won't go for the kill until after he's drawn enough cards that he is all but untouchable. Until then, the game can be thought of as having only four relevant resources if red player has enough land:

1. Blue player's Life Points.
2. Red player's nonland cards.
3. Blue player's counters.
4. Blue player's ability to draw more cards and with them more counters and more card drawers.

Early in the game there might be an additional fight over some cheap creatures, but once the board is stable it is unthinkable that the blue player will allow a red creature to do damage to him continuously since he is in the business of stopping cards that do damage to him. This is why the early creature damage a burn deck gets in is so important even if it doesn't put your opponent in immediate danger. Every few points done this way is equivalent to a free burn spell, which is not just a card but one of the cards that counts most. At the same time, those creatures often become a huge liability later in the game because they trade with cards that couldn't stop burn, trade inefficiently or are even outright blanked.

Suppose the burn player had nothing in his deck but copies of Shock. In this case, each spell he draws is worth two points of life, so if he had forty Shock variants and twenty zero-value Mountains then the average card in his deck is worth 1.33 damage. Then suppose the blue player's deck had nothing but Counterspell variants. Each counter variant that can stop a shock is worth 2 points of life to the blue player, while those that can't be cast at the right time or wouldn't counter a spell anymore (such as Mana Leak or Force Spike) are worth zero. The control player then needs, say, twenty-four lands and has one Morphling that eventually kills his opponent. That means that each card in his deck is only worth 1.17 cards even if all counters are functioning at all times. If you then assume that the burn player can play around the four Force Spikes the whole game, that goes down to 1.03, making every card draw an average of 0.3 damage for the red player. That means that he'll have to draw on average 60 cards to win the game. Even if you also get rid of four Mana Leak, that only gets him 0.43 damage per card which means drawing 45.6 cards. The Morphling will win the game before that more often than it won't, and two would be almost unstoppable. One card = two life.

The lesson here is that this is a bad equation if you're trying to deal twenty damage. Even Lightning Bolts tend to be bad, since you need seven unanswered Bolts to win. How often can you afford to have four or five less cards than your opponent for an extended period of time without something terrible happening? There's also the risk of something like Circle of Protection: Red that has to be in the back of your mind. The normal solution is to try to win with a combination of tempo and direct life attack; when a control deck stabilizes tempo and forces this type of battle at a high life total it is often considered to have won and different matchups have different life thresholds for that.

Now mix up the cards more and consider what happens when there are a variety of burn spells running around. Some do two damage, others do three or four and some might be huge like Ball Lightning or Blistering Firecat or even threaten to be continuous like Viashino Sandstalker. Yes, these are creature cards by card type but in this context they are burn spells. Now the battle is going to be over how the counters match up with the burn spells. Against a deck offering no resistance, this burn deck might consider its cards to have an average value of say 2.3 damage. That number may seem low for a deck with big burn but remember land is factored in at zero.

The blue player is now trying to line up his counters as profitably as he can with the big burn spells. Every card draw for the red player gives him 2.3 points of burn. A counter that stops a Fireblast will stop 4 points of that, but countering a Seal of Fire only blocks 2. Cards matter to the extent that they allow the players to control what happens to the blue players' life total, and often success will come down to how well he can line up. If his counters can be cashed in for an average of 3.5 life points, he's in good shape, but if he only gets 2 then he's going to run out of life points and die. If the blue player were to cast a card drawing spell, it could be considered equal in value to the value of all cards drawn, which means it is then equal in value to the amount of burn the counters soak up plus the number of cards the new card drawers will give him, and this allows the value of card drawing to be solved for since there is one equation with one unknown.

Lineup Theory

When entering a long term battle, it should often be considered in terms of lineup theory, especially when there is an interaction of counters, removal and threats. This is the most basic application of card impact. It will normally take the form of one player claiming he cannot possibly lose, and then explaining why by lining up his spells with his opponents' spells. It will go something like this: If I Naturalize these three artifacts and counter these nine threats then you can't kill me since your other cards are not a problem, and I have four copies of Naturalize and thirteen counters. That means that barring a random fluctuation early in the game I will be able to deal with all of your threats, and then eventually kill you in some other way.

The easiest lineup is counters and/or removal against threats. Often decks will have a weak link, without which they are unable to accomplish anything likely to win a game. For some combination decks that can be as simple as stopping one card: If its Goblin Charbelcher never resolves, a deck with no other damage sources can't possibly win. Back in the day when blue had a lot of quality counters, there were even matchups where a blue player could speak of using his twenty-one counters to stop your nineteen creatures. From December 1.x, a control deck could view Tinker as having only a relatively small number of threat cards that must be stopped: If I stop Harvey's Masticore, Chalice, Mindslaver, Helix, Incubator, Colossus, Stroke, Tinker and Upheaval then there's nothing he can do. That sounds like a lot but it's only nineteen cards, making this a practical approach for a deck with a lot of card drawing and counters like Psychatog. However, this excludes his mana, his Tangle Wires and his Rishadan Ports. At the same time, the Psychatog player wants to count his Force Spikes and his Mana Leaks as some of the counters he will line up with those threats.

By looking at the two decklists like this, it can be seen who has to make something happen and who does not. In this example both sides have cards that are dead long term, so getting full impact out of them early is important, as is getting what they can later. It is also a good way to see what the true value of answer cards are in a matchup. What am I going to get in exchange for my cards? Whatever I get will determine their value. It will show what I have to do in order to stabilize, and what I need in order to gain inevitability. It also saves you from the need to figure out what these cards you are stopping are worth, other than that they are worth more than the other cards you could have stopped instead. The two sides have canceled each other out.

It is also an ideal way to engage in battlefield selection. If I attempt to win by lining up my counters opposite his Goblin Charbelchers and Tinkers, then my opponent will be responding to that by trying to make his Duress line up with my Counterspell instead, or get the Charbelcher in under Counterspell, or use Mana Severance to increase the percentage of cards in his deck that I'm trying to line up with, or a combination of those and other factors. Watch carefully for those cards that are going to 'count' and which ones can be ignored. Control wars, or long games involving control decks, are often direct applications of lineup theory and the person who does a better job of it with their deck and in the game wins. Most people who lose either don't consider this in advance, attempt to do something they can't reasonably do under the system (usually they write off something they can't write off) or never had the tools to fight.

Definition: Speed

I would suggest this definition of speed:


Yeah, I know, gee thanks Zvi. But that's what speed is, and a lot of people try and use speed to measure something else. It isn't tempo. Now of course there are lots of types of speed - most often there's deck speed, but you can ask how fast any card is at what it does, or how fast you can get the mana required to cast it. You can also speak of the speed of an engine, or a combo, or a clock, or just about anything else.

Definition: Tempo Tempo is related to speed, but the two concepts are not one and the same. I've spent a lot of time recently trying to find the best definition of tempo. Life can be considered as a part of tempo, but I think that it is better to consider life loss as one of the results of tempo loss instead. I also don't think tempo can be measured as something as simple as the combined mana cost of your permanents in play, and this time I'm not even going to explore what would happen with that definition. Eric Taylor made the claim that mana and time are mostly interchangeable, and Chad Ellis explained why things are not that simple.

Instead, I'm going to use this one:


What That Means

Note that this relates it to inevitability, so I need to be careful to define what I mean by a better or worse situation and in what time frame spells don't resolve, but I think that the resulting interactions work exactly as you would hope that they would. Yes, a player can gain tempo or lose tempo when nothing happens because of these interactions even if all the players do is play lands. Remember the definition of inevitability: A player is said to have inevitability if and only if from the current position he will win a long game. A player is said to have inevitability in a matchup if and only if they have inevitability on turn one.

This also will allow tempo to have a very neat relationship with other resources, although it gives up the linear direct relationship with mana as too often illusionary the same way card impact and mana proved to be similar but unequal. Tempo can therefore be measured in effect per turn. If I play a first turn Phyrexian Negator, I've gained five damage per turn in tempo until my opponent deals with it. The rate at which my tempo is modified is the rate at which the players can get card impact onto the table, which of course doesn't count blanked cards or cards that blank those cards without the potential to do anything else. Whenever I'm measuring card impact it can be assumed that it has been modified into Effective Card Advantage, which combines the variable impact of cards with the theories on when those cards are blanked. The reason these concepts were introduced in the first place was to fix the problems with simpler models.

Most of the time, the change that tempo creates will be in the form of life points, but it can also be in the form of cards in your library (if nothing else, the card draw for the turn is almost always there), or in many cases in cards drawn or destroyed. When spells are cast, they do one or more of two things: They generate tempo by placing a resource on the table that generates an effect over time and/or have an immediate impact on at least one resource. Resources are things it is an advantage to have more of. To say something that is by definition true: The change in your resources over time is equal to the sum of the total tempo you have over the course of the game plus the total direct impact of all non-continuous effects on those resources that do not result from tempo. To express that as an equation:

t
Rt = ? (T + DI)
turn=1
Where
DI = direct impact
t = turn number
T = Tempo
Rt = Resources on turn t

I stopped here for several days to pause and think about whether what I just said was accurate. Originally the equation was slightly different, but I discovered that this version was easier to understand and contained all the relevant information. To me this feels a lot like one of the basic equations of macroeconomics because it uses a bunch of variables to say nothing but it says it in a highly useful way. It sounds like you're wasting time to say that the sum of all the money in the world is equal to the sum of all the money in the world added up in a different way, but that leads to some very non-intuitive conclusions. I don't think this will be that grand, but it is an excellent framework from which to quantify what is going on in a game.

Tempo in Terms of Different Resources and the Problem of Jayemade Tome

Jayemade Tomb comes up in a lot of old examples that look into what card advantage and tempo are, and it is important to get the right answer. Under this system, Jayemade Tomb counts as card tempo, which I'm going to use to mean tempo that results in the gain or loss of cards over time rather than other resources, but it only counts sometimes. A creature on the board that is attacking for damage is tempo, but if there is a need to be explicit it could be called life tempo because its impact is measured in life points unless something else is thrown in the way instead. You can extend that for all other resources including more tempo - yes, there is such a thing as tempo tempo and mana sources will often qualify. Note that you could break up the resource equation into its component parts this way:

lt = ? (Tl + DIl)
Tt = ? (TT + DIT)
Ct = ? (TC + DIC)
.and so on for other things.
Note: l = life, c = cards

The reason Jayemdae Tome is a problem is that it points out two things you need to get right. First, when is Jayemade Tomb tempo? If you get to use it, it's a card a turn and that is great card tempo, but if you don't use it the Tomb does nothing. This definition was structured to get that right automatically: If you're using it then there is a change in resources which means that you had an equivalent amount of card tempo. If you didn't use it, you chose not to have that card tempo, probably in order to have something else instead. In this case, you had no card tempo that turn. What you do have is the option to make that exchange, and that is the resource R you created when you invested in the Tome. Sometimes that will be the same as one card/turn, other times it will be trivial.

The other thing to make sure is that a Tome in play not being destroyed is worth at least one more card than a Tome in your hand while you don't have eight free mana, because when you would be investing in it you can instead use it. Under this system, drawing the Tomb gives you the option to create the option - which will indeed always be worth a card less (minimum zero, which is also correct) because it is useless unless at some point you use that option and at that point you've chosen to invest in the Tome instead of activating it, which of course is worth one card less on that turn, so you are at least one card down by not casting it minus the doubt that it will ever get used. Example checks.

Conclusion

What I've laid out is a powerful system that helps relate the various resources of Magic to each other within the context of a game. That is central to what Magic is all about. It needs to be applied carefully, with different techniques laid out for different types of Magic games. When a new situation comes up or new cards are introduced, the system must be expanded to cover the new ideas and situations. When I was evaluating Darksteel I often thought about how a new card could best be considered under this system. Put the time into understanding what is here. It will be worth it.

One subject that I thought would be incorporated and was not is planning. The way you decide how to take advantage of these relationships is by deciding on your plan. It tells you what is valuable, what you can afford to give up and what a good trade would be. Lineup Theory is the beginning of a potential discussion of how to plan entire Magic games from the first turn that if properly handled would be a monster as long as this one, and excluding the understanding of theory planning is the biggest thing separating the top players from the pack. I highly encourage everyone to give us your feedback, because I.m not trying to give the last word. The more discussion that takes place, the farther Magic theory will advance.

Thanks for reading,

- Zvi Mowshowitz