Eric Taylor
4/11/2002

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First of all, I have to say that most of what you read about Magic strategy is flawed. Of all the subjects in magic, there is one that is so important that it should be talked about constantly. Yet it so rarely talked about, this aspect of Magic has become the equivalent of the urban beggar. People walk over it, eyes averted, but certainly never, ever talk about it.

I, however, am going to talk about it, that thing that pervades every aspect of the game. That thing is probability. Put specifically, it's about playing the percentages...

1. The Mulligan
Many mages have a simple system: mulligan the one or no land hand, keep everything else. That is not playing the percentages.

You can and should play the percentages for the mulligan. Merely mulliganning the one or no land hand is too simplistic a system to let you play optimally. For instance, if you have a one land hand and you are trying to decide if you want to mulligan or not, you can look at your hand and see how many one and two turn plays you have and decide how likely it is that you can make reasonable plays in the first few turns of the game. For instance, if you have a bunch of two mana plays and already have the correct color land in your hand, you know that the likelihood of drawing a land in your next two draw phases in a 40 card deck with 17 land is 74% (if you figure it out that's 16c2 + 16c1*17c1)/33c2, using the notation nCk, for "n choose k" or n!/((n-k)!k!)). Not that you need to know this exact number, but you should know that it's pretty darn likely to draw a land in your next two turns, and if you already have a few low casting plays, why sure you should keep.

These kinds of numbers are hard to figure out. However, there's a an easy and practical way to get a handle on how often you should mulligan. That method is to look at the top of your deck after each mulligan, and keep track of how often you mulligan correctly and incorrectly.

Many mages refuse to look at the top of their deck after a mulligan to prevent them from going on "tilt", but unless you are very sure of your math, this is a simple and easy check to see that you have been mulliganning correctly. It is a simple way to decide, over the long run, if you have been playing the percentages correctly.

Here's a rule of thumb to be aware of: In limited, a single card is usually more valuable than missing a land drop early in the game, and you can recover from it more easily, but most mages tend to mulligan at the same rate in limited as in constructed, which is normally going to be incorrect.

Rule of Thumb: Mulligan more aggressively in constructed than in limited.

2. The Sideboard
The sideboard is also a critical place to play the percentages.

Suppose you are playing a deck that you want to sideboard Ghastly Demise and/or Slay for, but you only have 4 slots left. How many of each do you sideboard?

The answer is to play the percentages. Suppose you are putting these cards in against a monored deck and a monogreen deck. Slay is amazing vs the monogreen deck, but useless vs monored. Ghastly Demise is ok against both of the decks.

However, this alone is not enough information to figure out how many of both to place in your sideboard. You need more information to be able to play the percentages. That is, you want to try playtesting the sideboarded games and see how well the decks perform when you sideboard differing amounts of each card and see how it performs against both matchups and then take into account how prevalent both of the decks are.

For instance, suppose monogreen is 50% of the metagame while monored is only 25%. Suppose also that every additional Slay helps your win percentage by 10% (but only against monogreen), while every additional ghastly demise helps your win percentage by 5% against both decks.

In this case for instance, each Demise helps you by 5% times the prevalence of red and green that is 75% of the decks, while each slay helps you by 10% times the prevalance of monogreen (50%).

0 demise 4 slay = 20%
1 demise 3 slay = 19%
2 demise 2 slay = 18%
3 demise 1 slay = 16%
4 demise 0 slay = 15%

In this case you want 4 slays. You just give up on the Ghastly Demise. Why? Because in the long run you get more game wins percentagewise with the Slay. I'm not saying Slay is better than Demise. Nor am I saying that you always pack 4 of one and 0 of the other sideboard card. What I am saying is that you want to figure out how much a card helps you against each matchup, then add cards to your sideboard according to how much they increase your overall win percentage.

In real life, unlike my example, you usually don't get 10% additional wins for each additional card of a particular type you add to your sideboard. In real life, you generally get more ultility out of that first sideboard card and progressive less for each additional one.

A lot of times people will play a card because it's good against the best deck in the format. But you want to figure everything into account. How much does this card help you? Just how prevalent, exactly, is this deck? The single most common error people make is adding a bunch of cards to their sideboard against the best deck in the format, even if the best deck is not very common and even if those additional cards don't even help you much.

Rule of Thumb: Add cards to your sideboard which make the biggest difference in your win percentages against the most common decks.

Don't worry if you have to "give up" against a particular deck, if the deck is uncommon, especially if you find it hard to beat in the sideboard.

Playing the percentages here is like betting pocket aces in hold 'em. Sometimes you get beat by some guy who hits that straight on the river, but you've just got to dust yourself off and keep playing those aces. You certainly don't start playing the low cards in order to get revenge on your opponent the same way he got you.

Sometimes when you make your sideboard with some holes in it against a particular archetype you will face that archetype in a tournament and lose. That doesn't mean the next tournament you fix your sideboard to beat that one deck to get revenge, especially if it is not very well represented.

3. The Metagame
The metagame is sometimes Rock/Paper/Scissors. That is, a three-way metagame with no clear cut favorite. Other times, there is a clear favorite deck Rock, and Anti-Rock. That is, any other deck built merely to beat up Rock and which doesn't necessarily beat anything else. And sometimes the metagame is very diverse, with many deck archetypes being viable.

In the long run, if all the card sets stayed the same for a while, a metagame should have some average point about which it varies. This is the point where any deck type will win 50% of the time. If a deck wins more people play it more, and if a deck loses more they will play it less, and over time each tier one deck is represented at the amount that causes it to win as much as it loses. I'll call this state the "metagame equilibrium."

Nearly every metagame equilibrium state is unstable, due to a number of reasons: new deck archetypes coming out, rules changes, new sets, and more. All in all Magic is indeed the game Garfield envisoned. It is no chess, where you play the Ruy Lopez game after game after game. Instead, the cards, the decks, everything changes quickly enough so that the metagame is always shifting. Additionally, for purely psychological reasons, the metagame would probably oscillate around the equilibrium position even without the additional perturbations given by changes in the game.

The single most common error people make is adding a bunch of cards to their sideboard against the best deck in the format...

However, it is still useful to know what percentage of decks make up a metagame equilibrium, because knowing this and comparing it to the actual percentages of decks played by people in a given tournament will let you know you the optimal deck to play.

For example, let's take Pro Tour Osaka.

In the top 8 you had 3 black decks, 3 UG decks, 1 Psychatog deck, and one rogue black splash blue deck played by Oliveri. Discounting the Oliveri deck, to make things simpler, we get:

black = 43%
UG = 43%
psychatog = 14%

In retrospect, this seems like it is pretty close to the metagame equilibrium.

If this is the metagame equilibrium then, if 14% of the tournament plays psychatog, 43% play UG, 43% play black, it would mean on average all these decks would go 50%.

Here is where knowing the equilibrium metagame is useful. If you figure out the real metagame and compare it to the equilibrium metagame and notice any particular deck which can take advantage of the difference between the equilibrium metagame and the real metagame, that is the deck to play.

If, however, the metagame is close to the equilibrium position then the metagame has no influence on your choice of deck -- though there are still things to consider when picking a deck (for instance, pros usually pick decks which give more "play": decks which offer more choices in a given game, and thus more chances to outplay your opponent. Conversely, amateurs will typically pick a deck that has less "play", and wins or loses despite who is at the helm).

You can also look at it in a purely rock/paper/scissors way. UG beats black, black beats Pyschatog, Psychatog beats UG. But is a purely rock/paper/scissors method going to work, if you don't take into account the percentages?

Let's look at the real Osaka metagame: Day 1, UG was around 29%, monoblack 21%, Psychatog around 13%, and I'll put down the rest, 37%, as rogue. Day 2 UG was 38%, Black 30%, Psychatog 12%, and rogue weighs in at 20%.

What was the best deck, in retrospect, to play for this tournament?

If you think in a purely rock/paper/scissors way, you would make the single most common mistake most people make about the metagame: This is the assumption that Rock, Paper, and Scissors are equal in all regards. In the childhood game of Rock, Paper, Scissors, Rock beats Scissors 100% of the time, Scissors beats Paper 100% of the time, and Paper beats Rock 100% of the time.

But that's not how the real-life magic metagame happens. In magic, there can be (and almost always is) an unequal division between Rock, Paper and Scissors. If you don't take into account the equilibrium metagame, and just think of simple Rock, Paper Scissors, you can get tricked into playing the wrong deck.

Rock just doesn't beat Scissors 100% of the time in magic. Let's do the simple rock, paper, scissors analysis. If UG is rock, Black is scissors and Psychatog is paper, with percentages of around 30 or 40% for both UG and B, and percentages of around 10 to 15% for Psychatog, it seems that there is a lot of rock and a lot of scissors and very little paper. So to beat this metagame you want to play rock, because it beats scissors and loses to paper but since there's so little paper, rock should win. That's the simplistic rock, paper scissors analysis.

And that analysis is wrong.

If you increased the number of rock decks (that is UG) in this example, what happens is not that rock wins more. Rock would actually win less! The reason is that while Rock beats scissors decently, and scissors beats paper even more, paper just absolutely demolishes rock, so even though paper is not very well represented, you can't increase the amount of rock and have it win even more.

If you look at the metagame equilibrium for Osaka, you can see that:

B = monoblack decks = 3/7
UG = UG decks = 3/7
UB = Psychatog decks = 1/7
a = percentage of wins for B vs UG
b = percentage of wins for B vs UB
c = percentage of wins for UG vs UB
d = percentage of wins in the mirror (which has to be 50%)

By definition, at eqilibrium position all of these decks win 50% of the time, so adding together you get:

1) a*UG + b*UB + d*B = .5
2) (1-a)B + c*UB + d*UG = .5
3) (1-b)B + (1-c)UG + d*UB = .5

Line 1 is the equation for the amount of wins for black, 2 is wins for UG, and 3 is for Psychatog. All these equations say is that on average the decks win 50% of the time (given a metagame equilibrium).

There is a single degree of freedom left in these equations, so to solve it we need to get at least one of the deck win ratios. If, for instance, UG beats B about 60% of the time, then a=40%, b=80%, c=7%. Actually, you never need to figure out exactly what percentage of the time each deck wins. It is sufficient to merely know the metagame equilibrium, and from that decide how far the metagame is off from it, and then play the deck that can take advantage of it. But you can see with a skewed metgame like this, with different percentages of rock, paper and scissors making up the equilibrium metagame, you also get uneven win percentages. That is why you can't do a simplistic rock, paper scissors analysis.

Osaka in fact was an example of the metagame close to its equilibrium position from the very beginning. It really didn't matter what people chose as a deck; black, UG or Psychatog were all equally viable, and in the top 8 it came down to matchups, and the luck of a single elim tournament, to determine a final winner more than anything else.

Suppose there is an Odyssey block tournament held where the percentages of the decks are 1/3 UG, 1/3 Black, and 1/3 Psychatog?

What is the deck to play here? In this example Psychatog is far too well represented, as it should only be at about 10 or 15% in the equilibrium metagame, so you want to play black.

Now on to some general rules about the metagame.

Metagame Rule of Thumb #1: If a metagame is not at an equilibrium position, play the deck that beats the overrepresented deck.

You have to know the equilibrium metagame for this to work.

As I said before, there are metagames where there is just rock and anti-rock. And anti-rock can be broken down into a sub-metagame of various anti-rocks some of which really do beat rock some of which don't.

If you don't take into account the equilibrium metagame, and just think of simple Rock, Paper Scissors, you can get tricked into playing the wrong deck...

This type of metagame, by the way, is the type in which pros perform the best in. The reason for it is mostly about humility. Now you might expect me to say that it is the amateurs which are humble, but really, it is the pro. One difference between a pro and an amateur is that if there is a best deck and some homebrew deck, a pro will swallow his pride and just play the best deck, while an amateur will want to play his homebrew creation to prove to everyone that it is good. (Don't worry, the pros make up for this humility in deck choice by being arrogant in every other aspect.) What this means is that when there is a clear favorite, simple psychology leads most people to want to play anti-rock. This leads the rock deck to being underrepresented, and in the end causes it to usually be the deck you want to play. Which means:

Metagame Rule of Thumb #2: When there is a dominant deck, play rock. Rock is strong.

For the third and final metagame rule, sometimes the metagame is extremely diverse, with not just rock paper and scissors but many deck types, dozens of decks that are all viable. A lot of times we find out in restrospect that this kind of metagame was an illusion, such as the 1.x metagame that Bob Maher won with oath, seeming to have dozens of viable archetypes, only to find out a few weeks later that it was really rock and anti-rock, with Trix dominating. In either a diverse metagame or a metagame close to the equilibrium point, it doesn't matter from a metagame perspective which deck you play, so you want to choose a deck which suits your play skills best.

Metagame Rule #3: In a diverse metagame, or one close to the equilibrium point, choose the deck which you can personally play the best.

So what after all, is T2 most like? It is fairly diverse, and while the strongest frontrunner for rock right now is the Zevatog deck, it doesn't appear to dominate the way a Trix did. The metagame appears to be more like Osaka, a lopsided rock, paper, scissors metagame, with Frog in a Blender beating Zevatog, and some tough choices to figure out how well represented decks like Braids or BUG should be in the equilibrium metagame.

All things considered, I would probably suggest Rock, aka Zevatog. Theoretically decks like Frog in a Blender should hold down Zevatog, but like I said before, people enjoy playing their own creations instead of net decks, so not only will there not be enough Zevatog to be able to take advantage of it by playing a deck that can beat it like Frog in a Blender, I have a feeling that also the percentage of people playing Frog in a Blender won't be as close to the equilibrium metagame as it should be. Of course, each metagame is different, and it never hurts to take more than one deck to a tournament if scouting indicates a situation you can take advantage of.

www.neutralground.com is probably the best place to go for premier decklists right now in type 2, as the grudge match is very hard fought and gives rise to very good decks. Here's a copy of Zevatog from the Brainburst Type Two deck database:

Zevatog

Zev Gurwitz

Format: Old_Type_2(3/2002-6/2002) - Torment
Legal when Torment is current set

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