By the time this article goes up, EVO 2011 will have come and gone. For those not familiar with it, EVO is like the world championships of fighting games. Once upon a time, before I played Magic competitively, I was a Street Fighter player. And while I have been far more successful with Magic than I ever was in Street Fighter, there are still many things I miss about it. For one, I miss the rowdy crowds cheering for their favorite player during a heated match. Watching a Magic match just isn’t the same; it’s much more subdued, since you don’t want to give away information that’s supposed to be hidden. Could you imagine a crowd of a hundred people gathered around a table, yelling and cheering during an intense match of Magic?

So how does Street Fighter relate to Magic? One of them is the concept of Yomi, a subject that veteran Street Fighter competitor and game designer David Sirlin has written about at length. I highly encourage you to check out his articles at www.sirlin.net, but I’ll give you the general gist of it here. Sirlin’s articles have been written about in a Magic context before, but I hope I can bring a fresh angle to it. Yomi is the Japanese word for “reading,” or in Sirlin’s words, “reading the mind of the opponent.” Let’s say we have a game of rock-paper-scissors. We can break it down into the following matrix:

You can see that all three of your plays are exactly the same, so it makes no difference what move you make; you have the same expected value, and it’s purely based on luck. Now let’s introduce the concept of unequal rewards. Let’s say that if you win with rock, you win $5; if you win with scissors, you win $3; if you win with paper, you win $2; and all ties are worth $1. Let’s examine the new matrix:

Playing rock here is the obvious “best” strategy, since it has the best expected value given that your opponent’s plays are random. Clearly, the best choice is rock, right? Right? Wrong. When you make decisions, you have to take into account that your opponent is a rational being who also makes decisions. This is where we introduce the concept of Yomi. At Yomi Layer 0, you just play rock because it’s the obvious best play. You know that your opponent knows this, so you counter with paper, despite it’s being an intrinsically worse move. This is called Yomi Layer 1. At Yomi Layer 2, you next-level your opponent by playing scissors. Yomi Layer 3 is playing rock, which is the same as Yomi Layer 0. The system can never reach equilibrium, because once a strategy starts to become popular, its counterstrategy will then start to become popular, and so on.

While this concept can certainly be applied to choosing lines of play in a game of Magic, I’m more interested in how we can use it to describe the metagaming process. Magic, unlike a game of RPS, has variance. Rock will always defeat paper no matter what, but Caw-Blade doesn’t always beat U/B control, which is why we have to introduce probabilities into the mix. Let’s say we have a two-person tournament and each player has three decks to choose from: control, aggro, and combo. Control beats combo 70% of the time, and beats aggro 40% of the time. Aggro beats combo 30% of the time, and beats control 60% of the time. Combo beats control 30% of the time, and beats aggro 70% of the time. You’re playing for $1,000; loser gets nothing. We’ll also assume that both players are equally skilled in all three decks.

The expected value for each deck given that the opponent plays a random deck is $533.33 for control, $466.67 for aggro, and $500 for combo. This is where Yomi comes in again. Do you just play the obvious best deck, the deck that beats the obvious best deck, or the deck that beats that deck but loses to the obvious best deck? Now, I’m guessing most people don’t play two-person tournaments, so we must again expand our example. Let’s say there was a recent tournament where control made up half of the decks in the Top 8. Most people are just going to copy the lists or only make a few minor changes. We’ll call them the Yomi Layer 0 people. Some people will decide to be clever and play aggro instead, hoping to play against the control players. We’ll call them the Yomi Layer 1 people. Some people want to be even more clever and play combo, the Layer 2 people. We’re going to use some math here, but bear with me. I’m going to take you into Mordor, then lead you right back into the Shire.

Let’s say 50% of the field is control, 30% is aggro, and 20% is combo. Each round, a control deck is going to have a 50% chance of winning 50% of the time, a 30% chance of winning 40% of the time, and a 20% of winning 70% of the time. That equates to a 51% win percentage. (At least, I hope that’s right; my probability theory is rusty. If I’m wrong, please correct me in the comments.) Doing similar calculations for the other decks, aggro also comes in at 51% and combo at 46%. In this particular example, going to Layer 1 gives you no real advantage, and Layer 2 actually makes things worse. This won’t always be the case, as I could easily fudge some numbers to change the outcome. But the point here is that you don’t always gain an advantage by trying to be clever and not playing the best deck.

The last case I want to examine is accounting for the difference in player skill, which can drastically affect your decision in what deck to play. Keeping with the same example, let’s say the control deck requires a lot of decisions. A skilled player will have better win percentages across the board, and an unskilled player will have lower win percentages across the board. The aggro deck also has room for outplaying your opponent, but not as much as the control deck, so the difference in skill won’t affect the outcomes as much. The combo deck is pure luck, so play skill doesn’t affect the outcomes very much. So let’s say for our example someone who is more skilled than the average player gets a 20% edge for playing the control deck, a 10% edge for playing the aggro deck, and a 5% edge for playing combo. A player who is less skilled than the average player gets similar penalties. How will this affect the win percentages?

Skilled player:

Control 71%

Aggro 61%

Combo 51%

Unskilled player:

Control 34%

Aggro 41%

Combo 41%

So in this particular example, an average player is better off playing control or aggro, a skilled player should always play control, and an unskilled player should play aggro or combo. We went from having a relatively straightforward game, to one that has many variables that can affect the outcome. Of course, in the real world, there are more than three decks to choose from, and you won’t know what your matchup percentages are nor what the metagame will be like. The best you can do is make educated guesses based on the available information, and an honest assessment of how you measure up to the competition. I hope this discussion in game theory and Yomi will allow you to make more educated guesses in your future tournaments.

Next week, I’ll be bringing you coverage from my local PTQ, and after that I’ll be starting on an epic five weeks of Magic encompassing Canadian Nationals, GP: Pittsburgh, PT: Philly, and GP: Montreal.

Until next time,

Nassim Ketita