Sullivan Library – Learning From Outside Sources: Magic and Game Theory

Read Adrian Sullivan every Tuesday... at StarCityGames.com!
Tuesday, February 12th – Improving at Magic is a tricky skill to master. Sure, we can read the sites and practice every day, but true enlightenment is hard to come by. Outside these obvious avenues, how can we hone our talents? Adrian Sullivan believes that Magic can be found, well, anywhere. Today he takes inspiration from the classroom, and looks at how a little Game Theory can improve our skills for the better…

I’ve been back in school for a little while now, and I’m loving it. It’s funny how as you learn more, you begin to apply it to aspects of your life that you never would have conceived of before. Some things seem abundantly obvious. If you’re an economics, sociology, or computer science student, when you start delving into game theory, it doesn’t take much to recognize that there are ways in which game theory can apply to a game. It’s a very easy connection to make.

As you learn more about game theory, you can even begin to see the ways in which you can directly apply the theory to the situation. Some things are a little more surprising, however. I imagine that there are all kinds of moments where someone can apply some knowledge that they have to a moment in the game. A poker player can find a moment of odds calculation. That same poker player, or just someone who works with people a lot, might simply get a good read on a person. Heck, some people draw lessons from Jedi knights, so it takes all kinds…

Earlier this year I was sitting in my Rhetoric and Technology class, and we were talking about the way that technology’s use has implications for future technology. One concept that came up was the concept of path dependence, in which the more that a technology gets used, the more that it not only causes people to use it, but also can adapt the environment around it in response to that use. A perfect example of this in the “real world” of Magic is Tarmogoyf. Before people had discovered just how powerful Tarmogoyf is, it wasn’t actually necessary to play it. In playing it, though, you would have a huge edge. To keep up with this edge, you’d end up having to play. Eventually, nearly every deck that could did, and many others warped themselves so that they could.

This phenomenon is very rare, but it was illustrative to me… the bizarre ways that what I was studying in school could have an impact on my Magic game. Maybe this is just another example of the Discordian concept of the Rule of Fives: The Rule of Fives states that all things happen in fives, or are divisible by or are multiples of five, or are somehow directly or indirectly related to five. The Rule of Fives is never wrong.

Another way to think of the Rule of Fives is this — humans are particularly good at finding patterns. If we can imagine that there might be a pattern, we will find it.

Regardless of whether me seeing Magic in my classroom is an example of the Rule of Fives, I’m still getting enough out of it not to care.

Lesson 1 — Fortuna and virtu

My most recent experience takes me to Machiavelli. Machiavelli is famously misquoted as saying, among other things, “Might makes right” and “The ends justify the means.” These are pretty gross simplifications of Machiavellian thought. But he did say some things that recently got me thinking about Magic.

This weekend was pretty terrible for me. I went an unexciting 1-2-1. I liked my deck, but that doesn’t change the mediocre finish. As an additional fun moment of aggravation, my car decided to finally go off into that great car-yard in the sky.

Machiavelli said that there are two things which govern our lives — the capricious nature of fate (fortuna, the wheel of fortune) and our own merits (virtu). We are shuffling cards in this wacky game of Magic: the Gathering. In Magic, our merits are going to be our deck, our recognition of the metagame, our play skill, and any other aspect that we bring by virtue of the cards we hold in our hands and of who we are. But, once again, we are still shuffling cards.

Bad things happen. That is the nature of the game. This weekend, apologies to Richard Feldman aside, I lost two matches where I felt that the vast majority of the game was decided by manascrew and mana flood. This is not to say that I would have won any of those games or either of those matches, necessarily, if my draws had had a more typical mix of those cards, but certainly I would have felt more comfortable about my losses.

But that is how the game goes. If you can’t accept that sometimes in Magic you’re just going to get screwed, it’s time to find another game. It will happen to you. If you can accept the nature of the game, you’re going to be a lot happier than the person who cannot help but scream and shout about it for days to come.

Lesson 2 — Fate and fortuna

If you’ve ever read the novel Invisible Man, by Ralph Ellison, you know an aspect of the picture it paints. It is one in which someone’s fate can often be decided greatly by the larger forces around them. If you come from a certain background, you are largely tied forevermore to the limitations that fate has given you. If only they could shift it, perhaps we wouldn’t be so tied to fate’s capricious nature. We can bemoan our fate again and again, but the truth is, unlike real people living in the real world, we can shift our place in the world of Magic. We can choose a different deck that might have less of a problem with the randomness that can hit it. The reality, though, is that some people’s decks are going to be better equipped to avoid such problems from the start. Deck choice does matter in these situations, and thus we are under complete control.

I played my version of The Rock, and other than two Sensei’s Divining Tops I don’t really have much of a way to impact my draw. On the issue of my card/land mix, I am at the mercy of fortuna. Whereas some decks, by their very nature, come afforded with certain privileges, others do not.

Take a deck like the many varieties of Next Level Blue. Personally, I prefer the Gerry Thompson versions that live out there, for the very reason that Next Level Blue seems to do so well: it can minimize its randomness. While not unique to GerryT, the inclusion of Trinket Mage is a card that helps to minimize the randomness of the play of the deck. It does what it does.

Deck manipulation, in general, has always been one of my favorite ways to decrease the power of random chance in a deck. Brainstorm, Sylvan Library, Sensei’s Divining Top — all of these let the long game of a deck begin to approach a point of being overwhelming. (A short aside – I see most decks that include a card like Gaea’s Blessing using it woefully inappropriately, largely because they don’t seem to understand how they should be building their decks to use it.) We have to recognize that these elements in a deck are a part of what makes us choose a deck.

I chose a Rock deck with two Sensei’s Divining Tops largely because I felt that the metagame of the moment is diverse enough, I wanted to be able to have a chance against anything, and that the slots taken up by two Sensei’s Divining Tops would help me reduce the negative impact of fortuna in the long run. But what if I had chosen a different deck?

Take Dredge. With Dredge, the things that I need to have “going right” are fairly small. A Dredge deck can mulligan nearly infinitely, because it is only relying on a bare modicum of resources to get going. It needs to find a way to get a Dredge card into the yard, and then, generally, it will be good to go.

Clearly, there are ways to beat Dredge. In Machiavellian terms, we’re putting ourselves more in the hands of our opponent’s virtu when we choose a deck like Dredge, but we are also drastically reducing the way that fortuna rules us.

Dredge is able to do this because of the way that it “guarantees” the result of our draw phase. We know that we’re going to be able to get this effect off. Next Level Blue does this with a greater or lesser amount of deck manipulation. But it also usually includes an element of another great way to reduce chance: drawing cards.

Drawing cards is another surefire way to make sure you get the mix of cards that you want. For most decks, this is going to mean that you’ll have a card like Thirst for Knowledge or Dark Confidant. In other decks, this will mean a drawing engine like Life from the Loam. Whatever the case may be, when you have card draw in your deck, you’re reducing the chances that your deck will peter out on you via the brute force of more cards.

Other decks have their own ways of cleverly addressing this. The newest versions of Owen Turtenwald Red Deck Wins deck (laughingly titled, still, “Chocolate Rain”) have moved onto using Magma Jet as a means of choosing their fate. Part of the appeal of Countryside Crusher is its use in the same capacity. It may not give actual card advantage, but it can give you a density of cards that you can play that might as well be card advantage.

Our deck and card choices are under our control. Fortuna may rule us to some degree, but we have an influence in just how much that is.

Lesson 3 — Eric Bach, Algorithm Design, and Playing for Luck

In my first stint at school, I was not studying Rhetoric. I was studying Computer Science. Let me tell you, they are, in many ways, worlds and worlds apart.

I still remember my Algorithm Design class. My professor, Eric Bach, was a cryptography expert, and I heard rumors that he was someone the government paid special attention to when he traveled overseas because of his cryptography skills. For me, though, he was a bear-sized yet somewhat soft-spoken professor, just a bit on the “poor” side when it came time for teacher evaluations, however incredibly talented he might be in the field.

It was this professor that first instructed me in applied game theory. One of the biggest lessons was this: in a contest between opposing forces, the best play is usually to make the play that maximizes your minimum gain (astute game theorists will recognize this as ‘classic strategy’ in game theory), but sometimes, that simply won’t be good enough. You’re going to have to play to get lucky.

Tiago Chan wrote about his experience at Worlds, where he played for the element of luck. He couldn’t win unless everything went just his way. And so, he played for that chance. It went just his way, so he won, but importantly, it is worth noting that he wouldn’t have won it if he’d just played for the “best” play in every turn. He had to look beyond, and see where that would get him (in this case, it would leave him short of a win). Kai Budde is somewhat famous for these kinds of games. It’s hard to even think about Kai without thinking about Morphling, and how he played out a game, banking on it.

Most of the time, when you play for this late game situation, you lose. There is a reason that game theory refers to this element of playing for luck as “romantic strategy.” But that doesn’t mean that there isn’t something inherently potent about it.

You can make use of a kind of romantic thought even when you’re not in a particular game situation. Take the one-of, for example. Including a one-of in a deck is not usually correct, but sometimes it can be. I went into this in considerably more detail once, but one element I will revisit here is the way that a singleton can impact your deck’s overall performance.

You can’t count on it to show up, so you’d better not be building a deck with a one-of for that purpose. But if you have a deck that could potentially go to a long game, has card drawing, or relevant tutors, certain singletons will “via luck” make crazy things happen. One Upheaval in a deck dramatically changes how the deck will play out. It is absolutely possible that the card’s negative value (i.e., can’t be cast) will outweigh the positive effects that it has on a game, but regardless, the deck itself has a fundamentally different behavior as a result of the card. For my own Rock deck, for example, I determined that I didn’t regularly want Profane Command in my deck. Even two copies of the card were too mana intensive, and didn’t reap enough rewards. But I couldn’t argue with playtesting results that showed that one copy of the card was having a positive result on the Expected Value of my game.

I had sacklands and I had Tops as my library manipulation. Other than that, the only card draw I had was the draw phase. But between the minimal number of Commands and that manipulation and card draw, I was unlikely to ever draw the Command unless I wanted it. When I wanted it, it might not show up, but there would be an ever-increasing chance for it to appear. And in those games where I wanted it, it was a blowout.

Increasing your access to the positive sides of randomness is another key to winning.

Lesson 4 — The Zen of Sheldon Ross

One of my favorite books is Zen and the Art of Motorcycle Maintenance. I didn’t fully appreciate Robert Pirsig’s book until recently, though, as I’ve gotten more and more acclimated to academic studies of rhetoric. While the book set of a huge fad, which still somewhat continues, of “Zen and…” books, this one is less fluff and new age than one might expect. After many re-readings, it has definitely become a useful tome to me when it comes to thinking about words and rhetoric.

Meanwhile, one of my less favorite books is Sheldon Ross’s A First Course in Probability. It’s not that it is a bad book. In fact, probability fans out there, it’s a book you should own if you care about such things. It’s just that the last probability course I had kicked my ass a little bit, and this was one of the books for that course.

Combining thoughts from the two of these courses, though, is something a bit more esoteric. The lesson is this: let it go. It is chance.

People get upset a lot in Magic. Hell, they get upset a lot in life. There isn’t really much difference between the man yelling loudly at his smoking engine, as he waits for a tow truck, and someone else throwing their deck across the room after a bad match.

There are so many intersecting elements of probability going on in Magic. There is the probability of a poor draw, the probability of the opponent’s god draw, the probability inherent to a matchup, the probability of getting that matchup, and on and on. Fortuna, as Machiavelli might say.

We just have to move on. It is in how we respond to these moments that we are measured. Again, Machiavelli, this time, talking to us about our virtu. Results are not inevitable. A well-held response can make you turn that imminent loss into a win. Sometimes, at least.

But more importantly, keeping your cool in the face of the inevitable bad turns of fortune can simply make you live a life of higher quality. And, maybe I’m crazy here, but I bet you’re going to find yourself less apt to lose your next game, if you aren’t still fuming about your last one. And, further, I bet you’re going to be happier if you can move on as well.

Everyone has bad beats. It can be fun to kvetch about them, but ultimately they still happened. Finding that way to let them pass over and through you will make playing a game in which so much is dependent on chance all the easier, and all the more fun.

See you next week! And enjoy…

Adrian Sullivan