"The Theory and Design of Magic: The Gathering" Class Page

I know there was some discussion last year about doing a repeat of the class, but we decided not to, at least for this quarter. Both Tom and I have a few other, more important commitments, and with constant research and 24-7 office hours, we figured that it would be best not to repeat.

Even so, it remains possible (though honestly, unlikely) that we’ll pick it back up for a quarter in the future, so we’ll let you know here if that happens. I realize the material might be a little stale, but I’ll certainly leave this site up and all of the materials for anyone interested in what we put together.

As a preview to some content on the next podcast, I posted decklists that have been submitted to us from students here. Feel free to take a look, and if you have any feedback, I’m sure the students will be very appreciative. Either leave a comment or email Tom or me and we’ll pass it along.

If you’re thinking of other cards that they should be playing with, generally, we’re pretty full on Lorwyn forward thanks to Dave’s donation. That is, there are really no rares, and uncommons (especially good ones) are very sparse, but commons should be generally available, and other things might be gained with trades.

This has come up a couple times now, and I think it deserves its own post: what’s a good one-shot metric for Magic? As in, what’s the best way to boil down a situation into a single number?

The motivation for this is that pretty much all Game Theory problems depend on comparing the payoffs for you and other agents. You want to maximize this payoff in these games, so a question about “What should I do?” can simply be comparing a single payoff for that set of strategies.

What’s tricky is how to get Magic to fit into this scheme. First, Magic is a long series of choices, not just a single situation. Thus, when you transition from one turn to the next, it’s not like there’s some result and clear answer about whether you’re better or worse off. The game keeps going.

Typically, these situations are usually dealt with in Magic puzzles by making the challenge to win the game by the net turn. For example I’ve seen quite a few of those puzzles where they set up the cards and say, “How can you win next turn?” (with the implication that you’re a failure if you can’t win). The unfortunate part about this is that this only gives us a binary payoff of either win lose. And a lot of situations depend on more nuanced comparisons between the values.

So some of the metrics I’ve considered or had mentioned to me include:

• life totals. This is what I used in the first You Make the Play. The problem with this in my mind, is that it doesn’t come close to representing anything about the game. I’m comfortable being at 10 life when I just played a Wrath. Not so much when my opponent just sneak attacked a Progenitus. More generally, I’m really wary about using any in-game metric, whether that’s life totals, total mana, total permanents, accumulated beats/card advantage. They’re all meaningful, but none of them can entirely capture a situation
• turns to live. Also an interesting one. I think this one is better in that you assumingly abstract away most of the game to come up with this number. The problem I see with it, though, is that one must immediately ask, “Well, what does that mean to this deck or that deck?” Again, 4 turns to live means a lot more to a heartbeat deck than a turbo-fog deck. Granted, most of these situations are within a single deck, but it doesn’t give consistency between you and your opponent
• an evaluation function. This is what I talked about in minimax. I thinkt his is fair because people can agree that it could somehow exist, and it abstracts away the game. It does better than turns to live because we can also assume that it is normalized for all decks so that a 5 means that a player playing heartbeat would be just about as confident as another player playing zoo who also got a 5. This, however, is obviously very difficult, and I have no idea what such an evaluation function would look like. Heck, if you could figure it out, you could probably “solve” Magic. That, however, is not how things are, though we can imagine that we would come up with something else
• percentage to win. I feel like this is actually very similar to the evaluation function, except that 66% chance of winning means a lot more than 24. Both abstract the game away entirely and turn it into a number that somehow translates into your ability to win. This seems to be what I’ve drifted to, but Reyemile brings up the very valid point that it might not be fair to abstract away the game like this. From a theoretical perspective, this is vastly easier to work with, but given that the purpose of the course is to reevaluate these theoretical games into the much more concrete situation of Magic, I don’t think it’s fair for me to call it a day with this one.

Opinions? Any other methods you feel like would work, or pros/cons of what I’ve mentioned above that I didn’t put down?

So I posted a description of the class on both the mtgsalvation and wizards forums, to enthusiastic response and great feedback. I just got off the phone with Tom, and we did some rearranging of the syllabus based on feedback from everyone on that topic. Here’s a quick list of some of the people to thank (sorry if I miss you):

tcg_researcher, stsung, zombiefl12, tanishalf, drworm, sacrificial23

So based on that, we rearranged to the following order

• Week 1 – Overview of topics and the rules of Magic
• Week 2 – Deckbuilding Basics and “Card Advantage”
• Week 3 – Game Theory in Multiplayer games
• Week 4 – Game Design
• Week 5 – Statistics and Simulation in Deckbuilding
• Week 6 – Epistemic Logic and Limited
• Week 7 – Metagame and Applications of Graph Theory
• Week 8 – Magic-playing Artificial Intelligence
• Week 9 – Presentations

So a little commentary on the changes is in order as well.

We talked a lot about what we wanted to put in week 2, and we ultimately decided on deckbuilding and card advantage. When we think back to teaching some of our friends, it honestly didn’t take them long to start building their own decks. And that was unguided. Since we’re hoping that students will take us up on open office hours that first week, they should be familiar enough with the game to be ready to at least understand why decks are built as they are and what to look for. Obviously, deckbuilding takes a lot more skill than one can have in week 2, but it makes more sense to lay the ground early then hit harder later.

Card advantage also got lopped in there because we figured that although it’s considered an advanced magic topic, it really isn’t that surprising or rigorous when explained. It doesn’t really fit with any of the academic topics anyways, and works best when talking a little about card selection for deckbuilding.

Game theory and multiplayer is in week 3. We pushed it back a little because of the response, but in the end, we couldn’t see it being in the 2nd half. I think the pull for game theory early is greater than the pull for multiplayer late. The reason why I want these connected is because a lot of game theory deals with cooperative games, and it doesn’t make sense that players should cooperate in a duel (unless they’re trying to draw into the top 8, but whatever). And the reason why it’s in week 3 is because we feel like by this point, in a 10 week quarter, we need to talk about something real.

Week 4 is game design because zendikar is being released on october 2nd, and this class is on the 13th. That gives us  a week and a half to talk about it and read up and put together a presentation on it. We felt like game design could be either 3 or 4, but it goes 4 because game theory is 3 (for the reason above). Although we certainly mean to talk about game design in a larger sense, zendikar at least gives us the grounding in one set so that we can make sense for awhile before explaining the bigger picture.

Week 5 is uninteresting, and week 6 is epistemic logic and limited. When I thought of my examples, a lot dealt with limited formats, and since we moved it out of the first half and away from deckbuilding, we figured it still deserved a lecture slot.

Which means that something had to give, which was metagame. That’s now paired with graph theory. This happened because although tournaments are interesting, they’re not academic. And honestly, my understanding of metagame analysis showed that it maybe wasn’t the same “metagame” that we mean in magic. I think it came up as filler in the original syllabus anyways, so this is a way to put it back in its rightful place.

And AI finishes the course out because it’s my pet lecture that doesn’t really matter for the presentations. That way, we can kill a week on a very academic and very interesting topic that doesn’t really matter. It’s dead week type material.

Comments on the changes?

I seem to have an obsession with making new blogs. I think it has something to do with my belief that someone might care?

So what this is all about. This blog is going to chronicle the design of a course. Particularly, the course is about Magic: the Gathering, the card game. I’m thinking it might one day turn into the class page as well. So a little history about this.

At the end of winter quarter my freshmen year, Tom, the guy next door, brought his Magic cards from home to sell. I myself had played for 2-3 years until quitting mid-senior year in high school. I was very excited and soon, we had a play group in Tom’s room. Tom and I both play at a proficient and knowledgeable level, having both read articles and been familiar with some of the theory of the game. One of the silly ideas we threw around was teaching a class on the game. By that summer, we got the idea that we could teach a student-initiated course here at Stanford on it. We threw together an early syllabus and applied the fall of our sophomore year. Although we brought in a lot of interesting topics, the class still felt like something cobbled together to justify playing Magic. As such, we were rejected by the committee.

But we weren’t going to be blown off so easily. This spring, 2 quarters later, we re-applied with a new syllabus. This time, we changed out a lot of the Magic readings in favor of academic readings and re-designed the class so that the topics formed a more cohesive set. We moved from a course about Magic to a course that used Magic as a teaching tool for a lot of interesting topics. We worked to make the syllabus much more rigorous and were rewarded with apparently enthusiastic response from the faculty committee and approval to teach the class this fall.

So the purpose of this class is what I mentioned about: to find an interesting way to talk about what we consider interesting concepts using Magic instead of the stock examples. It’s actually amazing how closely the concepts of Magic are tied to real things. As such, the class is going to be meant for new or casual Magic players looking for something fun to do while getting a survey of a couple topics. These include:

Statistic & Probability – these are better known as the “mana curve” and “deck thinning” in Magic. Magic is a game where two players draw cards out of their deck. Trying to figure out when a card is going to be drawn and with what chance is absolutely stats.

Game Design – this one should be pretty obvious. Magic is a game. People design it. Thus, game design. Fortunately, Wizards of the Coast has had 2 excellent weekly columns on it: research & development in “Latest Developments” and design in “Making Magic.”

Game Theory – another one that is basically built into the name. Game Theory is about making decisions based on the decisions of others. That’s pretty critical in Magic because you’re constantly making choices based on what your opponent is doing.

Epistemic Logic – this is what you’re trying to do when you read your opponent or signaling in drafting. It’s the logic of knowledge. This has a lot of parts, but the part that I have exposure to deals with what agents know, what they know about what others know, etc. There’s some really interesting work formalizing this that we can apply to Magic

Graph Theory – this is the idea of a deck having good synergy. I personally am not doing the work for this, but the idea is that we can attempt to use graphs to represent decks and determine how effective it is based on what sort of topological surfaces the graph can be mapped onto.

Artificial Intelligence – honestly, this is just my chance to show off some of what I know about game AI. It’s reasonable to think that if a computer can play chess, it can play magic.

Of course, all this is gone into much more depth in the syllabus. I’m actually hoping that a lot of people will take a look at that and comment on it. The disclaimer is that I’m not an expert on any of this stuff. Far from. Instead, most of the academic stuff is going to be at a college 101 level. Thus, I’m likely misinterpreting/making mistakes on much of it.

So we’re going to meta out a level right now. This blog is about this class. What you’re likely to see on this page is just our research and progress in the class. That might include

• decklists of beginner decks that we’re building
• interesting articles we find around the internet
• slides from presentations we’re putting together

Hopefully, Tom will be posting stuff as well, but he’s probably not as blog-crazy as I am. Which is a good thing, in some ways.

Since we’re just starting now (Tom just got back into the country), it’ll probably be slow in the near future. In the meantime, I posted some links on the right of some of the sources we’re using.