Some thoughts back and forth

One of the things I’ve been trying to do is to get some opinions from some more prolific people in the Magic community. It seems like a pretty natural instinct to appeal to the most knowledgeable, and fortunately, I got a hold of Frank Karsten, recent Magic Hall of Fame inductee and Magic writer, including several pieces on Magic. This is going to be a somewhat long post, but here’s what our email exchange looks like. Feel free to add in on any of the points in either:

Frank to Tom and me

Course Syllabus

A Class? On That Silly Card Game?

Game Design:

  • “…by understanding the intent of design, one can become a significantly better player.”; you may (instead) argue that learning something about game design may also be useful for computer science students when making computer games or something like that.

Game Theory:

  • “The history of game theory comes more from political situations and the arms race”; I think historically, it actually originates from an analysis of parlor games and of economic situations of coalition formation (Von Neumann and Morgenstern’s 1944 Theory of Games and Economic Behavior).
  • “where the choices one must make choices”; the second ‘choices’ is superflous
  • “whether to bluff, call, or fold”; so in poker bluffing is equal to raising? J

Week 1 – Overview of topics and the rules of Magic

Week 2 – Deckbuilding Basics and “Card Advantage”

Week 3 – Game Theory in Multiplayer games

  • I never play any multiplayer, so I may be biased here … but I would move multiplayer (if you want to cover it at all) to the end of the class, or at least after probability and deckbuilding. I would rather first teach everything about the game itself and then afterwards move on to extensions such as multi-player Magic. Putting it in week 3 seems too early, especially when not everyone is a solid Magic duel player yet.
  • Note that game theory is not only applicable to multiplayer games but also to two-player games. I regularly roll dice on the Pro Tour to decide whether to block or not (since a mixed play leaves no strategic holes that can be taken advantage of by a good bluffer, as partially explained here, for example. A game-theoretical analysis of bluffing is also applicable to games such as poker.

Week 5 – Statistics and Simulation in Deckbuilding

  • Wait, what are those articles on e.g. tempo doing there? I don’t see what that has to do with statistics.
  • However, statistics can be a very useful tool in building decks and playtesting. In addition to the relevant and valid topics you want to tackle in this class, I can add some statistical questions that I had to answer in my preparation for Pro Tour Honolulu (these are real examples of how probability theory can be applied to relevant questions and are straightforward exercises on conditional probability):
    • With X lands and Y creatures in your Z-card deck, what is the probability that a Gift of the Gargantuan will yield either one or both?
    • When deck X has an A% chance of winning before sideboarding against deck Y and a B% chance of winning after sideboarding against deck Y, what is the probability of deck X winning a match against deck Y?
  • You could also discuss mulligan decisions here and use probability to show that keeping one-land opening hands is almost always a bad move. For example, take a one-land opening hand and calculate the probability of finding at least one land in the top 2 cards of your deck. From that extrapolate to the odds of winning the game if you keep the 7-carder and compare that to an (estimated) odds of winning the game if you go down to 6 cards. If the latter is higher (it almost certainly is), then you should mulligan.

Week 6 – Epistemic Logic and Limited

Week 7 – Metagame and Applications of Graph Theory

Week 9 – Presentations

  • You may want to plan this part out a bit further. Build a deck for what format? Do you assume that everyone has all the needed cards at his/her disposal?

General Resources

  • “the makes of Magic” -> “the makers of Magic”
  • You can also add
  • And my less formatted response:

    Week 1

    Our class is intended to be just as appropriate for beginners as it is for experienced players, so no assumptions about what the students know. Our first class is an intro to the rules, and we’ll get them into games shortly after that. We’re going to recommend that they heavily visit our 24/7 “office hours” to get experience playing over that first week so that we could begin talking about more real things starting week 2. Since Magic is more the context than the point of the class, we don’t want to waste any time on that.

    The motivation for the articles that we picked is that it would be more helpful for them to have references instead of explanations of the rules (especially since readings for the first week will be done after, not before that class). Of the 3 or 4 friends to whom Tom and I taught the game in our dorm room, they all picked up the game really quickly and, as soon as they were told, understood why you play instants during your opponent’s end of turn phase and what to look for in using counters. I’m trusting that students are pretty smart and see the biggest obstacle just being how much they know about existing magic cards and popular decks. It’s usually pretty easy to see how a deck works and why it might be good. It’s a lot more difficult to try to understand why that deck might be good in a given format, especially if you don’t know what cards are there.

    Do you think those are fair assumptions about how to put this together, based on your experience with new players? This is actually a fairly big concern that we have, because if we don’t get the class off on the right foot or have the proper basis for the situations to come, we’re hosed.

    Week 3

    I’m thinking the multiplayer is a dorm room bias because I actually got a lot of feedback telling us, like you mentioned, to move multiplayer to the end of the course. As I mentioned, Tom and I are mostly casual players, and when we play, it’s pretty much just whoever happens to be sitting in the room. Given that, I still usually prefer playing 1 on 1 games, but I think the move to multiplayer early gives us a wider space to discuss game theory without introducing additional rules complexity. Since a lot of games are cooperative (you get a lot more games when not everything is 0 sum), I think that makes more sense when you have potential allies and not just one guy across the table trying to beat your face. The goal of the class is to demonstrate interesting ideas with the side effect of developing better play skills instead of trying to develop a rock-solid basis for future pro magic players (though I’d be proud if that happened), so I figured I would bend things a bit to make way for what I think is interesting. Game theory, I think, just makes a lot more sense and is more approachable earlier in the class instead of hitting with graph theory. Given all that justification, though, I’d be happy to listen to alternative schemes and reasoning for structuring that.

    Week 5

    Yeah, I think mulligan does make a lot of sense with statistics. Combinatorics is obviously huge when determining the composition of an opening hand, and it just keeps on going from then on. That sounds like a great application; thanks.

    And if you happen to have real examples of some analysis that you’ve done, I’d be very interested to see it. Certainly don’t go through the effort to write it up if it’s not in an available format, but I think it’d be great to work in analysis from “real REAL” magic so that there’s something to present to the hardcore magic community and not just toy examples to satisfy the class.

    Week 9

    Pretty much our idea for how presentations and cards would go is that Tom and I have a decent supply of extra cards, mostly bulk commons (whoever needed 50+ copies of CoP:Red?), and we would build some initial decks for them and let the rest of those cards be their entire card pool. Though it might be an interesting experiment in game theory, we’re going to bar outside cards from getting into the class environment. That way, we don’t have to worry about the class becoming unbalanced or unfun just because someone was willing to invest more into the class. The only trickiness there is that some cards will be scarce; I’m sure the 1 or 2 sudden deaths we have will be greatly desired, but we’re not too worried about that. The card pool isn’t going to be super-cohesive or uniform, but when our budget is 0 and we’re running the class out of our pockets, that’s about what we’re willing to offer.

    And Frank’s response:
    Week 1 => My experience with newer players is very limited. The last time I taught a new player was during last century. Furthermore, a completely new player would benefit more from being taught by someone who learned Magic a couple months ago than by someone who plays on a much higher level. That makes it much easier for the teacher to relate to the new player. That’s something to keep in mind.

    Week 3 => I understand where you are coming from. If you keep it in week 3, I would personally name the class ‘game theory in single- and multiplayer games’ (rather than just multiplayer games) and focus on applications of game theoretical concepts to both types of games. That is, I would spend an entire class on multiplayer games that early.

    Week 5 => Can’t think of any relevant analysis I’ve done in the past from the top of my head, but I’ll take a look at archives sometime soon. I’ll let you know if I find anything.

    Week 9 => If three players all want the same Sudden Death, this may get annoying. Another idea is to split the class in 5 groups after a few weeks and let every group build a mono-color deck. Then unfortunately not everyone has their own deck, but there will be no unfair allocations of cards and the deck building process becomes a cooperative group process rather than something everyone does individually. Don’t know if this is more desirable, but I’m just tossing out ideas.

    More ideas then … as for week 8, you may also consider doing something with search algorithms in deck building. An AI that builds decks has to take into account that adding e.g. just 4 Channel or just 4 Fireball to a given deck won’t improve it, but adding 4 Channel and 4 Fireball to a deck makes it better (use any 2-card combo for this example). Theory on search algorithms that use this logic may be interesting, perhaps?

    Definitely some much better ideas in there than what we’ve come up with. Let me know if anything in there stands out to you as important.

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