Good afternoon,
I have been away from Magic for about 18 months. If this material has been presented elsewhere, please direct me there.
Question about game theory/deck selection
This is an extension of a thread that I found from approx. two years ago. You can read the original
here. I would like to try to explain two thoughts that I have on the game of Magic: the role of statistics in finding a "best deck", and how Magic players may have a general misunderstanding of the term variance.
I shall try to keep this narrative somewhat abbreviated because I'm guessing there are some of you already considering perusing other topics.
Some of you may know about games theory, and think it isn't terribly relevant to the process of competition. It is my belief that without a firm understanding of how the process of games theory works, you are putting yourself at a marked disadvantage. In this exercise, I would like to take an article written by
Bryce Paradis and Doug Zare and apply the corresponding material to the above topics.
Much of the material that I found in the old thread consisted of trying to figure out how to analyze a given meta and determine how to find the best dominant strategy. To me, this seemed like an effort to figure out which deck had the most (in terms of raw #) favorable matchups against the field. This looks like a good strategy from the outset of the problem, because most of the time your analysis of a field may be, "well, it looks like this deck is played more than that deck, so playing the deck that does well against it is best."
To properly understand this article, you must know the definition of some specific terms:
Game Theory Optimal (GTO): A strategy that yields the highest possible EV (or: “is optimal”) if your opponent always chooses the best possible counter-strategy. In a game of rock-paper-scissors the GTO strategy is to choose randomly from an equal distribution of paper, scissors, and rocks. If you play rock less often than paper, you will have less than ˝ equity against an all scissors strategy. Similarly, you must play paper at least as often as you play scissors, and scissors at least as often as you play rock. As a result, you must play paper, scissors, and rocks with equal frequency to guarantee ˝ equity against all strategies. So long as your opponent always chooses the optimal counter-strategy to whatever strategy you choose no strategy on your part can have a higher EV than this.
Exploitive Strategy: Any strategy which has a higher EV than GTO strategy against a particular opponent.
Exploitable Strategy: A strategy which has less EV against some exploitive strategies than GTO strategy. All non-GTO strategies are exploitable.
The question to you: What is the effect of treating the process of deck selection as "yourself vs. the field"?
This may sound redundant because it seems like you do this already, but I guess that many of you are not employing this strategy. In this sense, you have not chosen a dominant strategy but rather an exploitive strategy. Those of you reading the article may ask, "well, isn't an exploitive strategy good?" I am not convinced that an exploitive strategy is the best strategy
all of the time.
I would like opinion on what strategy people believe is optimal in a given tournament when recognizing the meta. While an exploitive strategy may function as the best strategy when there is an abundance of a specific deck/group of decks, it wouldn't be a GTO strategy when the meta is either balanced or unknown. Also, my question is if there are any decks that in a balanced meta, might affect a proper GTO strategy.
This quote from Bryce's article makes a lot of sense to me:
"Even though a GTO strategy may have less EV than an exploitive strategy, understanding what the GTO strategy is and being able to identify how our opponents’ strategy deviates from it can help you to better exploit your opponents. Further, an understanding of GTO strategy allows you to create balanced strategies which are difficult to exploit. These strategies can be used as a defense against tough opponents looking for an exploitive edge."
I intended to include examples of how you might identify non-GTO strategies in your opponent's, but I am not familiar with many methods of doing so outside of holdem. I'm wondering if because of the nature of the game, if more of this strategy configuration is done in the deckbuilding process than the actual game-state operation. I would like to guess that one example might be preparing your deck to shore up a difficult matchup while diluting the strategy against a prominent deck you may be evenly matched with. Since your opponent will often not choose the correct counter-strategy to your strategy, you might argue that such a rift exists when you're not playing the GTO deck in the first place.
This particular analysis seems like much more of a grey area when considering the game of Magic. I believe by understanding how changes in our deck affect our overall EV against a given field, we can become better equipped to select the best deck (i.e.
dominant strategy) and give ourselves the best chance of winning the tournament. In this encompassing analysis, you might question "well, haven't you taken into account all of the die rolls, bad hands and play mistakes?" In my opinion, this analysis should be contained in the initial EV calculation. You should be figuring the value of going first vs. going second, finding the probability of drawing an unplayable hand, and quantitively taking into account play mistakes (you might be able to figure these final two features as your expected "variance") before you finally begin to calculate your EV versus a specific deck.
I would also like to hear some opinions on the subject of variance. I feel that the variance a deck has in terms of consistancy should be noted whenever deck selection occurs. Obviously in most cases, you do not want to choose a high-variance deck for a long tournament. I am interested to hear the thoughts on variance in small versus large tournaments. It has occurred to me over time that most people do not adjust their deck choices based on tournament size (other than they may choose new, experimental decks when fields are small and decks they know well when fields are large). What experiences have you had with this phenomenon?
Hopefully this subject will spark some interesting and stimulating debate. I do not intend to introduce this material as new and innovative, but perhaps as something you do not think about often but still holds an important role.
