Today I begin an important and ambitious project on the application of complex systems theory to the understanding of our decision-making processes as we play Magic. This project is ambitious because it will be difficult to explain the concepts I intend to convey.
Decision-making is at the core of Magic. Part of what makes Magic so much fun and skillful is the degree and variety of decisions to be made. In Chess, the decisions generally center on planning moves with a limited number of game pieces. In Magic, you not only have to select “moves,” but you have to choose the pieces you want to play out of hundreds if not thousands of options and even more combination thereof. And then, even after you you’ve chosen, you have an opportunity to revise those decisions before the match is over (sideboarding). The type of decisions, if not the depth of decision-making, is far more complicated than almost any strategic game I’ve encountered.
Our current understanding of how Magic players make decisions is woefully shallow. More importantly, our understanding of why and where players are most likely to make mistakes suffers from the shallowness of our analysis. Boldly, I will attempt to rectify that situation over the next couple of weeks.
A lot of Magic theory tends to focus on the sciences that Magic players are most familiar with: game theory, economics, mathematics and the like. Research on human cognition and dynamic systems theory provide critical insights that are under-explored.
I strongly believe that a systems theory approach to Magic will help us understand our decision-making processes better. That in turn will help us make better decisions. To introduce you to systems theory, I’ve selected a great primer on the topic which I will use as the backdrop for this article series. The article I’ve chosen is MIT Professor John T. Sterman’s “Learning in and about complex systems.” The article can be found here.
These pair of articles may not be as exciting as a tournament report or deck primer, but they will be no less important. In some ways, these may be the most important articles I write about Magic.
“All learning depends on feedback” (Sterman 292). This axiom is the heart of any testing regime. Magic players test and tune decks on the basis of this principle. When you test, you acquire information that you then use to improve your decision-making. This information is called “feedback.” We use feedback to make adjustments. For instance, after testing your deck for a while, you may discover that you need more mana of a particular color. Specifically, you’ve found that your current list is not producing enough Green mana.
When you first constructed your deck, you assumed that you included enough Green mana to support your Green cards. Your mathematical or intuitive notions of deck construction led you to this conclusion. After testing, you discover that you don’t actually have enough mana. The way we might typically conceptualize this type of feedback loop might be a simple two pole model:
According to this model, we change our decisions according to information feedback. Decision makers evaluate the feedback in light of their desired goals and make adjustments to bring their desired outcome closer to reality. You may discover that you have too few lands in your deck, so you increase the number of lands until you achieve the goal of being able to cast your spells more consistently.
Consider this excerpt from Patrick Chapin article last week that illustrates this process at a higher scale:
Now, personally, I have trouble with the idea of only three Tarmogoyf, but DJ swears that it is correct and that he would much rather just have three more Wall of Roots.
This deck has not seen major tournament play yet. However, six consecutive FNM’s and City Champs Tournament first places has to be an indicator that it is at least worth examining this concept. DJ is a fine player, but one area he particularly excels at is deck building, often with Blue Midrange decks. There is a whole class of up and coming Pros originating from RIW Hobbies in Michigan, and DJ is one of the masterminds behind many of their decks. Keep your eyes on him, as I predict a high finish for him at Pro Tour: Hollywood, and he isn’t even qualified yet. Mark my words…
The idea is simple enough. Develop a board position with card advantage creatures and Planeswalkers, then slowly grind your opponent into nothingness with your never-ending stream of two-for-ones, which tend to start chaining together.
This deck is pretty much the definition of “with value,” as he has over twenty sources of card advantage, as well as the possibility of some tremendous tempo plays, such as Blink, Garruk into Goyf or Snag, and Venser or Snake into untap and Mulldrifter. In addition, Aeon Chronicler, manlands, and massive mana acceleration provide many powerful plans to choose from against control, aside from a large amount of card advantage threats.
Fighting aggro decks is simply a matter of dropping creatures at a similar rate to them, but packing some fatties and so many two-for-ones that they just can’t keep up. DJ did mention that he was having trouble with a U/G tempo deck, as well as a particular build of R/G, but it would appear that only the fastest of tempo-based aggro decks can compete with his ability to tie up the board with monsters while keeping a full grip.
I had suggested Riftwing Cloudskate to DJ, but he says that he tried it and it didn’t do enough. He says he had better things to do early, and never wanted to pay five main-phase for it. He already has plenty of things to Blink, so why does he need to play something to make his Blinks better? I am not positive on this, as it feels like Riftwing should be good, but I cannot argue with his results.
I think the Jace is a little out of place and should probably be the 4th Goyf, but DJ is known for his love of Planeswalkers. I suspect Jace may be appearing maindeck as a concession to DJ’s love of playing with him. Really though, I can’t blame him. Jace is definitely my idea of a good time.
DJ’s analysis of whether to run 3 or 4 Goyf, his rejection of Riftwing Cloudskate, and his us of Jace all reflect learning as a product of feedback loops. They are a product of testing and DJ’s intuitive and analytical processes.
In many ways this is a linear, non-systems theory way to approach learning. This is how most of us think about Magic. Our thinking is represented by the language we use to describe the use of this feedback. We say that we are making adjustments to “our decks.”
Systems theory teaches us, however, that all decisions are based on models (Sterman 294). Rather than making adjustments to our decks, in many, if not most, cases we are actually making adjustments to our model of the world. What do I mean by that?
Cognitive psychology and systems theory put particular emphasis on mental schemas (cognitive maps, etc), the mental models we have of the world around us. To concretize this in Magic terms, we all have a mental model of the metagame. For any given format, you have a mental map of the decks you expect to see in that format, their relative prevalence, and how various matchups should play out. Taking Legacy, in any given Legacy metagame I expect non-trivial amounts of Threshold and Goblins. I also expect Threshold to perform well. You also have a model of how your deck is designed to operate. You can often break up this model into turns, sometimes represented by your mana curve and the phrase “curve out.”
As I’ve just described, some of this takes place at a conscious level. You’ve mapped out the metagame, you’ve mapped out the internal operations your deck, and you’ve put some thought into how your deck will interact with metagame you anticipate.
That’s all well and good. The problem is that the feedback loop is incomplete. The feedback we receive not only is used to measure the impact of our decisions and help us make better decisions to achieve our goals, it also causes us to re-evaluate our model of the world itself.
To copy figure 2 from the Sterman article, here is how he represents a more realistic feedback loop:
In this two loop model, the real world is part of the loop and the information feedback informs our mental model of the real world. In the two-pole feedback loop, the real world is taken for granted as given — it is assumed “ceterus peribus.” A common assumption in that model is that the “real world” remains static in the decision-making process. In fact, it does not.
In short, feedback not only tells us how our decisions are working, but it also tells us more about the world itself.
The key point I’d like to emphasize in this article, and the point I’ve been building toward, is that to an astonishing degree these mental models are invisible or unavailable to us. They operate below consciousness.
Our basic approach to understanding decision-making in Magic based upon these models is that our decisions are often conscious, deliberate, and purposeful. Consider Chess computers. Chess computers calculate hundreds if not thousands or millions of permutations of lines of play and select lines of play that give them the greatest advantage.
Human beings tend not to think like that. In a previous article, I’ve described the two general processes that guide our decision-making and contribute to skillful play: forward thinking and pattern recognition.
Forward thinking is the logical computer approach of evaluating each line of play, step-by-step, and then selecting the best one.
Here’s how I described Pattern Recognition:
The more a player plays a deck, the more familiar the pilot becomes with various situations that typically arise in the course of a game. The more familiar the player is with those situations, a better feel the player will have for the plays that will lead to a game win.
Simply put, if you are a Fish player and you played turn 2 Null Rod instead of Meddling Mage and you find that every time you make that play you win the game, you will be more likely to make that play in the future.
This process of pattern recognition actually feeds the first process of forward thinking. The more familiar the pilot becomes with the outcomes of a particular line of play, the better the player will become at weighing the risks of various lines of play and arriving at the correct play. Thus, although forward thinking is important, forward thinking becomes more accurate and more deadly when aided by a great deal of pattern recognition.
Many players say that they play “intuitively.” What this means is that they have so much experience with their deck through pattern recognition that they no longer need to engage in full throttle forward thinking. They rely on pattern recognition more and more. Pattern recognition thus enhances forward thinking by making your evaluative capacity more accurate, but it also can come to substitute for forward thinking and help you play faster.
Most Magic players, including the very best, use Pattern Recognition or intuitive play more than they rely on full-throttle forward thinking. I once had a discussion with Patrick Chapin about decision-making. He described “intuition” to me as essentially unconscious processes that result a conscious decision. He described it as the powerful concatenation of multiple sub-conscious operations in his brain that overlaid and interacted with each other at that level. The product was generally the correct decision. Patrick was able to do this based upon years of experience of playing Magic at a high level.
Let me tell you an anecdote that might provide some insight into how this might occur. Over two years ago I purchased a locker at my gymnasium where I work out. A combination lock came with the locker. I memorized the lock combination within a few weeks. For roughly three or four times a week over the past two years, I’ve unlocked my locker using that combination.
A couple of months ago, I walked up to my locker and started spinning the lock numbers just as I do every time I go to the gym. This time, however, I started thinking consciously about what my combination is. And I couldn’t remember.
I was astonished. I had spun this combination of numbers hundreds of times, but now I couldn’t remember it? What I realized was that I had long stopped consciously recalling my lock combination such that I no longer knew what it was on a conscious level. I resolved to distract myself and think about something else. I started thinking about my work out, walked back up to my locker and spun the lock to the three numbers and my lock popped open.
This is not surprising. The human brain is not wired to run all of our routine operations at a conscious level. Everything from the articulation of sentences to speech recognition of vowels to the movement of our tongue, teeth, and lips when speaking is done at a level below consciousness.* We would not be able to communicate efficiently if we considered every word we spoke before we uttered it. Imagine trying to type if you needed to consciously think about each and every letter you were typing and the placement of each of those letters on the keyboard. It’s the same principle.
However, it is not simply that routine physiological processes operate at a level below consciousness. In the same way, much of our mental models of the “real world” are often unconscious. Here’s how Professor Sterman describes it:
“Most people do not appreciate the ubiquity and invisibility of mental models, instead believing naively that their senses reveal the world as it is. On the contrary, our world is actively constructed — modeled — by our sensory and cognitive structures.” (Sterman 294).
Take a look at this image
This is called a “Kanizsa” triangle. Here’s what Wikipedia says about the image: “In the accompanying figure a white equilateral triangle is perceived, but in fact none is drawn. This effect is known as a subjective or illusory contour. Also, the nonexistent white triangle appears to be brighter than the surrounding area, but in fact it has the same brightness as the background.”
The point here is that our brains are tricking us. Our neural structures are responsible for this illusion. The illusion exists between the “optic nerve and the areas of the brain responsible for processing visual information. Active modeling occurs well before sensory information reaches the area of the brain responsible for conscious thought.” (Sterman 295). Why?
Professor Sterman explains that it is a function of evolution. The survival of the human species depends upon the ability to rapidly interpret reality. We use unconscious mental schemas to do this. Cognitive psychologists explain that these schemas are cognitive structures that “enable the perceiver to identify stimuli quickly… fill in information missing from the stimulus configuration, and select a strategy for obtaining further information, solving a problem, or reaching a goal.”** However, because they are unconscious, we are generally unaware that these mental models even exist.
“Each person, and perhaps even every object that we encounter in the world, is unique, but to treat each as such would be disastrous. Were we to perceive each object sui generis, we would rapidly be inundated by an unmanageable complexity that would quickly overwhelm our cognitive processing and storage capabilities. Similarly, if our species were “programmed” to refrain from drawing inferences or taking action until we had complete, situation-specific data about each person or object we encountered, we would have died out long ago. To function at all, we must design strategies for simplifying the perceptual environment and acting on less-than-perfect information. A major way we accomplish both goals is by creating categories….Categories and categorization permit us to identify objects, make predictions about the future, infer the existence of unobservable traits or properties, and attribute the causation of events.”**
As that passage by Professor Linda Krieger suggests, the unconscious mental schemas that operate at the level of visual perception, as illustrated by the Kanizsa triangle, also operate at higher levels of knowledge. It’s not simply images that we unconsciously model, its categories too.
And this is, I contend, the heart of Intuitive Thinking. Magic players don’t have to consciously dredge up all of the possible lines of play. In testing, you’ve encountered most situations before. We use these cognitive schemas to help us quickly make decisions. This is what I mean by pattern recognition. This is also why experienced Magic players intuit answers so much more quickly and why it often takes years for Magic players to start really performing well (they sort of “take off.”).
Magic players unconsciously analogize. In a sense, almost every game of Magic you’ve played before is carried with you. The subtle cost/benefit decisions that inform any given decisions are weighed by the sum total of the games you’ve played before. This is also one reason why an expert with a particular archetype can pick up a similar archetype (say, Blue-based control or burn) in a completely different format and play the deck very well. Most importantly, it’s also why a player who doesn’t play Magic for a while can pick up a deck they were highly trained in piloting and play it just fine. This happens all the time in Vintage. I haven’t played Grim Long in nearly 9 months, but I could pick it up tomorrow and play it with a high degree of capability.
To illustrate the unconscious modeling of higher-level knowledge, Professor Sterman points to some consulting work of a team of MIT professors for a large global corporation. The corporation sought to reduce its supply chain delays in order to increase its global competitiveness. In the first meeting with senior managements, the MIT team presented this image:
Notice the incongruence between the length of the line and the number of days in each segment. The MIT team drew up this diagram to show that the company improperly focused on reducing order fulfillment lead time. As Professor Sterman describes: “What the figure reveals is the prominence of order fulfillment operations in the mental models of the people on the team and the insignificance in their mind of vendors and customers.” Most of its management operations and resources were geared toward that segment. There was not a single manufacturer representative or customer at the meeting, yet these were the processes that ate up the most time in the supply chain. Until the MIT consultant pointed this out, “the members of the group were as unaware of the illusory character of their image of the supply line as we normally are of the illusory contours we project onto the sense data transmitted by our optic nerves” (Sterman 296). Consequently, the distorted mental model of the supply chain significantly affected the company’s ability to reduce its supply cycle time.
The first step to ensuring that our decisions are sound is to recognize that we all have mental models of how our decks and the metagame works. We can’t possibly begin to make proper decisions until we first recognize that we have these mental models and begin to understand what they are. The two-pole model of decision-making will not suffice. We need to begin by realizing that it is not simply the impact of our decisions that we evaluate in processing feedback, but also the mental model of the world that we need to adjust.
Unfortunately, the feedback processes that would help us improve our mental schemas are confounded in some frustrating ways, as the consulting work by the MIT staff demonstrates. It turns out that even highly intelligent human beings are very poor at properly utilizing feedback to improve and correct our mental models.
Next week, I will begin to examine the major barriers to effective learning that will help us adjust our mental models and improve our decision-making.
* See Drew Westin’s book “The Political Brain.”
** Linda Hamilton Krieger, The Content of Our Categories: A Cognitive Bias Approach to Discrimination and Equal Employment Opportunity, 47 Stan. L. Rev. 1161, 1190 (1995).
*** Id. at 1189.