Information Cascades in Magic

In Magic, there’s one thing we all crave: information. Be it in the form of articles, or tech, or statistics, we can’t get enough of that sweet, sweet gold… but what if the information is leading you in circles? What if the information spawns faulty logic and inbred testing conclusions? In this excellent article, Pat examines the phenomenon of Information Cascades, and shares some pertinent tips regarding our creative process.

“In the early part of the Twentieth Century, the American naturalist William Beebe came upon a strange sight in the Guyana jungle. A group of army ants was moving in a huge circle. The circle was 1,200 feet in circumference, and it took each ant two and a half hours to complete the loop. The ants went around and around the circle for two days until most of them dropped dead.

March of the Army Ants

“What Beebe saw was what biologists call a ‘circular mill.’ The mill is created when army ants find themselves separated from their colony. Once they’re last, they obey a single rule: follow the ant in front of you. The result is the mill, which usually only breaks up when a few ants struggle off by chance and the others follow them away.”

The Wisdom of Crowds
Pg. 40, James Swrowiecki

Ghost Dad was a classic example of a circular mill (an information cascade, which I’ll get into later) in the Standard season just past. Many B/W options were available, none obviously (initially) superior to the rest. With B/W control and B/W Hand in Hand as default controlling and aggressive Orzhov strategies initially, Ghost Dad and Ghost Husk were two particular innovations people could select from, if they desired.

Early on, more people were drawn to the alluring nature of Tallowisps and Sleepless Pillories. As a result, others imitated them assuming they had some sort of good information that they were basing their decisions on (such as the idea that Thief of Hope and Strands of Undeath might be stronger than Nantuko Husk and Promise of Bunrei, or at least that Ghost Dad’s synergy made up for what it lacked in power).

As a result, players were convinced that Ghost Dad was not just decent, it was great! It got to the point where in the Team PTQ season, Ghost Dad was the most popular B/W deck, followed by Hand in Hand, followed by Ghost Husk. Out of 100 players playing Ghost Dad, perhaps 90 assumed it was good because everyone else said it was.

Now, in the long run, imitation has to be effective for people to keep doing it. People are not slavishly imitative (no matter how much it may look like everyone Netdecks). The results will carry information, despite a cascade. As I said, we’ll get into what exactly these “cascades” are and how they form, momentarily. First, let’s look a little more at what happened to the great Ghost Dad strategy.

Early on, Ghost Dad was winning, which fueled its popularity. However, while it was doing so, it became more and more clear this was a function of it being played so much. One need only look at the percentages of the time Ghost Dad players were qualifying versus Ghost Husk players.

“You know what I like? … Math.”
Brian Hacker

The results speak for themselves. Every week Ghost Husk won a higher percentage of the time than Ghost Dad. Every week this happened, it sent a signal to players that Ghost Husk was better.

In reality, Ghost Dad was a gimmick. It had surprise value in a tournament where people were not expecting Spiritcraft, Shoals, and auras. It took many players a few weeks to figure out how to play against it. It was even a reasonable metagame (albeit for a metagame that quickly vanished).

It was not, however, good. Its cards are notoriously underpowered, it is slow, it’s weak versus all the best decks, and it is easy to play around once you know how.

Ghost Husk, on the other hand, is a brutal, lightning quick aggressive force that is strong versus good decks, while containing about as much synergy as Ghost Dad.

All things considered, it is remarkable that Wizards R&D doesn’t make more “questionable choices” than it does, given the extremely small group of playtesters, and how (if not probable) it is for ideas to become inbred. This is a testament to the skill and independence of thought of Wizards R&D, as well as the importance of their “outside” playtest groups (which are not likely to make the same set of mistakes or oversights as the primary developers).

Independent individuals are more likely to have new information rather than the same old data everyone already has (hence, Wizards R&D’s use of outside play testers).

The smallest groups, then, are made up of people with diverse perspectives who are able to stay independent of each other (this doesn’t imply rationality or impartiality, though… you can be biased and irrational, but as long as you are independent, you won’t make the group dumber).

The interesting dilemma is that typically, the more influence a group’s members exert on each other, and the more personal contact they have with each other, the less likely it is that the group’s decisions will be wise (i.e. inbred play testing).

When a group of players first start testing with each other, they may have a variety of ideas to pursue. However, if the circle remains a closed, tightly knit group, everyone begins to imitate everyone else. While this can make the individuals individually “smarter” (i.e. make better card choices for a specific deck and tournament), it tends to make them “dumber” (i.e. less good ideas for card and deck ideas in general) as a collective due to everyone making the same mistakes.

For instance, if you have no idea what to play, copying Ghost Dad will greatly improve your chances for success in the short run. However, if everyone did this, they’d never discover Ghost Husk’s true strength. Imitation typically benefit’s the individual now; innovation tends to benefit the group eventually.

If you have a group of independent individuals with some information, and they each make a decision, that decision is based on two factors: primitive information and error. With a large enough group of independent people, the errors tend to cancel out. This leaves primarily useful information. As a result, groups of independent individuals (such as a compilation of PTQ winners) generally make the “best” decisions, as they have more useful information than any individual.

Chinese Whispers

This of course assumes that the individuals possess any useful information and that they are not unduly influencing each other, causing a cascade effect. Let’s take a look at what a cascade effect is and how information cascades are created.

First, say that someone organizes an unusual tournament. Fifty of the players are given identical U/W decks in some new format. They are matched up against another fifty players piloting R/G decks in this same new format. There is one round played and no one sees the results of anyone else’s match. A person at random is asked which deck he thinks won the most matches. Everyone else is able to hear his answer, though not his result. Then a second person is asked, then a third, and so on. Each person who guesses the “winningest deck” receives a box of product. Everyone, beyond the first person, has private and public information to base their decisions on. The private information is the result of your match. The public information is what everyone else chose before you were asked.

Clearly, the first person will base his decision on the result of his match and how it played out. Now, let’s say you are the fourth person asked. Your goal is to guess correctly and win the product. In your match, U/W won easily. However, the first three players all select R/G as the deck they think won the most… What do you name?

Most people would go with the group (against their own results), which is the rational thing to do. This would produce the correct answer more often than not, but would also usually start a cascade, essentially dooming everyone else if they were wrong.

The information cascade is a chain reaction of decision-making where almost everyone involved is basing their decision on the decisions of others, who in turn base their decisions on others, regardless of personal information. Now, often these cascades carry a useful message to everyone quickly (such as when you are at a street corner and everyone starts crossing. Even if you can’t see the walk sign, it is a fairly safe bet that the crowd knows what it is doing). However, if the first couple of people were in error, the cascade can send a harmful signal to all (everyone panicking and trying to run out of a movie theater when someone yells “Fire”).

On the other hand, let’s suppose the participants were each paid a box if the group arrived at the correct answer by a vote (still taken one at a time, as before). Now the group can essentially assure itself of success if everyone places their vote based on their private information rather than the group’s decisions. Even if the first three vote R/G, you would still say u-w to give the group the most useful information about your match. This would make you more likely to “guess” wrong, however the group is more likely to be collectively right. Encouraging people to make incorrect guesses actually makes the group as a whole smarter. Quantity and variety are actually better for the group than focusing on quality.

Let’s look more at information cascades, but now consider why they don’t happen more often in Magic. First of all, not all decisions are made sequentially. Each week, players all simultaneously select what they will play. The sequential effects thus often take several weeks. Also, Magic cards are peculiar in that there are two huge (relatively) advantages to being contrary and selecting something you know to be a “weaker” deck.

1) Obviously you have surprise value, such as cards or strategies your opponents may not be expecting or prepared for.

2) “Weaker” (in the abstract) decks can post winning percentages versus the “best” decks, which means if enough people play the “best” decks, the “weaker” decks that beat them may be “better” choices (for the metagame).

Of course, there are also other reasons people want to play strategies other than the “best,” such as enjoying a different strategy more, or not owning the cards for the “best” deck.

Information cascades can be useful for spreading information quickly and efficiently, such as crossing the street corner on Memory Jar and Skullclamp (do we really need to wait around for everyone to test thoroughly these cards and determine just how broken they are?). However, the fundamental problem with an information cascade is that after a certain point, it becomes rational for people to stop paying attention to their own private knowledge and to start looking at and imitating the actions of others. If everyone is relatively almost as likely to be right about something, and everyone before you has made the same decision, it is rational to do what they did. But, once an individual stops relying on his own information and starts imitating the group, the cascade stops being informative.

This is how decks like Ghost Dad come to be regarded as “good” (read: not terrible). The first few people who played it insisted it was good (no doubt surprise value, metagame, and fun were factors). As a result, people began to accept it as a given that Ghost Dad was a Tier 1 deck. Everyone (or many, anyway) thought everyone else was making decisions based on what they knew, when in reality they were all making them based on what they “thought” the people before them knew.

The solution? Those army ants that wander off. The overconfident individual who insists he or she is right and the crowd has it wrong.

Do such people exist? Of course, and there is no shortage of such Planeswalkers in Dominaria. One reason is that people are, in general, overconfident (Mirari’s Wake much?). They overestimate their ability, their level of knowledge, and their decision-making prowess. They are more overconfident with hard problems than easy ones (side note: two exceptions to this are professional bridge players and weathermen. It really does rain 30% of the time weathermen predict a 30% chance of rain).

Anyhow, this is not good for the overconfident decision makers themselves, generally, since it means that they are more likely to choose poorly. But it is good for society as a whole (well, in this case the Magic community). This is because overconfident people are less likely to get sucked into a negative information cascade, and in the right circumstances can even break them. This is why many great deck builders are often chronically overconfident (hi Flores).

In short, cascades are created by people valuing public information more than private information. Overconfident people don’t do that. They tend to go on “gut” and place a higher value on private information. When they do so, they disrupt the signal that everyone else is getting. They make the public information seem less certain. That encourages others to rely on themselves rather than just follow everyone else.

Everyone effectively votes on what they think the best deck is for that week. People lay it out, see the results, and then vote again. People like Michael Flores, Alan Comer, Erik Lauer, Eric Taylor, Mark Herberholz, Darwin Kastle, and Andrew Cuneo may make nine bad decks for every good deck they design, but it is this diversity, this variety of options, that gains the collective the greatest opportunity to make the best decisions (my apologies to the Japanese deck builders who have come to dominate in the past five years… I look forward to getting to know you all better in the years to come).

Groups are better at deciding between possible ideas than coming up with them. Innovation is an individual enterprise. We have already seen how intelligent imitation can be useful, but how can we avoid slavish imitation, when few will admit that they’re mindlessly conforming or herding?

Intelligent imitation depends on an initial wide array of options and information. Also, there must be a willingness of at least some people to put their own judgment ahead of that of the group, even when it’s not sensible to do so (i.e. the overconfident people). Where does this leave us? First, innovators are good for the collective, even if they hurt themselves at times by the choices they make. If you want to increase your edge in the “deck tech” department, obviously it is useful to test with a variety of creative players. Jon Finkel may be friends with Mike Flores, but he certainly values him highly as a playtest partner. Why? Creativity can be more valuable than individual performance.

On the other hand, if you are one of those chronically overconfident players (come on, keep it real…), it may serve you to listen a little more to what the rest of your buddies have to say. This is particularly true for eccentric players, and players you test with less or influence less. Variety is the spice of life, involving yourself with 2 or 3 playtest circles will increase your chances of choosing the best deck (for that tournament) exponentially.

Still, mindless imitation of those around you (or on the Net…) is akin to being one of those army ants that marches in a circle until death. Mark Herberholz found himself in a circular mill in the beach house in Hawaii. Almost everyone had convinced each other that their B/G/W control deck was the deck. Mark wandered off, though, deciding that his perception (Heezy Street) was better than the group’s perception (the failed Beach House deck). Heezy, of course, went on to win the Pro Tour, beginning a cascade of his own. Are Scorched Rusalka, Frenzied Goblin, Dryad Sophisticate, Scab-Clan Mauler, Giant Solifuge, and Flames of the Blood Hand really the best cards for a Gruul deck? Perhaps for that tournament, perhaps even now, but it is undeniable that there are a lot of other R/G cards worth considering that many write off, just assuming that everyone else was playing Marks’ build for a reason (how many people tested all the options and arrived at Mark’s build versus how many took it for granted that someone else already had?).

Now personally, I do think Marks’ build was the best. For that tournament, I wouldn’t have changed a single card in the main deck. That makes what followed an example of a positive cascade. The cascade, in this case, allowed everyone to very quickly decide what the best Gruul deck was and if they wanted to be R/G mages or not (instead of spending large amounts of time determining if R/G is even playable).

Basically, it is a fine line one walks between choosing what is “best in a vacuum” (knowing when to go with the crowd, i.e. Necro) versus what is “best in a given situation” (which often involves being that upstart who insists that they know something everyone else doesn’t, i.e. Turbo-Stasis).

The truth is, people that net deck all the time would tend to improve their group’s decision making by innovating a little more, even if their ideas are usually bad or even terrible. But it is their friends / playtest partners who would benefit the most, since it would expose the group to more ideas and possibilities at the cost of individuals using “less safe” ideas.

If everyone does this, it maximizes the group’s gain, but it is actually most beneficial in the small picture for any one individual to “play it safe” and let everyone else innovate (assuming your goal is to win the most games now).

What this means is that typically, people who net deck do better than people who innovate. This makes sense, since net decks are generally good and new strategies are generally not. However, if you want to get an edge over the netdeckers, innovation is the way; you just need to be able to generate enough ideas that you can select the best.

The nut high is for everyone in your group to innovate (though not at the same time), and not just ride the coattails of a few. This is particularly true for players who want to contribute more to your circle’s performance than just their own. If actual tournament play is not your strong suit, supplying a variety of ideas (again, even if most are bad) to your group will bring everyone up.

The flip side to this is that those times you want to maximize short-term performance (i.e. PTQ or Pro Tour), it can actually be disadvantageous to always be trying innovative ideas.

Typically, one’s ideas are not as good as one thinks. This means if you are consistently choosing on idea that ducks the crowd, you are probably putting yourself at a disadvantage. Of course, people do have good ideas (sometimes get to have them). The key is to find a group of playtest partners who recognize the difference between your good and not-so-good ideas, and who are willing to say so. Also, be careful to sort among your friends’ strong and weak ideas. Long story short, if you typically net deck, you should innovate more. If you typically go rogue, you should imitate more (both assume your goal is to win more).

The most effective strategy for a group of gamers to win the most when it counts involves diversity and innovation at their highest when it doesn’t matter, and heavier imitation (though not slavish) when individual performance does.

Of course, knowing who to imitate is a whole other story…

Until next time,

Pat Chapin.