Category Archives: ProTrader

UNLOCKED PROTRADER: Advanced Economics & MTG Finance – Part 1

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By now it’s no secret that I treat MTG investing very seriously. So seriously, in fact, that I compare the performance of my MTG portfolio loosely with that of the S&P 500. And why not? If I’m going to legitimately invest real dollars in original dual lands, shock lands, booster boxes, etc. then it only seems appropriate that I compare the return on these investments with that of other investment opportunities.

But my holistic approach to investing doesn’t stop here.

This week I want to dive into a more advanced economics topic out of the field of game theory by applying one of the most well-known truisms of game theory to our favorite MTG topic: buyouts. That’s right. I believe that we could potentially apply an advanced economics concept to understand something reactionary and emotional in the MTG Finance community. Think I’m crazy? Think it can’t be done? Well, allow me to at least try.

Nash Equilibrium

Before I jump into concept application, I need to establish a few assumptions first. These suppositions are not very far-fetched, so I don’t think you’ll have difficulty accepting my thesis because of these assumptions.

First, let’s assume that when a buyout of a certain card occurs, everyone attempting to purchase the card does so “simultaneously.” That is, when we’re ready to pull the trigger and make our purchase, we aren’t waiting for someone else to take their turn making a decision before us. We click the buttons as fast as we can to purchase the copies we want. And in the meantime, everyone else is doing roughly the same thing. In other words there is no turn taking or prescribed order.

Second, we have to acknowledge buyouts occur in a non-cooperative manner. For example, when Den Protector spiked during the most recent Pro Tour, I wasn’t colluding with others in an attempt to obtain the market price I wanted. No strategy was involved in this regard. I rushed to eBay and TCGPlayer and picked up a bunch of copies as quickly as possible. I may have mentioned my actions on Twitter, but this communication was ex post facto. And even if I had cooperated with a friend, it’s not like the whole MTG community speculating on a card would ever work together – it’s an aggressive business we’re in!

With these assumptions in place, I will borrow Wikipedia’s eloquent definition of “Nash Equilibrium”:

“In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.”

John Nash was the famous economist who developed this theory and later earned a Nobel Prize for his work in the field. You may also recognize the name from the movie showcasing his genius and his struggles with schizophrenia, A Beautiful Mind.

NashHis Nash equilibrium concept describes motivations for people’s behavior when interacting non-cooperatively. (Aside: In game theory, any such interaction is referred to as a “game.” This is not comparable to playing a game of Magic – rather, the game I’m describing is the decision process of where we buy our cards and for how much during a buyout).

If we want to look at the definition of Nash equilibrium above, we can use specific terms to describe MTG buyouts. The first part of the definition describes the “solution,” or the actual outcome of everyone’s buyout decision (i.e. total copies purchased, where they were bought from, resulting price spike, etc). The second half of the definition is a bit more advanced. Essentially, the suggestion is that all parties involved know everyone else’s best strategy. In MTG buyout terms, we need to make one more assumption: the best action at the beginning of a buyout like Den Protector’s is to buy up copies at or near the starting price.

Den

When a buyout happens due to legitimate demand, the card’s price jump is more likely to stick. Therefore, purchasing copies at or near the starting price during a buyout is definitely the best strategy – it makes you the most money! Everyone knows this, and everyone knows that everyone else is also eager to buy those $1.50 – $2.00 Den Protectors before they double or triple in price.

Thus, we say the Nash equilibrium of the buyout is that everyone buys up more and more copies of the card and the price catapults higher. This is the best strategy because those who bought at $1.50 – $2.00 can in turn sell their copies for profit.

Prisoner’s Dilemma

With Nash equilibrium established, I next need to define the crux of this week’s article: The Prisoner’s Dilemma. It’s this canonical example of game theory that I believe can be applied to MTG buyouts in a profitable way. But before jumping ahead, I first need to share another definition. Wikipedia defines the prisoner’s dilemma as “a game analyzed in game theory that shows why two purely “rational” individuals might not cooperate, even if it appears that it is in their best interests to do so.”

Originally framed by Merrill Flood and Melvin Dresher, the Prisoner’s Dilemma is a concept that can be applied to a diverse number of real-life interactions ranging from cola advertisements to nuclear stand-offs. My argument is that this sophisticated game theory dogma also applies to buyouts of Magic cards.

Explaining the Prisoner’s Dilemma is best done by example. The namesake explanation involves two strangers caught robbing a store together. They are brought to the police station where they are interrogated individually. The police do not have sufficient evidence to convict the prisoners of an armed robbery charge – only illegal possession of a weapon, which of course merits a much lighter sentence. So in an attempt to drive out a confession, they offer each prisoner separately the same deal: rat out your friend by confessing, and you will be rewarded with no imprisonment.

What’s the Nash equilibrium in this case? Put yourself in the shoes of one of the prisoners. If you assume your partner in crime is going to confess, then there are two possible outcomes: you don’t confess and take the fall, letting your partner walk freely while you suffer 20 years in prison for armed robbery and lack of cooperation with the police; OR you do confess, earning you and your partner a lighter, yet-still-strict sentence of 5 years in prison for cooperation. Given these two options, your best choice is to confess at least ensuring you avoid an unnecessarily long prison sentence.

Now what happens if you assume your partner is trustworthy and he is going to remain silent? Once again you have two choices: if you also remain silent, then the police cannot convict you of the armed robbery (there’s too little evidence) and you both receive a one-year sentence for illegal possession of a gun. On the other hand, if you confess, your partner would go to prison for 20 years while YOU get to walk away a free person. Given these two options, your best outcome is still to confess, since it means you don’t have to do any time in prison! That’s the best possible outcome for you!

The picture below depicts this interaction in a 2×2 grid.

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dilemma

No matter what you assume your partner will do, the best decision you can make is to confess. And that’s what happens – both prisoners confess netting themselves the five-year prison sentence.

The advanced part of this comes into play when we compare the actual outcome with the optimal outcome. It is undeniably ideal for both prisoners to remain silent – it nets them the least number of total years spent in prison! But because of the selfish assumptions of Nash equilibrium (i.e. there’s little emotional motivation for helping the other prisoner), both prisoners end up with a worse outcome because they do not cooperate.

How does this apply to Magic? I’ll argue there are two applications.

Application 1: Instead of dealing with prisoners and robberies, we’re dealing with purchasing a quantity of a Magic card at a particular price. We’re all faced with the same decision point during a buyout – do you pull the trigger quickly and grab copies or not? The more copies you buy, the more opportunity you have for profit.

In this game, buying up a ton of copies is equivalent to confessing and cooperation involves collusion. How do the outcomes look?

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If everyone rushes out and purchases a ton of copies in an attempt to make bank, many participants in this game are stuck paying too much. As we’ve seen many times in the past, a buyout leads to a card’s spike followed by a race downward in price as people try to sell their copies for a quick buck. Savor the Moment is a recent example of this trend.

Savor

Notice how copies are scooped up aggressively starting in the $2.50 range in late March and ending in the $5.50 range, only to see a drop back down to around $3.25 most recently. When everyone decides to aggressively buy, the price jumps too high, too quickly. In these cases many people are left holding excess copies they are unable to sell for much profit because the higher price inevitably leads to a glut of supply as people try to cash in on the spike. Of course, those who don’t jump in with their hard-earned cash are in the worst shape of all. They own zero copies and they are stuck either paying a higher price or waiting for a drop that may never occur (usually the price ends up higher than the starting price but lower than the peak). No one wants to be in this scenario as it’s the worst possible outcome.

So what does everyone do? They all buy up as many copies as they can, sending the price higher and higher! Missing out on the “next big opportunity” is just too painful.

My argument is that this is another example of the Prisoner’s Dilemma. We all “defect” by purchasing a ton of copies while leaving those on the sidelines regretting their inaction. But this leads to a subsequent market glut and difficulty in liquidating copies at a profitable price. I’d argue the best possible outcome would be if the people who wanted copies most purchased the playset they need and those who don’t really want copies just ignore everything. Such cooperation would mean that the people who want copies would get their copies, but those who don’t simply stay away. The price may tick up a tiny bit, but there would definitely not be a huge spike. Then people who decide they don’t want their playset anymore could sell for a small profit and there would be no race to the bottom. And those who didn’t buy before aren’t faced with paying 50-100% more should they decide they want to obtain copies.

To me, this is the very definition of a healthy market. When a card increases or decreases in price it does so slowly and due to the natural shift in supply and demand. Crucible of Worlds is a great example of a card that has never been “bought out,” therefore leading to healthy price appreciation and no huge drops.

Crucible

Wrapping It Up

So what’s the course of action here? Unfortunately, there is really little we can do to avoid the trap that is the Prisoner’s Dilemma. There’s a reason why both prisoners tend to confess, and Coke and Pepsi choose to advertise, and countries choose to invest in nuclear weapons, etc. etc. It’s not the optimal outcome for the entire population, but it is what inevitably happens thanks to Nash equilibrium.

I think the best thing we can do is at least make ourselves aware of this phenomenon before buying into the next spike. It would be naive of me to believe everyone can suddenly cooperate – it’s against human nature. But if we could at least communicate a little better as a community then perhaps we can soften the blow for those left holding the bag in a buyout. For example, when we make our purchases we could be more transparent with how many copies we’re buying and how much we are willing to pay for said copies. We could also make it public what our strategy is for selling – timeline and desired sell price.

Lastly, we could strengthen our relationships with others throughout the community. One thing Nash equilibrium always assumes is that everyone behaves rationally and in their best interest. Friendships and emotional attachment are disregarded. But of course these things DO exist in reality. By developing stronger ties with the rest of the MTG community, maybe we can all be slightly more sensitive to market manipulation. We’ll never eliminate price spikes altogether, but maybe we can help our friends avoid losing money by buying into the hype too late.

I’m out of words for this week’s column, but perhaps you’ve noticed something. I only shared one application, but I said there were two! In similar fashion to a “You Choose the Scare” R.L. Stein novel, I’ll pose the question to my readers: did you enjoy this topic enough that you’re curious to hear my second application as a Part 2 to this article? Or would you prefer I moved back to more traditional MTG Finance writing? Leave your opinion in the comments section, and we’ll let the majority rule!

Until then, thanks for reading!

Sig’s Quick Hits

  • There’s another reason I used Crucible of Worlds as an example in my article. Nonfoil copies of the rare are completely sold out at Star City Games. Tenth Edition copies are sold out at $30.79 and Fifth Dawn copies are sold out at $32.35. If these don’t see reprint in Modern Masters 2015, there’s no reason they won’t continue to slowly chug higher.
  • I honestly thought Bosium Strip was a forced buyout that would result in a subsequent price drop, just like my Savor the Moment example. But this has not been the case. Perhaps not enough copies of the card exist for the market to truly be “flooded” by eager speculators. In any event, SCG is sold out of the card at $4.89 and Channel Fireball currently has a buy price of $2.50!
  • Another card that has healthily grown in price over time is Umezawa’s Jitte. The card has always been popular in various formats where it isn’t banned, but it’s never really in the spotlight. Star City Games has only 3 total copies in stock, with 0 NM copies at a $36.55 price tag.
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PROTRADER: The Magic Market for the Rest of Us (Well, You): Trading

By: Travis Allen

I began playing Magic beyond the kitchen table at Zendikar’s release five years ago, way back in 2009. At the time I think the most expensive card I owned was Doubling Season, and I’m pretty sure it was about $5. I knew next to nothing about how much most cards were worth, or what was good to trade for, or what might spike in price next week. I was focused solely on making gigantic Cytoplast Root-Kins and sacrificing Leveler while Endless Whispers was in play.

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ProTrader: Magic doesn’t have to be expensive.

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Bayesian Statistics: You Should Probably Read This Article

By: Travis Allen

Over this past summer, I read Nate Silver’s book, The Signal and the Noise: Why So Many Predictions Fail – but Some Don’t. I mentioned it in an article previously as being an excellent book for anyone who is interested in the type of content that appears here weekly. I’m not the only one who enjoyed it either; multiple people on my Twitter feed proclaimed fascination with it upon release. Chas Andres (@chasandres) was a particularly vocal supporter, and ended up writing a piece or two over on SCG about some of the book’s content shortly after it came out.

Possibility Storm

Today I want to discuss what was to me one of the most interesting, informative, useful, world-view-altering portions of the book. The Bayesian Theorem, and specifically Bayesian interpretation, is so broadly applicable to every aspect of our lives (MTG included) that it’s difficult not to consider every day occurrences through its lens.

The theorem was developed by Thomas Bayes, a statistician and minister from the early 18th century. The work was published posthumously, and received a pretty lukewarm reception initially. It wasn’t until the topic was revisited some time later that it became considerably more popular, and is now a major component of statistics.

Here’s the basic idea: Everything is a probability. Nothing – nothing – is 100% guaranteed. New information we obtain allows us to more accurately predict what will happen, but we’ll never be completely, unquestionably certain.

Let me show you the equation in its simplest form. Don’t be terrified.

d92e290c66d423e4798a22a3690cbd31

That isn’t so bad, is it? It’s just three simple letters a few times. (The book uses a slightly different equation, but the results are the same.) I’m not even going to force you to figure it out. I’m going to point you to the Wikipedia page, and if you’re curious about the math, it will do a far better job explaining it than I could. Instead, I’m going to explain it with some examples.

This first example I stole right out of Nate’s book. Imagine a woman going through a dresser drawer, and she finds a pair of panties that aren’t hers. Her first instinct is to assume her husband is cheating on her. That’s a pretty severe leap to make without any additional evidence though, isn’t it? If this woman had no reason to suspect her husband before, is it really appropriate to condemn him already? Someone without Bayesian interpretation may do that, but not this woman. She’s going to approach this with ~math~.

In order to get some numbers to plug in, she needs to do some guesstimating. The first thing she has to put a number on is what she thought the probability of her husband cheating on her was before she found the panties. This can be difficult, especially if you’re holding incriminating evidence in your hand. But she thinks rationally, and decides she had no reason to suspect him before this. She also happens to know that 4% of married spouses cheat each year. That seems like a good number to start with. So her prior expectation of her husband cheating on her – her “prior” – is 4%.

Next, she has to figure out the probability of the underwear being there assuming her husband is actually cheating on her. Basically she says to herself “If my husband is cheating on me, what are the odds I would have found this underwear?” He would probably be trying to cover his tracks if he was having an affair, so she wouldn’t expect to always find this incriminating evidence even if he was cheating. She decides to go with a coin flip – 50%. If he’s cheating on me, there’s a 50% chance I would find evidence like this.

Finally, what are the odds that this underwear is there if he isn’t cheating? Well, the number of reasons for strange panties in your house is pretty limited, and many of them are going to be quite suspect. Maybe he bought the panties for her as a gift, or received them as some promotional giveaway whilst walking through the mall, and forgot he put them there. Perhaps they’re his (no judgments.) Regardless of why, the chances of this underwear being there if he isn’t cheating are pretty small. She decides it’s maybe a 5% chance the underwear would show up if he isn’t cheating on her.

She then takes her three numbers and runs them through the equation. Her prior expectation of his cheating, 4%, the probability of finding the underwear if he is indeed cheating, 50%, and the probability of the underwear being there if he isn’t cheating, 5%. It spits out an answer of 29%. Her new expectation of his infidelity is 29%.

In a vacuum, that seems kind of low. She finds this women’s underwear, and it’s barely more than 25% likely that he’s cheating on her? How is that possible? It stems from the fact that she really didn’t expect he was cheating on her at all beforehand. If that prior expectation was higher, perhaps because he was working late all the time or being overly protective of his phone, then the end result would have been a lot higher than 29%.

Let’s try this out with a more on-theme example. Let’s try and figure out what the chances are that True-Name Nemesis is getting banned at the next B&R update in light of a new piece of information. 

True-Name Nemesis

We’ll begin with our prior. Right now, without any additional knowledge, what do we think the odds are he’ll get banned? Well, they don’t ban cards in Legacy very often. We could just look at the total number of banned non-ante cards in the format as a percentage, but I feel that is a bit misleading in this context. People have reasonable suspicion TNN may get the axe, but nobody is eyeballing Lightning Bolt in the same way. Let’s say that right now, TNN is maybe 5% to get banned. 5% is a much greater chance than any random Legacy card, and simultaneously reflects Wizard’s proclaimed hands-off approach.

Now, we consider new information. How about this tumblr post from one Mr. Mark Rosewater? Hmm, that’s pretty damning. Look at the language he uses. “Well aware of the public’s feelings” and “will impact how we act in the future.” Make no mistake – that is severe word choice. He easily could have said something along the lines of “TNN is new and we want to give a resilient format like Legacy a chance to try to solve the problem first.” Instead, he made no attempt to indicate they are giving the format time to shake out. He acknowledged people hated it, and said they would react.

So, what’s the chances that Mark would say this if they are planning on banning the card? I would put it pretty high, say, 80%. There is really no stronger answer he could give here.

Finally, what are the odds he would say this if Wizards wasn’t planning on banning TNN? Well, Mark has been known to be purposefully misleading before. We’ll say there’s maybe a 15% chance he would use language this strong even if they weren’t thinking of banning it in the near future.

Given those three numbers – 5%, 80%, and 15% – our final probability of TNN being banned in the upcoming announcement is 22%. That may feel a little low, but remember our initial expectation of it being banned was only 5%. It jumped 17 percentage points after this announcement from Mark. That’s a big jump.

Perhaps you are more convinced Wizards is going to ban TNN, and your prior expectation without any additional information is not 5%, but 30%. With that single change in number, the odds TNN gets banned rises to 70%. That’s a pretty solid chance of him being banned.

These examples show you what happens when you utilize real numbers, but what I really want you to focus on is the underlying principle. When we discuss things that will happen in the Magic world, it’s always a probability. When someone says Genesis Wave or Threads of Disloyalty or Spellskite is going to jump in price, what they mean is “I believe, given the information I have, the probability of this card rising in price is high enough that I feel justified proclaiming it, and I’m betting that it will happen.”

Aside: Notice my use of the word “betting” there – speculation is really just informed gambling. You’re playing odds. They’re considerably better than casino odds, of course, but at the end of the day you’re putting money up against the chance of something happening. 

You may not be aware of it, but you are probably using this principle frequently when you play the game as well. Imagine you’re playing against a control deck, and the board is empty. You cast a reasonable threat that will kill your opponent in a turn or two. Your opponent lets it resolve. Well, before you cast the spell, you were pretty sure he had a counterspell in his hand. After he let this resolve though, you swing way the other way – why wouldn’t he counter it if he could? You now feel pretty confident that he doesn’t have a counter. Then you pass the turn, he plays a land and passes back. You go to declare attackers, and he Downfalls the creature. Suddenly, you have once again found yourself pretty sure he has the counterspell. The reason he didn’t counter the threat last turn was that he didn’t need to. Threads of Disloyalty

See how with each piece of information, you update your expectation of what your opponent is holding? All (decent) players do this. Recognize this, and try extending the practice into more areas of your life. Use the concept, and in situations where you feel you have good numbers, maybe even use the equation. You’ll find you rush to conclusions far less, are more equipped to plan for contingencies, and in general have more reasonable expectations of what may come.

All of the predictions in my article last week were formed based on frequent Bayesian interpretations. Every time new product is spoiled, an announcement is made (or not made,) or someone from Wizards says something, I factor that into my expectations of an event, and see how it influences the probability. I would be lying if I said I explicitly used numbers, but I definitely find myself mentally ballparking percentages all the time.

Holding to Bayesian interpretation will also help you be more objective. Say you hold some belief that you are very certain about, perhaps 99.99% sure of. A single piece of evidence to the contrary is not going to sway you far from that belief. But if you remove your personal prejudice from the issue and fairly factor in each new piece of information, you may find that your previous rock-solid belief is now considerably less so. Holding a firm belief is not foolish, but doing so in the face of bountiful evidence certainly is. Don’t be that guy. Be the guy willing to learn and grow.

There’s a lot more information about Bayesian statistics out there. If this tiny taste I’ve given you piques your interest, I highly encourage you to do some more reading. In the meantime, go forth and be probabilistic!

  • Genesis Wave spiked on Tuesday afternoon, and as I write this, the cheapest copy is $6 on TCGPlayer. If you have any, sell now. Yes, the card could end up more expensive, but it’s far more likely it doesn’t. (Probability and the Greater Fool Theory all in one!)
  • With Genesis Wave spiking, Primeval Titan is on the edge. There’s been chatter about him online lately, paired with a slow rise over the last few months. He’s going to be in any deck with Wave. It won’t take much to push him over the edge at this point. He’s not going to be $25, but $12-$18 seems pretty reasonable.
  • I don’t have any specific results to point to, but I like Threads of Disloyalty. It’s been rising for months, it’s always been floating around Modern, it only has one printing, and continues to get better in the face of awesome small creatures. I doubt it’s going to be bought out tomorrow, but I wouldn’t hesitate to grab copies where you can.

 

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