by Charlie Rinehart-Jones
Game Theory is the study of rational decision makers in economics – it is meant to illustrate what players will do to gain the most utility possible. This economic philosophy is founded on the idea that players are always acting in their own best interests. I’ll get to how this relates to Magic quickly, but to understand the concepts i’m going to discuss, we will need understand the concept of utility.
Utility, generally speaking, is the measure of the preference of one thing over another. In layman’s terms, it is the amount that one of the players want something compared to all other things. Utility can go into negative numbers and it often does. Now, Utility as derived from Utilitarianism has been proven to be false, the system is breakable in a couple different ways and therefore people can’t actually just use Game Theory to determine what are all of the best decisions in their life and what they should or shouldn’t do. This is because of some very complicated logic puzzles that I can’t properly explain, but are very well illustrated online.
We use tables to understand the basic decision trees that people can make with Game Theory.
Here is an example of a Game Matrix, where the players payoffs are symmetrical. You would read this as; if the red player chooses strategy A, while blue player chooses strategy B, Player Red would receive 1 utility, while player blue would receive 3 utility.
The Prisoner’s Dilemma in Magic
The Prisoner’s Dilemma, is a thought experiment in Game Theory that comes with the premise that two people are caught robbing a bakery. Now they are each brought into separate holding cells, the police tell them that each of them can rat on the other, and if they do then the smaller gun charge will be dropped. Now if they both rat on each other then they will both go down for the gun robbery. If they both stay quiet then they will both be punished for the gun charge only. This Game Matrix looks like this.
Take a minute and try and figure out the “trick” to the Prisoner’s Dilemma.
You don’t even need to know the math to “solve” Game Theory to figure out that you always want to rat on your opponent. If red player stays quiet, then the blue player can rat on them and get off scot free. If the red player rats, then the blue player should still rat because then they can at least get off on the gun charge. Anyway, as you can see each play always wants to rat no matter what. This is referred to as the “dominant strategy” in Game Theory. There are plenty of great online resources if you simply want to learn about this online. Now it’s time to apply this to magic.
Simple Game Theory in Magic
A great example of the Prisoner’s Dilemma in Magic is when your drafting. Say there is a format, like triple Shadows Over Innistrad, where Green-White was a significant amount better than all of the other archetypes you could draft, but with the obvious limited caveat that everybody can’t force Green-White and the colors Red and Black are just fine as well, especially if everybody is trying to force Green-White. Now here is where Game Theory comes in. Let’s say after staying open in pack one, you commit to Green-White late in pack one and then get a couple early good picks in pack two, but then quickly realize you are being cut from your right in one of those colors – let’s say green. You are now presented with the choice to re-diversify your picks or remain in Green-White.
While we can’t accurately create a game matrix because of all of the variables involved in a draft, we can explain the decision tree in a game theory oriented way. If the person to your right choses to continue drafting green after being cut all of the second half of pack one by you, then this means that there were enough good green cards for them to stay strong and keep picking those cards. Operating from a Game Theory perspective, and assuming that they are acting in their own best interests every pick, then what we can assume is that you should not jump ship from your green cards at all. You are going to get the first crack at most of the best green cards at the table in pack three, so while your utility may be lower now you can assume that, if your opponent is drafting well, then this is the optimal line of play.
It is a false advertisement when some players tell you to jump ship if you realize that you are being cut in draft. Assuming all the players in the draft are acting in their own best interests (and why wouldn’t they) then they would also have to understand that either that same quality of green cards will not flow back to them when the packs re-change direction in pack three or that there is an abundance of green cards to go around. This almost resembles the Prisoner’s Dilemma because regardless of what the player to your right does, you want to remain in the color that is being cut, and if the color isn’t being cut then you obviously want to draft it because nobody else is. This does not however mean that you should force the best colors, because you will never get to that strong end of pack one if everyone is only picking the green and white cards, this situation is simply when you are battling with the person to your right.
Thanks for reading!