Game Theory in Magic: the Gathering
Magic: the Gathering is an exceedingly popular trading card game in the style of Yu-Gi-Oh! and Pokemon. It has been around for approximately 20 years and is only growing larger every year. Magic has a couple of crowds of people that play it. There are the casual people who have fun slinging spells around the kitchen table with their friends, and there are the more competitive folks. Every Friday night at game shops around the country, tournaments of Magic are held for prizes. These tournaments have varying sizes: I have competed with more than 100 people as well as with less than 15. There is also a professional circuit of tournaments, the Pro – Tour, and regular Grand Prix events that are open to the public. The prizes of these larger events reach into the tens of thousands of dollars. For the first crowd of people, applying game theory to their kitchen table games is simply excessive and they would not have fun doing so. But for the second crowd, it is easy to see that applications of game theory to their choices in their tournament play could have very real benefits.
The challenging nature of playing competitive Magic and the monetary costs associated with it have created a great number of resources and articles online that discuss how best to play the game and the best decks to make. The first article linked below by Frank Karsten brings up many of the ways that game theory can be applied to Magic: the Gathering. In one of his examples he walks the reader through solving a metagame that includes 3 decks with perfectly defined matchups against each other organized into a payoff matrix. The example results in choosing between the decks with a random chance associated with each. His application of game theory is perfect, but he openly admits that it is a drastic oversimplification. The obvious thing to point at might be player skill, since skill can tilt any matchup away from the odds that it might normally have. This is certainly a factor, but a more important factor is how at most all tournaments, the number of people aware of game theory that have thought about payoff matrices is very small. Because of this limitation in addition to people’s incomplete collections of cards, metagames aren’t quite as dynamic as the example that is given. When the metagame has enough people that your choice of deck doesn’t dramatically change its composition and it can be assumed to be static to some extent, it becomes far easier to evaluate payoff matrices and pick a deck in a way other than weighted randomness. All that I am saying is that if you are smart enough to apply game theory to a game that involves other people, you should not assume that everyone or even a majority of people have thought to do the same. In many cases, this should make choices even simpler to make than if everyone is assumed to be as smart as you.
http://archive.wizards.com/Magic/magazine/article.aspx?x=mtgcom/daily/fk41
http://thoughtscour.com/the-best-magic-theory-articles-of-all-time/