The Big Game: Probability, Statistics, Game Theory, and Magic
The final question arises: How do all these concepts come together as a whole? The various mathematical aspects of Magic do not make up the game individually; they do together as pieces of a puzzle. That being said, there exists a relation between the various mathematical components of the game. Each part of it helps form the framework of the basic situations that a Magic player encounters every game.
Take the following situation. Put yourself in my shoes. The date is February of 1999 and you are trying to qualify for the Junior Super Series. You know that the majority of the decks will be combination decks based around getting a combo out and winning on the third or fourth turn. Using your knowledge of game theory, probability, and statistics, what deck will you play? What will your chances be of winning?
Here is how the situation was: The field was made up of about 40 people. It would be a fair estimation to say that 30 were playing combo decks, based around winning very fast with a card combination. Knowing that most creature-based decks will lose to combo decks, it is also a fair assumption to say that there would not be many creature-based decks. That prediction was true. Therefore, a control deck appeared to be the best deck to have played. I ended up playing a deck with 20 countermagic cards in it, with very little creature removal. That way I could counter most of the combo threats, and present my own three-card instant win combo. It was a control deck that had the capability to with instantly with a combo. The massive amount of countermagic made it very strong against combo decks, since they would have trouble getting their combo out.
I had playtested with Zev over thirty games against his combo deck, which he had already qualified with. I won about sixty percent of the games, simply because his deck was both very fast and had the capability to win against control decks. Given that I could beat the average combo deck 75% of the time, and that 75% of the field would be combo, I had one piece of the puzzle solved. The other 25% of the field would be a random assortment of decks. Some creature swarm decks, some control decks, and some other miscellaneous decks. Some which I could beat almost all of the time, some which I had little chance against. To say I would win 25% against fast decks and 75% against slow decks was a fair assumption. I did not expect to play against any random decks in most of the tournament simply because they would be eliminated very soon. Therefore my chances were about this much:
|Deck Type||Chance of Win * Chance of Match-up|
|Various Combo Deck||75% * 75.0% = 56.3%|
|Various Speed Deck||25% * 12.5% = 3.1%|
|Various Control Deck||75% * 12.5% = 9.4%|
|Total Win Percentage||68.8%|
This gave me an extremely high chance of winning. Knowing the metagame, that is, what decks other people were going to be using, was an extremely effective tactic. While I would lose to fast decks, I guaranteed myself a win against the slower decks and especially the combo-reliant decks.
In round 1, I played against a combo deck called "Spiral Blue" and won. In round 2, I played against another Spiral Blue deck and lost, as the deck was played by a pretty good player, and the only other match I had played against this deck was in round 1. In round 3, I played against a fast red deck and lost. That was the small price I paid for playing the metagame. However, I faced two other combo decks in round 4 and 5 and won against them both. The 3-2 record put me into the top 8. I had won 75% against the combo decks (3-1) so my estimate was very good. In the top 8, I played against a control deck and won, and then two combo decks and won against both of them. The last round was, incidentally, the same opponent from round 2. This time around, I got luckier perhaps. Whatever it was, I had won because I knew the chances and played the metagame correctly.
Knowing which deck to play is a definite game theory application. The decision making process formed by game matrices and relative probabilities constitutes a calculation of chance. The statistics that I used in order to formulate my chances of winning against each deck are strikingly similar to those used during my win-loss ratio calculation experiment. Such a technique is very handy when trying to win a major tournament. While I do not win them on a regular basis, I do fairly consistently. Statistics and probability are only an average. They are not a fixed value. Instead, they serve as an approximation. Knowing how to use them is what makes a player more informed. Understanding underlying probabilities and then applying suitable playing strategy is important to success in most card games. This will be the case in many casino games just as it is playing Magic.