Mathematics Project Abstract
THE MATHEMATICS OF MAGIC: THE GATHERING. WHAT CAN PROBABILITY TELL US?
Presenter:
David S. Pai, Illinois Mathematics and Science Academy, 1500 West Sullivan Road, Aurora, IL, 60506; chrono13@imsa.edu
Advisor:
Dr. Don Porzio, Illinois Mathematics and Science Academy, 1500 Sullivan Road, Mathematics, Aurora, IL, 60506; 630-907-5968; dporzio@imsa.edu
Abstract:
Magic: The Gathering is a collectible card game that was created by mathematician Richard Garfield in 1993. It is a game of luck and strategy. As with any other card game involving luck, probability should be able to help determine how a deck will perform. My first trial involved working with a simple deck of just two kinds of cards. The two cards worked together and could win by the fourth turn. Since a player starts with a seven card hand in a sixty card deck of two different cards , I calculated the eight possible starting hands and the probability of getting each of those hands using multinomial coefficients. Then, by finding the possible paths to victory through the first four turns, I could backtrack and find the probability of winning with the deck on the fourth turn. This is a system for finding the probabilities of having a certain hand by a certain turn. Thus, this system works for any deck that can win by a certain turn given a certain combination of cards in the right order. In other words, this sytem can calculate the possibility of winning on a certain turn with any "combo" deck.