## Friday, March 18, 2011

### Gaming Math - Problem 17

Recently, University of Illinois computer science professor Sheldon Jacobson has developed a mathematical model to predict the distribution of seeds in the Final Four of the NCAA basketball tournament. (The NCAA basketball tournament consists of 64 teams divided into 4 regions with 16 teams each. It is a single-elimination tournament, and within each region the teams are "seeded" from 1 to 16, with the teams in order from strongest to weakest. The team that wins in each region goes to the "Final Four".) There is a web site allowing you to explore the results of the model. A key finding, reported in media coverage about this web site, is that the most likely combination of seeds is not (1,1,1,1), but rather (1,1,2,3).

Problem 17: Seeds of Victory

According to the web site, the probability that all four 1-seeded teams will go to the Final Four is 1 in 31.82, while the probability that two 1-seeded teams, one 2-seeded teams, and one 3-seeded team will go to the Final Four is 1 in 14.05.

In the article, Jacobson made the following statement:

"But I can tell you that if you want to go purely with the odds, choose a Final Four with seeds 1, 1, 2, 3.”

For concreteness, suppose that you are asked to pick, for each region, which team is going to the Final Four, and you are only considered "successful" if you correctly pick all four regions. Assuming that the probabilities given by Jacobson's model are accurate, is it true that picking a (1,1,2,3) split is more likely to be successful than a (1,1,1,1) split?