Aaron Brown Blog | Valuing The Super Bowl Squares | Talkmarkets

Aaron Brown

Professor and Author

I was born in Seattle, Washington in 1956. I was a quant nerd and computer geek before anyone (including me) knew what those things were.

On Wall Street I worked as a portfolio manager, trader, head of quantitative research and head of mortgage securities for various firms. But ... more

Valuing The Super Bowl Squares

Date: Monday, January 29, 2018 8:07 PM EDT

Super Bowl Squares is a game of pure luck as usually played. Players buy boxes on a 10x10 grid for a fixed price (I use \$50 squares, meaning a \$5,000 pool, for my calculations, but stakes run from a penny to thousands of dollars). Players indicate ownership by writing their names in the box, but all boxes have the same chance of winning.

After all 100 boxes are sold, the person running the pool randomly assigns the numbers 0 through 9 to the rows, and then again to the columns. The rows represent the last digit of the Eagles' score, the columns represent the last digit of the Patriots' score. In a typical game, 1/8 of the pool is awarded based on the first quarter score, 1/4 on the halftime score, 1/8 on the third quarter score and 1/2 on the final score.

For example, suppose you wrote your name in the upper left box and the digit selected for the first row was 3, and the digit selected for the first column was 1. You will win something if the score at the end of any of the first three quarters or the end of the game (this may not be the end of the fourth quarter score due to the possibility of overtime) has a final digit of 3 for the Eagles and 1 for the Patriots, for example Eagles 13, Patriots 21. The rows by convention represent the NFC team, while the columns represent the AFC team. Eagles 3, Patriots 1 is the most average square this year, with an expected value of \$48.65 for a \$50 contribution. Eagles 1, Patriots 3 is slightly better with an expectation of \$54.73. The table below shows all the results.

The best square this year is Eagles 0, Patriots 7 with an expectation of \$262.45, more than five times the contribution. 0's, 3's and 7's are always good and if both your numbers are among those, you have a very good square. The worst square is 5,5. Not only are 5's unlikely final digits of a score, but they only come up much on high scores, like 35 or 45. These mostly occur at the ends of games, and if both teams have a 5 it could easily be the same score (35-35 or 45-45) meaning the game will go into overtime and the score will change. 2's, 5's and 8's are bad. 1's, 4's, 6's and 9's are in between, good if you pair them with a 0, 3 or 7; bad if you pair them with a 2, 5 and 8.

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