Before the Super Bowl, someone in our office comes around with a 10×10 grid on which folks pay $10 to write their name on a square. One person can buy many squares if desired. Once all squares are filled with names, the digits 0-9 are assigned randomly on both the horizontal and vertical axes. Each axis represents the last digit of the score of one of the teams. So, if you chose square (4,3) and the score at the end of a quarter in the Super Bowl was 24 to 13, you would win $200. If the final score was 34 to 23, you would win an additional $400. Because of the vagaries of football, not all squares are equally likely to come up. The folks at dataists have created probability matrices based on historical Super Bowl data. My coworker Jon used similar data to create a cool web app.

However, players don’t know which combinations they will be assigned before writing their names on the grid. The only decision they can make is about how many squares to buy. I wanted to see if there was an advantage to purchasing more than one square. Using the dataists’ code, I ran some simulations to see what the optimum choice was in terms of how many squares to purchase. As you can see, after 10,000 simulations, there is no clear relationship between the number of squares purchased and profitability. Note that the graphs show absolute profit, not relative. Also, as we run more and more simulations, the gap between maximum and minimum profits for all squares diminishes, suggesting that the expected net profit is essentially zero regardless of the number of squares chosen as the number of simulations approaches infinity. In conclusion, it seems like Super Bowl pools are fun, but not a good way to reliably make money.

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