Guest Post: E[V] of Super Bowl Boxes

A guest post from Jason Laso re: Super Bowl Boxes. The following has been lightly edited:

I guess sharp people were looking for an edge before deciding how many squares to buy or where to put them on the board. Or maybe some people were just intimidated by the idea of gambling in general (I mean who in their right mind would ever devote a significant portion of their life to something ridiculous like that). Don’t worry, I’ve got your back.

I simulated 500,000 Superbowls to come up with some brute force analytics on Superbowl Squares. Here is a graph of how likely you are to win at least one quarter based on how many squares you purchased (assuming random placement on the board):

Buying 1 square means you will win at least 1 quarter 3.3% of the time. Buying a second square increases your odds to 8.1%. To have at least a 25% chance, then you’d need to buy 7 squares. And if you’re looking for more of a coin flip than a longshot, then you’d need to buy 16 squares to have a 50/50 chance for winning at least 1 quarter.

An interesting follow up question was then posed to me: what if you just bought an entire row/column and tried to maximize your chance to win big by owning every permutation of one number (i.e. if you put your name down on every square in a row and that row that turns out to be the KC 7 row, then you’d have all of KC 7 – SF1, KC7 – SF2, KC7 – SF3, etc.).
Not so fast. Here is the expected return on investment (ROI) by which row you randomly drew:

Great news if you happen to draw the row/column with 0 (+66% ROI), 7 (55%), 3 (26%), or 4 (24%). However, the other 6 row/columns (1, 2, 5, 6, 8, 9) all show a negative expectation. The worst possible outcome would be to draw the row with 2, which would show a 50% loss. If you deliberately bought an entire row/column as outlined above, then you are expected to lose about 13% of your investment on average. If you instead bought squares and just placed them at random, then you are only expected to lose about 11%.

So all-in-all, try not to stress too hard about how many squares to buy or where you should put them on the board. In the end, the house always wins 😉