According to a recent survey from Morning Consult, a quarter of Americans are likely to bet on the Super Bowl. Of those, two-thirds will partake in the popular Super Bowl party game of “boxes” or “squares,” meaning nearly 20% of the country will be using modular arithmetic on Sunday, knowingly or not.
For those not familiar with the game, participants are assigned squares on a 10 by 10 grid. Every column and every row is randomly given a number between 0 and 9, with the columns corresponding to the final digit of one team’s score, and the rows corresponding to the final digit of the other team’s score. Typically, there are payouts for the winners at the end of each quarter, in addition to the final game score.
In Super Bowl LV, for example, if the columns represented the Buccaneers’ score and the rows represented the Chiefs’ score, then whoever had the square in Column 1 and Row 9 of the grid would have been a winner, given the final score of 31-9 in favor of the Bucs.
Some squares are vastly better than others. Across 55 Super Bowls, there have been 220 quarterly payouts, and 100 of them have gone to squares with a 0. That’s not surprising given that games start at 0-0 and the two most common scores in football, seven and three, add up to 10.
On the flip side, some squares have participants giving up before the game starts. Scores ending with a 5 have been tough to come by in Super Bowl history, with the entire row and column of possibilities yielding only 10 winners out of 220.
That sample size, however, is too small to make exact conclusions about each square’s worth. Furthermore, since the NFL moved the extra point back 15 yards in 2015, there has been greater variety in scores due to more frequent chunks of six and eight points. For instance, an early missed extra point in Super Bowl LII set off a domino effect that led to the first ever 9-3 win and the first ever 2-2 win, followed by a 9-6 and a 3-1 after halftime in what was the wackiest Super Bowl of all time from a squares perspective.
Analyzing every NFL game since 2015, we find that the majority of squares (74 out of 100, to be exact) are a losing proposition, including all of those with a 2, 5, 8 or 9. Assuming a $1 buy-in with a payout of $25 at the end of each quarter, the 2-2 square is worth a measly three pennies while the 0-0 square is worth a whopping $7.15.
Of course, every game is different. In defense-oriented matchups, squares with a 0 are more valuable, as the chances of a scoreless first quarter are higher than usual. The same was strangely true for Tom Brady’s 10 Super Bowls, half of which were tied 0-0 after 15 minutes of play.
If your square hits at the end of the first quarter, you should not only celebrate, but remain optimistic for the rest of the game. In nearly half of Super Bowls (27 out of 55), one of the winning squares has earned a second payout in the same game.
If you’re assigned 5-5, don’t be discouraged. Just go find the person at your party who got 0-0 and offer them $7 to switch. If they bite, you’ll have increased your expected cash total for the night by 11 cents. If not, take solace in the fact that there’s a first for everything.