I gamble like I invest, I take the easy money. The bookies and the established betting firms always have the advantage, there’s no money to made there (unless you have inside information of course). However, we had a small Super Bowl gathering and everyone had money to gamble with! I was able to take advantage of this with a small ($10) bet on the favorite with 1:1 odds giving an expected value of $16 (based on the 80% consensus for Patriots to win). That wasn’t the important betting though.

The real money was in the last digit betting pool we had going. They typically call these ‘Super Bowl Squares’ because the way it works is that you create a 10×10 grid listing the numbers 0-9 on the top along with a team and do the same thing for the side with the other team. Each square then represents a unique combination of the last digits of each team’s score. Each square can then be sold for a set amount and the square representing the last digits of each team’s score at the end of each quarter gets 1/4th the total amount (since four quarters). However, some squares are more likely to win than others since the chance of a score ending in certain numbers is much higher than a score ending in others.

The accepted way to deal with this is to sell the squares before randomly assigning the digits to them, that way each square is probabilistically worth the same as any other square. Fortunately, that’s not the way we did it; we were allowed to pick our squares after knowing the digits, allowing an enormous advantage to the more mathematically inclined. Of course I wasn’t going to let easy money get away, so I found this handy chart that listed the frequency of each digit appearing in football teams’ scores at the end of each quarter since 1994 and quickly bought up the 15 best squares (the ones that had a probability of at least 2%). The combined expected value of just these 15 squares (based on an even split between four quarters as opposed to the 10/10/10/70 weighting in the last column of the linked chart) was roughly 40 times a single square.

Since the squares were a dollar each, I spent $15 for an EV of $40. Combined with the bet on the Patriots, I spent $25 for an EV of $56; that’s the only way to bet. I ended up giving four of those 15 squares to my sister since I’m just a nice guy, so I really only spent $21 for an EV of ~$40. That’s buying money for 50 cents on the dollar and I won’t have it any other way; whether it’s for Super Bowl squares or neglected stocks, I want to buy money for a fraction of its worth.

I ended up losing the Patriots bet for $10 but the 15 best squares won all four quarters for $100. Interestingly the four squares I gave to my sister won two of the quarters and the other 11 that I bought won the other two. After adding it up, I ended up winning $50 for $21 and my sister had won $50 for $4. Probabilities certainly don’t guarantee a win (Patriots had 80% chance to win!), but in the end they always prove lucrative for those that pay more attention to them than their opponents.

After explaining the odds to them, it seems I have been banned from their betting pools :) Oh well, back to betting in the stock market where there will always be plenty of people letting emotion and faulty logic make silly decisions for others to profit from. Fortunately the pool of available money for the taking is also much much larger than $100.

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