Someone good at math...

[Schneed10]

Math nerd to the rescue. The first assumption is that you have a 50% chance of getting a game right against the spread. Over the long haul that's about right.

In any given week, if you pick 12 games and select randomly, you have a 1 in 144 chance of getting all 12 games right (12 games raised to the power of 2, because each game has 2 possible outcomes). That translates to 0.7% chance of succeeding each week.

If you put $12.50 in to play that week, then the expected return is $1800. In other words, if the prize for that week is more than $1800, then the house is losing money, and you could arbitrage the opportunity by buying up all 144 possible combinations. (= 12.50 / 0.7%) If the prize for that week is less than $1800, then you'd lose money by buying up all 144 combinations.

But I'm pretty sure a 12x12 box means you need to get 12 games right every week for 12 weeks in a row. Odds of that happening are 1 in 20,736 ( = (12 * 12)^2). That translates to a percentage chance of winning: 0.0048%.

If you pay $12.50 per week to play for 12 weeks, so a total of $150, the expected return would be $3.1 million (= $150 / 0.0048%). So if the house is giving away $1 million as a prize, they're making out real well on the deal. Assuming they can drum up enough participants to cover it. By buying up all 20,736 combinations, and thus guaranteeing yourself a win, you would lose $2.1 million.

Not to mention the possibility of someone else lucking into a winning combination. What if you have to split that million dollar prize with someone?

There was a prominent company that tried to arbitrage the Mega Millions lottery. They did the math and figured that if they bought every combination possible, they'd make out on the deal. The math was right, and they did win, but they forgot to factor in both the taxes they'd have to pay and the possibility that they'd split the pot. There was one other winner, and then they had a tax bill. The people who made this decision were fired. Wish I could remember who and when it was, but my statistics professor loved to tell that story.