Back in 2011, a Boston Globe article came out about how a few folks repeatedly won tens of thousands of dollars on a Massachusetts lottery ticket game due to how the jackpot rolled over if it went unclaimed long enough. Essentially, at certain times the odds showed a expected positive return for everyone, but you’d have to buy a lot of tickets to even out the chances of bad luck. (This is why folks can win in the short-term in Las Vegas casinos, but the house always wins over a large number of bets.)
Mark Kon, a professor of math and statistics at Boston University, calculated that a bettor buying even $10,000 worth of tickets would run a significant risk of losing more than they won during the July rolldown week. But someone who invested $100,000 in Cash WinFall tickets had a 72 percent chance of winning. Bettors like the Selbees, who spent at least $500,000 on the game, had almost no risk of losing money, Kon said.
The Globe article basically made the bettors out to be villains, the “rich” against the “poor”. This Felix Salmon article argues that the game was fine, as technically everyone had the same odds (rich or poor) and the game actually generated a lot of money for the state. Buying that many tickets also took a lot of work:
As a result, while some people did indeed essentially treat Cash WinFall as a full-time job, it wasn’t necessarily a particularly lucrative or easy job for any given individual: it would take one couple ten hours a day, for ten days, to sort through their tickets to find the winners, the proceeds from which would then be shared among 32 consortium members. On top of that, every member of every consortium could reasonably expect to be audited by the state Department of Revenue every year. Which isn’t exactly fun.
A new HuffPost longform article takes a deeper, more personal look at the retired “couple next door” who discovered the edge and eventually made millions off of it. All that it required was “6th grade math”, according to Jerry and Marge Selbee:
The brochure listed the odds of various correct guesses. Jerry saw that you had a 1-in-54 chance to pick three out of the six numbers in a drawing, winning $5, and a 1-in-1,500 chance to pick four numbers, winning $100. What he now realized, doing some mental arithmetic, was that a player who waited until the roll-down stood to win more than he lost, on average, as long as no player that week picked all six numbers. With the jackpot spilling over, each winning three-number combination would put $50 in the player’s pocket instead of $5, and the four-number winners would pay out $1,000 in prize money instead of $100, and all of a sudden, the odds were in your favor. If no one won the jackpot, Jerry realized, a $1 lottery ticket was worth more than $1 on a roll-down week—statistically speaking.
“I just multiplied it out,” Jerry recalled, “and then I said, ‘Hell, you got a positive return here.’”
How much did they win?
By 2009 they had grossed more than $20 million in winning tickets—a net profit of $5 million after expenses and taxes—but their lifestyle didn’t change. Jerry and Marge remained in the same house, hosting a family gathering each Christmas as they always had. Though she could have chartered a private jet and taken everyone to Ibiza, Marge still ran the kitchen, made her famous toffee candy and washed dishes by hand. It didn’t occur to her to buy a dishwasher.
Would you have done the same thing if you knew about this edge? In my opinion, this is what makes the story fascinating. First, you have to find the inefficiency. Then you have to trust your findings enough to bet on them. You must risk your time and money upfront, throw in some ingenuity, and profit only if you are right. Then you have to bet big enough to make your winnings significant before the edge disappears (and they all eventually do). Putting all those things together is quite difficult. I’d be willing to bet some other people discovered the positive expected return, but still didn’t take the risk.
With Cash WinFall, if you had a knack for math, you could get an edge. If you were willing to spend the money, you could get an edge. If you put in the hours, you could get an edge. And was that so terrible? How was it Jerry’s fault to solve a puzzle that was right there in front of him? How was it Marge’s fault that she was willing to break her back standing at a lottery terminal, printing tickets?
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