Andrea Estes discovered that an obscure state lottery game called Cash WinFall could be -- and was -- gamed by sophisticated stats geeks. " data-share-img="" data-share="twitter,facebook,linkedin,reddit,google,mail" data-share-count="false">

Last year, the Boston Globe’s Andrea Estes discovered that an obscure state lottery game called Cash WinFall could be — and was — gamed by sophisticated stats geeks. The secret was in the fact that the odds of winning the jackpot were so remote — just one in 9.6 million. As a result, it was almost certain that the jackpot would not be won in any given week.

Because the jackpot was basically never won, it couldn’t just keep on rising indefinitely. So Cash WinFall had a mechanism for distributing it: when the jackpot rose above $2 million, it would “roll down” into smaller prizes. For instance, if you got five out of six numbers correct in a normal week, you would win $4,000; in a roll-down week, you would win $40,000.

A bunch of what can only be called professional lottery players jumped on this quirk, and would buy up hundreds of thousands of dollars’ worth of tickets in roll-down weeks, when the swollen jackpot was certain to get distributed. By buying so many tickets, they pretty much guaranteed that they would buy enough winning tickets to turn a profit — in a typical roll-down week, they would win back 15% to 20% more than they gambled.

Weirdly, the big risk here was the 1.4% chance that the jackpot would be won — as happened, for instance, on July 10, 2008. That worked out very well for the winner, Wenxu Tong, the general partner of a company called Tong’s Fortunelot Limited Partnership, who took home nearly $2.5 million. But all the other consortiums trying to game the system that week all did very badly, losing hundreds of thousands of dollars.

There was a tinge of scandal to Estes’s reporting. “Cash WinFall isn’t being played as a game of chance,” she quoted Mohan Srivastava as saying. “Some smart people have figured out how to get rich while everyone else funds their winnings.’’ And a few days after her story appeared, the Boston Globe ran an editorial under the headline “Lottery game is fatally flawed; treasurer should shut it down”. The argument? In any lottery game, according to the paper, “the odds should be stacked equally against rich and poor”. And eventually, earlier this year, Cash WinFall was indeed phased out.

Now Gregory Sullivan, the state inspector general, has written a 25-page report on the Cash WinFall game, which is well worth reading; Estes, naturally, has written it up for the Globe, under the headline “Lottery officials knew about Cash WinFall’s flaws, IG says”. She never mentions, however, the report’s conclusion: those “flaws” ended up being very profitable for the state, and were a way for Massachusetts to get significant lottery revenues not only from the poor but also from the rich.

Over the course of seven years, professional gamblers spent about $40 million on Cash WinFall, and won about $48 million. As Sullivan says, “the Lottery benefited substantially from the large betting groups”. He explains:

The Lottery designed Cash WinFall to pay out 60 cents of every dollar wagered, leaving 40 cents for the Lottery to run its own operations and distribute to cities and towns in the form of local aid. Like all Lottery games, Cash WinFall was designed to make money and the more Cash WinFall tickets the Lottery sold, the more money the Lottery made.

As a result, those $40 million in extra tickets worked out to a good $16 million in excess revenues for the Lottery fund — money which went to good causes, and which wouldn’t have been available had Cash WinFall not been gamed.

The mathematics of the roll-down were a feature of the game: it was specifically designed so that in roll-down weeks total payouts would be $1.15, or sometimes more, for every dollar wagered. Cash WinFall was designed that way because the game it replaced, Mass Millions, went a whole year without paying out a jackpot, and eventually gamblers just gave up on it.

Although it was relatively easy to game Cash WinFall in theory, it was much harder to do so in practice. Most stores with lottery terminals gave short shrift to players seeking to tie them up for hours at a time, especially when they could be presenting thousands of “free bets” won in previous rounds. In humid weather, or when the terminals were running low on ink, the machines could be unreliable. And it was hard to come up with a way of identifying the handful of winning tickets among the hundreds of thousands of losing ones. What’s more, reports Sullivan,

Tax compliance was also a headache for high-volume bettors. Every time Random Strategies turned in a batch of winning tickets, the Lottery generated a W-2G for every member of the group. Even small investors in the MIT group – for example, someone who won $800 over the course of a year – would get dozens of W-2Gs every year and have to spend hours accounting for their winnings on their tax returns. The hassle prompted some people to cash out and leave the investment pool, Mr. Harvey said. The tax hassle was one reason that the MIT group, which began with 40 to 50 people, dropped to a couple dozen participants in the years after graduation and ended with 10 members at the conclusion of Cash WinFall earlier this year.

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.

It’s worth underscoring that although the professional bettors made a profit on Cash WinFall, that doesn’t mean for a minute that the lottery made a loss. Quite the opposite: the lottery profited from those bettors to the tune of millions of dollars. In Cash WinFall, the lottery kept just 40% of the amount bet; 60% is returned to bettors in the form of winnings. That 60% never belonged to the lottery; it was always going to go to bettors, one way or another. In many weeks, bettors ended up receiving less than 60% of the amount bet, because the jackpot wasn’t claimed. That just meant they had another chance, the following week, to win the money in the jackpot. And in roll-down weeks, thousands of bettors would share the jackpot money between them. The professional consortiums dominated those pools, but they still, always, saw 40% of their money going directly to the lottery.

It’s worth quoting Sullivan’s conclusion at some length, if only because Estes is so mealy-mouthed about it:

I have concluded that Cash WinFall was a financial success for the Lottery. It generated about $300 million in ticket sales, with nearly $120 million of that going to Lottery operations and the pool of funds distributed to cities and towns. The high-volume bettors were a financial boon to the Lottery, collectively buying roughly $2 million in tickets for a typical roll-down drawing – 40 percent of which the Lottery would keep to redistribute to cities and towns. Cash WinFall was designed to attract a huge influx of betting by distributing a windfall to bettors whenever the jackpot reached $2 million. The emergence of individuals and groups buying large volumes of tickets was legal and financially advantageous to the Lottery… No one’s odds of having a winning ticket were affected by high-volume betting. Small bettors enjoyed the same odds as high-volume bettors. When the jackpot hit the roll-down threshold, Cash WinFall became a good bet for everyone, not just the big-time bettors.

At the margin, the more professional consortiums there were playing Cash WinFall, the more money the lottery made. What’s more, the biggest problem with most lotteries is that they act as a highly-regressive tax on the poor. In this case, however, Cash WinFall was also a 40% tax on the rich professional bettors who played only during roll-down weeks. (And of course those bettors had to pay income tax on their winnings, as well.)

I’m not a fan of lotteries in general. But it seems to me that if you’re going to have a lottery, then it’s better to have one which extracts money from the rich and the poor than it is to have one which extracts money only from the poor. The tone of the Globe’s reporting was unfortunate here: I can easily see a world where some other reporter might have celebrated the plucky consortiums who had worked out how to make money from the game, causing lots of other well-heeled punters in Massachusetts to follow suit. Even if they didn’t have a particularly high chance of winning, I can definitely see a lot of over-educated Cambridge types dropping a hundred bucks or so on lottery tickets during roll-down weeks, just because they could afford to lose the money and they knew that statistically their expected payout was going to be positive.

Instead, the whole thing turned into a silly scandal, with the Globe and the state worrying about picayune transgressions of the rules, like whether tickets were paid for before or after they were printed. Eventually, Estes even extracted an apology from Massachusetts state treasurer Steven Grossman, underscoring the idea that Cash WinFall — a lottery designed to be gameable — was some kind of scandalous failure, when in fact it turned out, by lottery standards, to be a success.

If I were running the Massachusetts lottery, I’d look at what happened in Cash WinFall, and create a game designed to be as attractive as possible to consortiums and the rich. Make it really easy to buy hundreds of thousands of dollars’ worth of tickets at a time; maybe even have e-tickets which can have hundreds of thousands of lines, and which can be redeemed individually. Tell the rich that if they get their timing and strategy right, this is a way they can make real money. While, of course, appealing to regular weekly punters as well. You’d essentially be broadening the lottery tax base, and increasing revenues, by appealing to the people who can most afford to play.

But that’s not going to happen: the likes of the Boston Globe editorial board would inevitably call such a game “fatally flawed” since the strategic element would appeal to the rich more than to the poor. But the rich like games combining luck and strategy. Why not give them what they want?