Why Cash WinFall is a model for future lottery games

By Felix Salmon
August 10, 2012
Andrea Estes discovered that an obscure state lottery game called Cash WinFall could be -- and was -- gamed by sophisticated stats geeks.

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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?

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Comments
28 comments so far

I agree with your basic point. The key to success lies in the marketing. If it’s presented as “something new” aimed specifically at consortiums or people with money, and pitched as such (that’s the key) it might very well fly… and succeed.

Posted by WilliamCowie | Report as abusive

“In this case, however, Cash WinFall was also a 40% tax on the rich professional bettors who played only during roll-down weeks.”

Felix, this is nonsense. The lottery was a massive transfer from unsophisticated players who played during non-roll-down weeks to (mostly sophisticated) parties participating during roll-down periods. If the professionals profited, it came from *somewhere*. If 40% of their wagers were nominally going to the state, then by basic arithmetic 55% of their ROI was coming from bettors in previous periods (the remaining 60% ROI simply handed back to them by lottery structure). There’s no other way to get to $1.15 for every $1 wagered.

Your statement at most points out that the state profited from this bizarre transfer. I’m sure there are all sorts of other ways for the state to take a cut of money going from the unsophisticated to the sophisticated, all while wasting MIT grads’ effort on socially useless activity. To call this a ‘model for future lottery games’ is contrarian pablum.

Posted by absinthe | Report as abusive

I’m with absinthe on this. You make a big song and dance about how 40% of of money gambled goes to the state but the really important sentence is “Over the course of seven years, professional gamblers spent about $40 million on Cash WinFall, and won about $48 million.” So if you do the math then sophisticated gamblers got $24 million of their own money back and the balance of $24 million comes from the unsophisticated gamblers. Your conclusion back near the start, “significant lottery revenues not only from the poor but also from the rich”, is plainly incorrect as this ended up being just a tax on the unsophisticated player with regressive transfers to sophisticated players during roll-down weeks.

Posted by MartinBarry | Report as abusive

I’m confused. If the sophisticated players are winning more money than they spend, how is that a tax on them? Isn’t the Globe’s objection that the “richies” get more money and the state gets more money, so it’s the unsophisticated players who are getting even less than they might have? Having the marks fill up the pot on ordinary weeks so that the MITers can drain it o

Posted by Ivanonymous | Report as abusive

People, the way that lotteries work, the money going to the winners *always* comes from the losers. That’s inevitable. To say “the winners’ money comes from the losers” is just to say “this is a lottery”.

Posted by FelixSalmon | Report as abusive

Actually, my math’s a bit off due to the multi-period nature of the game. (In reality, if they have 115% ROI even though the state takes 40% and some other percentage is deferred to the future pool, the ROI from prior bettors will be strictly higher than 55%. But this is somewhat mitigated by the fact that some of that flow comes from sophisticates, and there is a chance to capture the pool in the next period.)

The broader point is that it’s unhelpful and deceptive to look at the mechanics of the game and make statements such as the one I quoted. It’s simply rhetoric that ignores facts like fungibility and redistribution. The net effects (who lost money, who gained money, how much did the state keep) say everything you need to know about what this game ‘accomplished’. Sullivan’s conclusion is merely that the game was beneficial for the state (and that unsophisticates who happened to play at the same time as the sophisticates were not disadvantaged – but this was not the main fairness consideration).

Posted by absinthe | Report as abusive

“People, the way that lotteries work, the money going to the winners *always* comes from the losers. That’s inevitable. To say “the winners’ money comes from the losers” is just to say “this is a lottery”.”

Yes, but typically the only redistributive issue with a lottery is that poorer people play and so that it’s a regressive tax. (Poorer people pay, poorer people win, and the government takes a cut.)

This lottery had a different structure, which was that poorer people paid, a handful of poorer people won, a much larger quantity of ‘rich’ people won, and the government took a cut.

To say that this was a ‘model lottery’ simply because the government got a larger pie or bigger cut ignores the redistributive aspects entirely.

Posted by absinthe | Report as abusive

I really like government-sponsored lotteries. They are a tax that I can choose whether or not to pay, and I choose not.

Posted by Curmudgeon | Report as abusive

Felix, you need to be a little less gullible.

While the average profit was 40% of revenues, it is absolutely incorrect to state that the average profit off the pros was 40% of revenues. In fact the pros made a profit!

From the numbers cited, it sounds like roughly half of the betting volume occurred in “roll down” weeks. An average player (proportionate to betting value) would have a 0% payout in half the weeks and a 120% payout the other half. Averages out to a 60% payout. But this isn’t the same as having half the WEEKS paying at the 120% rate. I’m sure the volume was much higher for the “roll down” weeks, because of the pros jumping in on the action.

The pros were extracting a 120% payout on their ENTIRE betting, without ever laying a bet at a 0% payout. By doing so, they depress the frequency of the “roll down” weeks and thus the average payout for the poor schmoe who bets equally each week. If there was truly significant professional participation in this game, then the average payout for the rest was greatly reduced.

Posted by TFF | Report as abusive

Whups, missed the numbers the first time through. (Felix’ error was obvious even in a quick scan. This isn’t Lake Wobegone.)

Revenue:
Small-time players: $260M tickets
Big-time players: $40M tickets
Total: $300M

Expenses:
Towns: $120M
Small-time players: $132M
Big-time players: $48M
Total: $300M

Thus the actual payout for your small-time players was around 50%, not the stated 60%. Instead of structuring the game to encourage the big-time leeches, why not simply institute a 50% payout rate? You’ll still get $260M of action from the small players, and you’ll be able to return an *additional* $8M to the towns.

Posted by TFF | Report as abusive

Curmudgeon, yes, you can choose whether or not to play.

But to the extent that the proceeds of a state lottery fund needed and necessary public services that all enjoy (for example, in California the super lotto plus partially funds public schools), you should feel *BAD* that money is being extracted from those less likely to have extra money for discretionary purchases to pay for things that people *WITH* lots of money to pay for discretionary purchases (such as political campaign contributions or private school tuition) have used their political power to avoid having to contribute toward the funding of.

Lots of people realize this and still put their heads in the sand and say “well, less well off people are making a free choice to play lotteries”, but of course the fact that they are less well off is exactly what motivates playing the lottery.

Posted by Strych09 | Report as abusive

TFF, it may be a quibble, but Felix’s point is that 40 cents out of every dollar bet is used to fund lottery operations and send money to municipalities. The sophisticated bet $40 million that (presumably) would not otherwise have been bet, therefore, that resulted in an additional $24 million “profit.”

Now, his other point is that the money would have been won in any case, and in general he’s almost certainly correct there too. The complaint is that those who understood how the game worked were able to place bets that, over time, gave them an advantage over others that some think should not have been possible.

I don’t think I care enough about lotteries to pass a value judgment here.

Posted by Curmudgeon | Report as abusive

Strych09, you’re right, but if it were up to me, I would find the money through real taxes, not fake ones like lotteries (assuming the taxpayers want those services). But our governments have decided to take the coward’s way out, and I just refuse to play their game.

Posted by Curmudgeon | Report as abusive

Strych09, the ‘earmark’ of lottery revenue to specific projects (like public schools) is in most cases just marketing. Revenue is fungible. I’m not aware of any cases where we actually tie funding of schools to lottery revenue. Lottery revenue is a simple substitute for other sources of state revenue.

Posted by absinthe | Report as abusive

Curmudgeon, the point TFF was making is that the tickets bought by the sophisticated bettors resulted in LESS profits for the state than it would have earned with a better structured lottery.

For example, if the stated evened out the payout scheme and increased the rake to 48% then the revenue would have been $260M instead of $300M. Of this, $124.8M would go to the towns (an increase of $4.8M) and $135.2M would go to the small time players (an increase of $3.2M). Everyone wins, except for the sophisticated investors.

Posted by Nathan_M | Report as abusive

Nathan, then of course you can argue that the sophisticated players wouldn’t have put their $40M into the pot. To structure this to the advantage of state revenue, perhaps you have to give them the opportunity to profit. I don’t approve or disapprove, but the goal of maximizing revenue to the state seems to have been achieved.

Posted by Curmudgeon | Report as abusive

Felix has a very simple and valid point: it is the definition of the game that the government earns 40% of ticket sales. From this it follows that if anyone buys a ticket it must increase revenue, because sales have increased. That is an analytic truth, given the game design.

However, if the return on investment for sophisticated gamblers is positive (as suggested in the article), then it is also an analytic truth that the government cannot be earning revenue from that segment – the effective payout is 120%! This tension can only be resolved if professional gamblers buying tickets reduces the prize payout experienced by other players. If we assume the pros earn back 20% and the government gets 40% of the ticket price, a pro purchasing a $1 ticket results in a 20 cent transfer from existing unsophisticated ticketholders to the pro, and a 40 cent transfer from existing unsophisticated ticketholders to the state. The pros increase government revenue, but it is not them who pay for it. Quite the opposite.

To sum up: participation by rich, sophisticated gamblers does increase government revenue, but the revenue doesn’t come from them. It comes from the fact that their participation make the odds worse for unsophisticated players. This is the only way to reconcile the positive ROI for that segment with the structure of the game, and that’s why someone might be inclined to think it is an objectionable structure.

Posted by circusricardo | Report as abusive

I don’t like the state-owned gambling business. If we’re going to be socialist and all, let’s do that with more useful industries.

Those picayune transactions, as you call them, actually matter if you want the state-owned gambling industry to be both fair and perceived to be fair. You want to build a lottery game that facilitates large consortiums and creates business practices to make it easy, that’s one thing. But to let proprietors of the stores in which lottery tickets are being sold cut corners on their own, that starts to create the beginnings of a corrupt environment. And that’s just something I don’t want my government doing.

Posted by SaulTann | Report as abusive

Curmudgeon, the basic point is that the state could make more and the small times players could also make more without the $40m revenue from the sophisticated players.

It’s better for both the state and the small time players for the lottery to be structured better and have $260m in revenue than it is to have the existing structure and an additional $40m in revenue from sophisticated players.

The existing structure may have maximizing lottery tickets sales, but that is not the goal. The goal is to maximize proceeds to the state and that goal was not achieved.

Posted by Nathan_M | Report as abusive

Nathan and circus put it better than I did…

Curmudgeon, Nathan is already subtracting the $40M from the revenues. You can forgo that revenue, and by reducing the payout rate come up with a scenario that is still better for both the small-time gamblers and for the state.

Felix may be right that this approach is attractive to lottery officials. They aren’t interested in giving money to the towns. They aren’t interested in returning money to their bettors. Their sole interest is to increase the revenue stream, and thereby justify their own worthless lives. (I take that back. They are occasionally interested in funding their political campaigns with those revenues under the guise of “advertising”.)

Posted by TFF | Report as abusive

Felix is exactly right Cash Winfall is one of the best designed lotteries which has ever existed.

The state of Mass advantaged itself in two ways:

#1 even before the game changing globe articles the word was out on the street that orginized syndicates were playing the lottery because it was “profitable.” This pulled in tens of thousands of small fish.

#2 Lots of the “smart money” was comming in from out of state. It’s rare for a state to pull in serious outside money into a local lottery. This point was slyly left out of the inspector generals report Mass was tickled pink that out of state players were dumping money into Mass.

Posted by y2kurtus | Report as abusive

I think you completely missed the point here, Felix, and you don’t frequently do that.

The outrage doesn’t come from the state not making enough money. It comes from the fact that having access to extra capital increases the probability of winning disproportionately, such that your expected payout is positive; and that payout comes at the expense of people who can’t follow the same strategy. Sure, only buying tickets on the roll down weeks would have expected positive return, but you can’t depend on actually making a profit in a reasonable timescale without buying a whole lot of tickets.

Posted by BarryKelly | Report as abusive

Yes, TFF, I was incorrect in my last post. But reducing the payout may have other undesirable characteristics from the standpoint of maximizing revenue. I dislike gambling and especially government-sponsored lotteries. But I’m in a minority, so the only way I can show my dislike is by not participating. I’m also an applied mathematician by training, and there is no logic to gambling.

Posted by Curmudgeon | Report as abusive

Curmudgeon, you have some good points there. I would prefer not to sponsor gambling. I would especially prefer not to spend money on advertising promoting gambling.

The Massachusetts Lottery is a crooked organization, a tool for the self-enrichment of political hacks. So I definitely am inclined to treat anything they do with skepticism.

But beyond that, I disagree that the purpose of the state lottery should be to maximize revenues. If it provides a legitimate service by offering an honest game, then that ought to be the focus. The money raised should be secondary.

Posted by TFF | Report as abusive

State sponsored lotteries are usually more about psychology than math. As long as the lottery profits and the proceeds are used by local governments for projects with social benefits (a dubious premise in MA), it should attempt to maximize revenue. It boils down to a simple question about human nature:
Is it better to tax someone 40% and have them be happy to pay the tax? Or is it better to tax them 24% and have them be furious that they must pay it?

Posted by k9quaint | Report as abusive

“Cash WinFall was also a 40% tax on the rich professional bettors who played only during roll-down weeks”

Sorry but that is 100% wrong.
If you are down 40% then you can’t be up 15%.

Cash Windfall was an EVEN-MORE highly-regressive tax than other lotteries.

This is a terrible post.

The losers from non-jackpot weeks were subsidising the professionals.

If the professionals hadn’t played then the regular non-professionals would have shared more of the tickle-down from the had-to-be-won jackpot money.

This is very simple maths.

Posted by TinyTim1 | Report as abusive

“Cash WinFall was also a 40% tax on the rich professional bettors who played only during roll-down weeks”

Sorry but that is 100% wrong.
If you are down 40% then you can’t be up 15%.

Cash Windfall was an EVEN-MORE highly-regressive tax than other lotteries.

This is a terrible post.

The losers from non-jackpot weeks were subsidising the professionals.

If the professionals hadn’t played then the regular non-professionals would have shared more of the tickle-down from the had-to-be-won jackpot money.

This is very simple maths.

Posted by TinyTim1 | Report as abusive

“Cash WinFall was also a 40% tax on the rich professional bettors who played only during roll-down weeks”

Sorry but that is 100% wrong.
If you are down 40% then you can’t be up 15%.

Cash Windfall was an EVEN-MORE highly-regressive tax than other lotteries.

This is a terrible post.

The losers from non-jackpot weeks were subsidising the professionals.

If the professionals hadn’t played then the regular non-professionals would have shared more of the tickle-down from the had-to-be-won jackpot money.

This is very simple maths.

Posted by TinyTim1 | Report as abusive
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