Broken Lotteries

Earlier this year, I wrote about Mohan Srivastava, a geological statistician who has cracked multiple scratch lottery tickets. This means that he can accurately sort winning tickets from losing tickets before removing the latex. Here is how the trick works, at least in a standard tic-tac-toe lottery ticket:

The trick itself is ridiculously simple. (Srivastava would later teach it to his 8-year-old daughter.) Each ticket contained eight tic-tac-toe boards, and each space on those boards—72 in all—contained an exposed number from 1 to 39. As a result, some of these numbers were repeated multiple times. Perhaps the number 17 was repeated three times, and the number 38 was repeated twice. And a few numbers appeared only once on the entire card. Srivastava’s startling insight was that he could separate the winning tickets from the losing tickets by looking at the number of times each of the digits occurred on the tic-tac-toe boards. In other words, he didn’t look at the ticket as a sequence of 72 random digits. Instead, he categorized each number according to its frequency, counting how many times a given number showed up on a given ticket. “The numbers themselves couldn’t have been more meaningless,” he says. “But whether or not they were repeated told me nearly everything I needed to know.” Srivastava was looking for singletons, numbers that appear only a single time on the visible tic-tac-toe boards. He realized that the singletons were almost always repeated under the latex coating. If three singletons appeared in a row on one of the eight boards, that ticket was probably a winner.

The next day, on his way into work, he stopped at the gas station and bought a few more tickets. Sure enough, all of these tickets contained the telltale pattern. The day after that he picked up even more tickets from different stores. These were also breakable. After analyzing his results, Srivastava realized that the singleton trick worked about 90 percent of the time, allowing him to pick the winning tickets before they were scratched.

It turns out, however, that problems with the state lottery system extend far beyond a few poorly designed scratchers. One of the most troubling things I discovered was a series of reports produced by the Massachusetts state auditor that documented a history of "non-random" payouts to a short list of individuals in the state:

The reports describe a long list of troubling findings, such as the fact that one person cashed in 1,588 winning tickets between 2002 and 2004 for a grand total of $2.84 million. (The report does not provide the name of the lucky winner.) A 1999 audit found that another person cashed in 149 tickets worth $237,000, while the top 10 multiple-prize winners had won 842 times for a total of $1.8 million. Since only six out of every 100,000 tickets yield a prize between $1,000 and $5,000, the auditor dryly observed that these “fortunate” players would have needed to buy “hundreds of thousands to millions of tickets.”

These numbers suggest, of course, that someone has broken a lottery game. While the Massachusetts state lottery insisted that such payouts were a symptom of tax evasion - professional "cashers" were redeeming the tickets of others, often with fake Social Security numbers - that doesn't seem to be the case. Rather, a new investigation by the Boston Globe has found that a game has been plundered, albeit in a slightly less dramatic way than Mohan's cracked tic-tac-toe scratcher. It's not that people can defeat the code - they've just realized that, under certain conditions, the average payout exceeds the cost of the ticket. (This is the same method that made Voltaire rich back in the early 18th century.) Andrea Estes and Scott Allen explain:

Billy’s Beer and Wine sold exactly $47 worth of lottery tickets the day before Marjorie Selbee arrived, just another sleepy day for the liquor store in this tiny Western Massachusetts town. But from the moment the 70-something woman from Michigan entered the store early July 12, Billy’s wasn’t sleepy anymore.

Over the next three days, Selbee bought $307,000 worth of $2 tickets for a relatively obscure game called Cash WinFall, tying up the machine that spits out the pink tickets for hours at a time. Down the road at Jerry’s Place, a coffee shop in South Deerfield, Selbee’s husband, Gerald, was also spending $307,000 on Cash WinFall. Together, the couple bought more than 300,000 tickets for a game whose biggest prize - about $2 million - has been claimed exactly once in the game’s seven-year history.

But the Selbees, who run a gambling company called GS Investment Strategies, know a secret about the Massachusetts State Lottery: For a few days about every three months, Cash WinFall may be the most reliably lucrative lottery game in the country. Because of a quirk in the rules, when the jackpot reaches roughly $2 million and no one wins, payoffs for smaller prizes swell dramatically, which statisticians say practically assures a profit to anyone who buys at least $100,000 worth of tickets.

During these brief periods - “rolldown weeks’’ in gambling parlance - a tiny group of savvy bettors, among them highly trained computer scientists from MIT and Northeastern University, virtually take over the game. Just three groups, including the Selbees, claimed 1,105 of the 1,605 winning Cash WinFall tickets statewide after the rolldown week in May, according to lottery records. They also appear to have purchased about half the tickets, based on reports from the stores that the top gamblers frequent most.

“Cash WinFall isn’t being played as a game of chance. Some smart people have figured out how to get rich while everyone else funds their winnings,’’ said Mohan Srivastava, an MIT-educated statistician who gained fame in gambling circles when he found a flaw in a Canadian scratch ticket game that allowed him to pick the winners more than 90 percent of the time.

It is hard to say precisely how much each gambler has won because they have a year to claim prizes and the lottery does not track winning tickets of less than $600. But the Selbees have already claimed nearly $1 million in prize money this year, entirely in tickets valued at $802 to $24,821. Their final haul will undoubtedly be considerably larger.

The sole appeal of these lottery tickets is their randomness - they are peddling the possibility that anyone can win. But I think it's becoming increasingly clear that that's not always the case, and that several of these games have been systematically broken. It would be bad enough if these lotteries run by state governments were simply a regressive tax, encouraging those who can least afford it to spend their income on a form of gambling with terrible odds. But the reality appears to be even worse than that. These odds aren't just terrible - they're unfair.