Drew
02-07-2011, 12:20 AM
Mohan Srivastava, a geological statistician living in Toronto, was working in his office in June 2003, waiting for some files to download onto his computer, when he discovered a couple of old lottery tickets buried under some paper on his desk. The tickets were cheap scratchers—a gag gift from his squash partner—and Srivastava found himself wondering if any of them were winners. He fished a coin out of a drawer and began scratching off the latex coating. “The first was a loser, and I felt pretty smug,” Srivastava says. “I thought, ‘This is exactly why I never play these dumb games.’”
The second ticket was a tic-tac-toe game. Its design was straightforward: On the right were eight tic-tac-toe boards, dense with different numbers. On the left was a box headlined “Your Numbers,” covered with a scratchable latex coating. The goal was to scrape off the latex and compare the numbers under it to the digits on the boards. If three of “Your Numbers” appeared on a board in a straight line, you’d won. Srivastava matched up each of his numbers with the digits on the boards, and much to his surprise, the ticket had a tic-tac-toe. Srivastava had won $3. “This is the smallest amount you can win, but I can’t tell you how excited it made me,” he says. “I felt like the king of the world.”
Delighted, he decided to take a lunchtime walk to the gas station to cash in his ticket. “On my way, I start looking at the tic-tac-toe game, and I begin to wonder how they make these things,” Srivastava says. “The tickets are clearly mass-produced, which means there must be some computer program that lays down the numbers. Of course, it would be really nice if the computer could just spit out random digits. But that’s not possible, since the lottery corporation needs to control the number of winning tickets. The game can’t be truly random. Instead, it has to generate the illusion of randomness while actually being carefully determined.”
Srivastava speaks quietly, with a slight stammer. He has a neatly trimmed beard and a messy office. When he talks about a subject he’s interested in—and he’s interested in many things, from military encryption to freshwater fossils—his words start to run into each other.
As a trained statistician with degrees from MIT and Stanford University, Srivastava was intrigued by the technical problem posed by the lottery ticket. In fact, it reminded him a lot of his day job, which involves consulting for mining and oil companies. A typical assignment for Srivastava goes like this: A mining company has multiple samples from a potential gold mine. Each sample gives a different estimate of the amount of mineral underground. “My job is to make sense of those results,” he says. “The numbers might seem random, as if the gold has just been scattered, but they’re actually not random at all. There are fundamental geologic forces that created those numbers. If I know the forces, I can decipher the samples. I can figure out how much gold is underground.”
Srivastava realized that the same logic could be applied to the lottery. The apparent randomness of the scratch ticket was just a facade, a mathematical lie. And this meant that the lottery system might actually be solvable, just like those mining samples. “At the time, I had no intention of cracking the tickets,” he says. He was just curious about the algorithm that produced the numbers. Walking back from the gas station with the chips and coffee he’d bought with his winnings, he turned the problem over in his mind. By the time he reached the office, he was confident that he knew how the software might work, how it could precisely control the number of winners while still appearing random. “It wasn’t that hard,” Srivastava says. “I do the same kind of math all day long.”
That afternoon, he went back to work. The thrill of winning had worn off; he forgot about his lunchtime adventure. But then, as he walked by the gas station later that evening, something strange happened. “I swear I’m not the kind of guy who hears voices,” Srivastava says. “But that night, as I passed the station, I heard a little voice coming from the back of my head. I’ll never forget what it said: ‘If you do it that way, if you use that algorithm, there will be a flaw. The game will be flawed. You will be able to crack the ticket. You will be able to plunder the lottery.’”
The North American lottery system is a $70 billion-a-year business, an industry bigger than movie tickets, music, and porn combined. These tickets have a grand history: Lotteries were used to fund the American colonies and helped bankroll the young nation. In the 18th and 19th centuries, lotteries funded the expansion of Harvard and Yale and allowed the construction of railroads across the continent. Since 1964, when New Hampshire introduced the first modern state lottery, governments have come to rely on gaming revenue. (Forty-three states and every Canadian province currently run lotteries.) In some states, the lottery accounts for more than 5 percent of education funding.
While approximately half of Americans buy at least one lottery ticket at some point, the vast majority of tickets are purchased by about 20 percent of the population. These high-frequency players tend to be poor and uneducated, which is why critics refer to lotteries as a regressive tax. (In a 2006 survey, 30 percent of people without a high school degree said that playing the lottery was a wealth-building strategy.) On average, households that make less than $12,400 a year spend 5 percent of their income on lotteries—a source of hope for just a few bucks a throw.
Photo: John Midgley
Mohan Srivastava, a geological statistician living in Toronto, realized that the logic he used to find gold deposits could also crack lottery cards.
Photo: John Midgley
There was a time when scratch games all but sold themselves. But in the past two decades the competition for the gambling dollar has dramatically increased. As a result, many state lotteries have redesigned their tickets. One important strategy involves the use of what lottery designers call extended play. Although extended-play games—sometimes referred to as baited hooks—tend to look like miniature spreadsheets, they’ve proven extremely popular with consumers. Instead of just scratching off the latex and immediately discovering a loser, players have to spend time matching up the revealed numbers with the boards. Ticket designers fill the cards with near-misses (two-in-a-row matchups instead of the necessary three) and players spend tantalizing seconds looking for their win. No wonder players get hooked.
Srivastava had been hooked by a different sort of lure—that spooky voice, whispering to him about a flaw in the game. At first, he tried to brush it aside. “Like everyone else, I assumed that the lottery was unbreakable,” he says. “There’s no way there could be a flaw, and there’s no way I just happened to discover the flaw on my walk home.”
And yet, his inner voice refused to pipe down. “I remember telling myself that the Ontario Lottery is a multibillion-dollar-a- year business,” he says. “They must know what they’re doing, right?”
That night, however, he realized that the voice was right: The tic-tac-toe lottery was seriously flawed. It took a few hours of studying his tickets and some statistical sleuthing, but he discovered a defect in the game: The visible numbers turned out to reveal essential information about the digits hidden under the latex coating. Nothing needed to be scratched off—the ticket could be cracked if you knew the secret code.
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.
His next thought was utterly predictable: “I remember thinking, I’m gonna be rich! I’m gonna plunder the lottery!” he says. However, these grandiose dreams soon gave way to more practical concerns. “Once I worked out how much money I could make if this was my full-time job, I got a lot less excited,” Srivastava says. “I’d have to travel from store to store and spend 45 seconds cracking each card. I estimated that I could expect to make about $600 a day. That’s not bad. But to be honest, I make more as a consultant, and I find consulting to be a lot more interesting than scratch lottery tickets.”
Instead of secretly plundering the game, he decided to go to the Ontario Lottery and Gaming Corporation. Srivastava thought its top officials might want to know about his discovery. Who knows, maybe they’d even hire him to give them statistical advice. “People often assume that I must be some extremely moral person because I didn’t take advantage of the lottery,” he says. “I can assure you that that’s not the case. I’d simply done the math and concluded that beating the game wasn’t worth my time.”
When Srivastava reported his finding, he was referred to Rob Zufelt, a member of the lottery corporation’s security team. After failing to make contact for a few days, he began to get frustrated: Why wasn’t Zufelt taking his revelation more seriously? “I really got the feeling that he was brushing me off,” Srivastava says. “But then I realized that to him I must sound like a crazy person—like one of those people who claims that he can crack the lotto draw because last night’s number was his birthday spelled backward. No wonder they didn’t want to talk to me.” Instead of trying to get Zufelt to return his calls, Srivastava decided to send him a package. He bought 20 tic-tac-toe tickets and sorted them, unscratched, into piles of winners and losers. Then, he couriered the package to Zufelt along with the following note:
In the enclosed envelopes, I have sent you two groups of 10 TicTacToe tickets that I purchased from various outlets around Toronto in the past week… You go ahead and scratch off the cards. Maybe you can give one batch to your lottery ticket specialist. After you’ve scratched them off, you should have a pretty solid sense for whether or not there’s something fishy here.
The package was sent at 10 am. Two hours later, he received a call from Zufelt. Srivastava had correctly predicted 19 out of the 20 tickets. The next day, the tic-tac-toe game was pulled from stores.
The official explanation from the Ontario Lottery and Gaming Corporation is that the tic-tac-toe game suffered from a “design flaw.” According to Tony Bitonti, a senior manager of media relations at the Ontario Lottery, the printer of the game, Pollard Banknote, provided “written assurances” that “none of the other instant games it printed were impacted by this.” As a result, the Ontario Lottery continued to sell scratch tickets with baited hooks. The story of the broken game got little public attention. It was, however, cited in a 2007 investigative report by the Ontario ombudsman, who was investigating retailer fraud.
Srivastava, meanwhile, was becoming even more interested in scratch tickets. “It got to the point where I knew I needed to get back to my real job,” he says. “But I found it hard to believe that only this tic-tac-toe game was flawed. What were the odds that I just happened to stumble upon the only breakable game the very first time I played the lottery? Of course, I knew it was possible that every other scratch game was totally secure. I just didn’t think it was very likely.”
He began by looking at other tic-tac-toe games in the US and Canada. Srivastava soon discovered that it wasn’t just an Ontario problem. At the time, one of his best friends was living in Colorado, and Srivastava asked him to send along a few tickets. It turned out that the same singleton trick also worked on the Colorado game, albeit with only a 70 percent level of accuracy. (Colorado Lottery officials did not respond to repeated requests for comment.)
Srivastava was even able to break a Super Bingo game (sold in Ontario in 2007), which also featured an elaborate baited hook. In this case, he says he could sort winners from losers with a 70 percent success rate. The Ontario Lottery says the Super Bingo game didn’t have the same flaw as the tic-tac-toe game but that it was pulled off the Ontario market in March 2007 as a precaution.
In North America, the vast majority of lottery tickets—everything from daily draw Pick 4-style games to small-stakes tic-tac-toe and bingo scratchers—are produced by a handful of companies like Scientific Games, Gtech Printing, and Pollard Banknote. These publicly traded firms oversee much of the development, algorithm design, and production of the different gambling games, and the state lotteries are largely dependent on their expertise. Ross Dalton is president of Gtech Printing, and he acknowledges that the “breakability” of tickets is a constant concern. (Several other printing companies declined to comment.) “Every lottery knows that it’s one scandal away from being shut down,” Dalton says. “It’s a constant race to stay ahead of the bad guys.” In recent years, Dalton says, the printers have become increasingly worried about forensic breaking, the possibility of criminals using sophisticated imaging technology to see underneath the latex. (Previous forensic hacks have included vodka, which swelled the hidden ink, and the careful use of X-Acto knives.) The printers have also become concerned about the barcodes on the tickets, since the data often contains information about payouts. “We’re always looking at new methods of encryption and protection,” Dalton says. “There’s a lot of money at stake in these games.”
.
The second ticket was a tic-tac-toe game. Its design was straightforward: On the right were eight tic-tac-toe boards, dense with different numbers. On the left was a box headlined “Your Numbers,” covered with a scratchable latex coating. The goal was to scrape off the latex and compare the numbers under it to the digits on the boards. If three of “Your Numbers” appeared on a board in a straight line, you’d won. Srivastava matched up each of his numbers with the digits on the boards, and much to his surprise, the ticket had a tic-tac-toe. Srivastava had won $3. “This is the smallest amount you can win, but I can’t tell you how excited it made me,” he says. “I felt like the king of the world.”
Delighted, he decided to take a lunchtime walk to the gas station to cash in his ticket. “On my way, I start looking at the tic-tac-toe game, and I begin to wonder how they make these things,” Srivastava says. “The tickets are clearly mass-produced, which means there must be some computer program that lays down the numbers. Of course, it would be really nice if the computer could just spit out random digits. But that’s not possible, since the lottery corporation needs to control the number of winning tickets. The game can’t be truly random. Instead, it has to generate the illusion of randomness while actually being carefully determined.”
Srivastava speaks quietly, with a slight stammer. He has a neatly trimmed beard and a messy office. When he talks about a subject he’s interested in—and he’s interested in many things, from military encryption to freshwater fossils—his words start to run into each other.
As a trained statistician with degrees from MIT and Stanford University, Srivastava was intrigued by the technical problem posed by the lottery ticket. In fact, it reminded him a lot of his day job, which involves consulting for mining and oil companies. A typical assignment for Srivastava goes like this: A mining company has multiple samples from a potential gold mine. Each sample gives a different estimate of the amount of mineral underground. “My job is to make sense of those results,” he says. “The numbers might seem random, as if the gold has just been scattered, but they’re actually not random at all. There are fundamental geologic forces that created those numbers. If I know the forces, I can decipher the samples. I can figure out how much gold is underground.”
Srivastava realized that the same logic could be applied to the lottery. The apparent randomness of the scratch ticket was just a facade, a mathematical lie. And this meant that the lottery system might actually be solvable, just like those mining samples. “At the time, I had no intention of cracking the tickets,” he says. He was just curious about the algorithm that produced the numbers. Walking back from the gas station with the chips and coffee he’d bought with his winnings, he turned the problem over in his mind. By the time he reached the office, he was confident that he knew how the software might work, how it could precisely control the number of winners while still appearing random. “It wasn’t that hard,” Srivastava says. “I do the same kind of math all day long.”
That afternoon, he went back to work. The thrill of winning had worn off; he forgot about his lunchtime adventure. But then, as he walked by the gas station later that evening, something strange happened. “I swear I’m not the kind of guy who hears voices,” Srivastava says. “But that night, as I passed the station, I heard a little voice coming from the back of my head. I’ll never forget what it said: ‘If you do it that way, if you use that algorithm, there will be a flaw. The game will be flawed. You will be able to crack the ticket. You will be able to plunder the lottery.’”
The North American lottery system is a $70 billion-a-year business, an industry bigger than movie tickets, music, and porn combined. These tickets have a grand history: Lotteries were used to fund the American colonies and helped bankroll the young nation. In the 18th and 19th centuries, lotteries funded the expansion of Harvard and Yale and allowed the construction of railroads across the continent. Since 1964, when New Hampshire introduced the first modern state lottery, governments have come to rely on gaming revenue. (Forty-three states and every Canadian province currently run lotteries.) In some states, the lottery accounts for more than 5 percent of education funding.
While approximately half of Americans buy at least one lottery ticket at some point, the vast majority of tickets are purchased by about 20 percent of the population. These high-frequency players tend to be poor and uneducated, which is why critics refer to lotteries as a regressive tax. (In a 2006 survey, 30 percent of people without a high school degree said that playing the lottery was a wealth-building strategy.) On average, households that make less than $12,400 a year spend 5 percent of their income on lotteries—a source of hope for just a few bucks a throw.
Photo: John Midgley
Mohan Srivastava, a geological statistician living in Toronto, realized that the logic he used to find gold deposits could also crack lottery cards.
Photo: John Midgley
There was a time when scratch games all but sold themselves. But in the past two decades the competition for the gambling dollar has dramatically increased. As a result, many state lotteries have redesigned their tickets. One important strategy involves the use of what lottery designers call extended play. Although extended-play games—sometimes referred to as baited hooks—tend to look like miniature spreadsheets, they’ve proven extremely popular with consumers. Instead of just scratching off the latex and immediately discovering a loser, players have to spend time matching up the revealed numbers with the boards. Ticket designers fill the cards with near-misses (two-in-a-row matchups instead of the necessary three) and players spend tantalizing seconds looking for their win. No wonder players get hooked.
Srivastava had been hooked by a different sort of lure—that spooky voice, whispering to him about a flaw in the game. At first, he tried to brush it aside. “Like everyone else, I assumed that the lottery was unbreakable,” he says. “There’s no way there could be a flaw, and there’s no way I just happened to discover the flaw on my walk home.”
And yet, his inner voice refused to pipe down. “I remember telling myself that the Ontario Lottery is a multibillion-dollar-a- year business,” he says. “They must know what they’re doing, right?”
That night, however, he realized that the voice was right: The tic-tac-toe lottery was seriously flawed. It took a few hours of studying his tickets and some statistical sleuthing, but he discovered a defect in the game: The visible numbers turned out to reveal essential information about the digits hidden under the latex coating. Nothing needed to be scratched off—the ticket could be cracked if you knew the secret code.
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.
His next thought was utterly predictable: “I remember thinking, I’m gonna be rich! I’m gonna plunder the lottery!” he says. However, these grandiose dreams soon gave way to more practical concerns. “Once I worked out how much money I could make if this was my full-time job, I got a lot less excited,” Srivastava says. “I’d have to travel from store to store and spend 45 seconds cracking each card. I estimated that I could expect to make about $600 a day. That’s not bad. But to be honest, I make more as a consultant, and I find consulting to be a lot more interesting than scratch lottery tickets.”
Instead of secretly plundering the game, he decided to go to the Ontario Lottery and Gaming Corporation. Srivastava thought its top officials might want to know about his discovery. Who knows, maybe they’d even hire him to give them statistical advice. “People often assume that I must be some extremely moral person because I didn’t take advantage of the lottery,” he says. “I can assure you that that’s not the case. I’d simply done the math and concluded that beating the game wasn’t worth my time.”
When Srivastava reported his finding, he was referred to Rob Zufelt, a member of the lottery corporation’s security team. After failing to make contact for a few days, he began to get frustrated: Why wasn’t Zufelt taking his revelation more seriously? “I really got the feeling that he was brushing me off,” Srivastava says. “But then I realized that to him I must sound like a crazy person—like one of those people who claims that he can crack the lotto draw because last night’s number was his birthday spelled backward. No wonder they didn’t want to talk to me.” Instead of trying to get Zufelt to return his calls, Srivastava decided to send him a package. He bought 20 tic-tac-toe tickets and sorted them, unscratched, into piles of winners and losers. Then, he couriered the package to Zufelt along with the following note:
In the enclosed envelopes, I have sent you two groups of 10 TicTacToe tickets that I purchased from various outlets around Toronto in the past week… You go ahead and scratch off the cards. Maybe you can give one batch to your lottery ticket specialist. After you’ve scratched them off, you should have a pretty solid sense for whether or not there’s something fishy here.
The package was sent at 10 am. Two hours later, he received a call from Zufelt. Srivastava had correctly predicted 19 out of the 20 tickets. The next day, the tic-tac-toe game was pulled from stores.
The official explanation from the Ontario Lottery and Gaming Corporation is that the tic-tac-toe game suffered from a “design flaw.” According to Tony Bitonti, a senior manager of media relations at the Ontario Lottery, the printer of the game, Pollard Banknote, provided “written assurances” that “none of the other instant games it printed were impacted by this.” As a result, the Ontario Lottery continued to sell scratch tickets with baited hooks. The story of the broken game got little public attention. It was, however, cited in a 2007 investigative report by the Ontario ombudsman, who was investigating retailer fraud.
Srivastava, meanwhile, was becoming even more interested in scratch tickets. “It got to the point where I knew I needed to get back to my real job,” he says. “But I found it hard to believe that only this tic-tac-toe game was flawed. What were the odds that I just happened to stumble upon the only breakable game the very first time I played the lottery? Of course, I knew it was possible that every other scratch game was totally secure. I just didn’t think it was very likely.”
He began by looking at other tic-tac-toe games in the US and Canada. Srivastava soon discovered that it wasn’t just an Ontario problem. At the time, one of his best friends was living in Colorado, and Srivastava asked him to send along a few tickets. It turned out that the same singleton trick also worked on the Colorado game, albeit with only a 70 percent level of accuracy. (Colorado Lottery officials did not respond to repeated requests for comment.)
Srivastava was even able to break a Super Bingo game (sold in Ontario in 2007), which also featured an elaborate baited hook. In this case, he says he could sort winners from losers with a 70 percent success rate. The Ontario Lottery says the Super Bingo game didn’t have the same flaw as the tic-tac-toe game but that it was pulled off the Ontario market in March 2007 as a precaution.
In North America, the vast majority of lottery tickets—everything from daily draw Pick 4-style games to small-stakes tic-tac-toe and bingo scratchers—are produced by a handful of companies like Scientific Games, Gtech Printing, and Pollard Banknote. These publicly traded firms oversee much of the development, algorithm design, and production of the different gambling games, and the state lotteries are largely dependent on their expertise. Ross Dalton is president of Gtech Printing, and he acknowledges that the “breakability” of tickets is a constant concern. (Several other printing companies declined to comment.) “Every lottery knows that it’s one scandal away from being shut down,” Dalton says. “It’s a constant race to stay ahead of the bad guys.” In recent years, Dalton says, the printers have become increasingly worried about forensic breaking, the possibility of criminals using sophisticated imaging technology to see underneath the latex. (Previous forensic hacks have included vodka, which swelled the hidden ink, and the careful use of X-Acto knives.) The printers have also become concerned about the barcodes on the tickets, since the data often contains information about payouts. “We’re always looking at new methods of encryption and protection,” Dalton says. “There’s a lot of money at stake in these games.”
.