-------------------------------------------- LOTTERY FRAUD: SOLVING CRIMES USING MATH By Jeffrey S. Rosenthal Professor, Department of Statistics, University of Toronto, and Author of "Struck by Lightning: The Curious World of Probabilities" (Published in the RCMP Gazette, 70(1), 2008, pp. 18-19.) On the CBS television series Numb3rs, crime-fighting mathematician Charlie Eppes boldly declares, "Everything is numbers!" Well, that might be an exaggeration. But my recent investigations into lottery fraud have convinced me that statistical analysis can indeed be used to uncover fraudulent behaviour that might otherwise pass undetected. Many lottery players simply hand their tickets over to the local store clerk, asking if they have won anything. This runs the risk that an unscrupulous clerk might pretend that a winning lottery ticket won nothing (or just a tiny prize), and then later claim the big lottery jackpot for themselves. Does such fraudulent behaviour actual occur? How often? Statistical analysis can find out! In 2001, Bob Edmonds, a 75-year-old citizen in Coboconk, Ont., claimed that a local retailer had defrauded him out of a $250,000 winning lottery ticket. Subsequent investigation proved him correct, and in 2005 the Ontario Lottery and Gaming Corporation (OLG) finally settled with him for $150,000. However, the OLG fought the case very hard before settling (incurring $425,000 in legal costs), and insisted on a "gag order" to keep the settlement confidential. This raised suspicions about whether the OLG was hiding other, similarly fraudulent wins by other store clerks. The CBC television program The Fifth Estate asked me to investigate. So what did the numbers say? Through a Freedom of Information request by the CBC, it was ascertained that in the period 1999-2006, there were a total of 5,713 major (i.e., $50,000 or more) Ontario lottery wins, of which about 200 (3.5%) were recorded as being won by people who worked in stores that sold lottery tickets. (Now, store clerk wins were only recorded if the lottery winner answered yes when the OLG asked if they worked at a store. Some winners might have lied, so the true figure is probably even higher than 200.) The question was, is 200 wins a lot? Too many? How many major prizes should we have expected these sellers to win? And, what are the odds that they would win 200 or more of them honestly, i.e. by pure luck alone? To answer these questions, we first needed to know the total number of retail lottery sellers at any given time. The OLG said they didn't know this figure, so we had to sort through the numbers and figure it out. There are 10,300 lottery ticket sales locations in Ontario. A Fifth Estate survey indicated there were about 3.5 sellers per location, or about 36,050 sellers total. By contrast, an OLG executive had testified in court that there were "50,000 or 60,000" such sellers. Then, just five days before the Fifth Estate program was to air, the OLG unexpectedly presented a brand new table, now claiming a total of 140,000 sellers -- which turned out, on closer inspection, to mean 101,000 active sellers plus 39,000 annual "turnover" (i.e., former employees, who weren't actually relevant to the count). We also needed to know how much these sellers spend on lottery tickets, as compared to the general adult population. Again the OLG said they didn't know. So, the Fifth Estate did another survey, concluding that the average lottery seller spends about 1.5 times as much as an average adult. (The OLG later conducted their own survey and got a similar answer, 1.9. And Corporate Research Associates Inc. (CRA) studied this same question in Atlantic Canada and obtained a factor of 1.52 -- virtually identical to the Fifth Estate figure.) From all of these numbers, what can we conclude? Using the figure of 60,000 sellers (from the OLG's court testimony), together with the spending factor of 1.5 (from the Fifth Estate and CRA surveys), we would expect that in the absence of fraud, lottery sellers would win about 57 of the major prizes between 1999 and 2006 -- far less than the 200 they actually won. And, the probability of their winning 200 or more by pure luck alone would be unimaginably small: less than one chance in a trillion, trillion, trillion, trillion. Even taking the largest OLG estimates, i.e. 101,000 sellers spending an average of 1.9 times as much as the general adult population, we would still expect just 123 major seller wins over this time period. The probability of their winning 200 or more major prizes would then be less than one chance in seven billion -- again absolutely inconceivable. So, no matter how you sliced it, it was clear that lottery sellers were winning significantly more major lottery prizes than could be accounted for by chance alone. The statistics had proved the existence of widespread lottery fraud. Regarding store type, only about one-fifth of the retail lottery sellers work at independent convenience stores, but a much high percentage of the defrauding instances occurred in such stores. (The OLG wouldn't tell the CBC precisely how many, but an OLG "FAQ" web page later admitted that 53% of the recorded insider wins were specifically from sellers at convenience stores.) And this large number of convenience store wins could not have arisen purely by chance. It was also interesting to consider retail store owners as a separate group, disregarding non-owner employees. Those owners won about 83 of the major wins between 1999 and 2006. We didn't know the precise number of retail store owners (and again, the OLG wouldn't say), but even under the most generous assumptions, we would expect at most 25 owner wins -- far fewer than 83. This provided still more evidence of fraud. When the Fifth Estate episode finally aired in October 2006, the story immediately became front-page news. I was flooded with media interview requests, the issue was debated in the Ontario legislature, the government was put on the defensive, and the Ontario Ombudsman launched a full investigation. At first, the OLG tried to "refute" our statistical findings. They hired their own consultants, denied there was significant lottery fraud, and insisted that the Edmonds case was simply an "isolated incident". But the evidence against them was overwhelming. By the time the Ombudsman issued his report, five additional specific cases of lottery fraud had been identified, the OLG's handling of the situation was thoroughly criticised and discredited, the OLG's CEO had been fired, and everyone agreed that reforms were needed. On the positive side, the OLG has now instituted some specific policy reforms. Customers are instructed to sign their lottery tickets before redeeming them. And self-checker machines allow customers to easily learn what they've won before handing their tickets to anyone else. Other provinces also got involved. Soon after the Fifth Estate program aired, British Columbia's Ombudsman launched a similar investigation, which found the B.C. lottery system "open to fraud by retailers trying to cheat customers", and led to the firing of the British Columbia Lottery Corporation's CEO too. And a study I wrote for the Nova Scotia Gaming Corporation found that in the period 2001-6, the number of major lottery wins by Nova Scotia retail store owners was also inconceivable by pure chance alone -- so lottery ticket sellers must have defrauded customers there, too. I never expected this issue to become so big, or to have such wide repercussions. But it does illustrate that statistics has an important role to play in determining the extent of fraud. We all know that seemingly random occurrences can accumulate into hard evidence. (As the James Bond nemesis Auric Goldfinger put it, "Once is happenstance, twice is coincidence and three times is enemy action.") The challenge is to recognise situations where statistical analysis might help, and use careful probabilistic modeling to determine whether or not the observed results could have occurred through pure chance alone. Or, in the words of an anonymous student who recognised me the day after the Fifth Estate broadcast: "Solving crimes using math -- that rocks!" --------------------------------------------