Anyone with even the most elementary knowledge of computers, even if they are unable to spell “algorithm” much less tell you what it means…are capable of understanding that computer programs are wonderfully open to do and say whatever the programmer(s) wish. Lotteries are taxes on the gullible, the stupid and the hopeless. Better to take those lottery bucks, put them in a savings account, you will realize a far bigger windfall than you would via the lottery. A ticket every now and then, for fun, is a harmless waste of money – you have as much chance of winning as the next guy – about less than zero but if you accept that and still don’t mind tossing your money away? Have a time but when that money could be used to buy grocery staples for the home? Choose the milk and bread – walk away from the scam artists of Loto-Quebec. It’s a high tech shell game.
Two lottery enthusiasts suing Loto-Québec
MONTREAL – One afternoon last August while at the Internet café he frequented, Michael Amar purchased a Loto-Québec 6/49 and asked that 10 Extra combinations be added to his lottery ticket.
Such was the Montrealer’s habit, to take one chance on the 6/49 and 10 chances on the Extra. What was unusual was that Amar looked long and hard at the Extra numbers on his ticket sold by café operator Rajib Ullah.
“I said to Rajib, ‘Oh my goodness, I’m going to get two bucks … because I have all the possibilities on the last digits.’ ”
He meant that every digit, 0 to 9, appeared at the end of the 10 sequences of seven. The first digits also ran through 0 to 9, with no repetitions. Startled by the pattern, the two men bought and printed a series of Loto-Québec tickets over several months, always maximizing the Extra option. Sure enough, neither the first digits nor the last digits included repetitions. Every purchase saw them buying 10 combinations that featured one combo that ended in 0, one in 1, one in 2, one in 3 and so on right to the combo ending in 9. Such a lineup guaranteed them exactly one $2 win for matching the final digit of whatever winning number was selected in the Extra drawing. But they weren’t impressed.
“I’d rather not have any guarantees of winning a small prize to have better chances to win multiple prizes and the grand prize,” Amar said.
If you buy 10 Extras on a single ticket, “you cannot win on more than two Extras. The first and last digits are the gatekeepers to the (larger) prize categories … and they do not repeat.”
Truly random sequence of numbers would, of course, include occasional repetitions. That is why the men began exploring random numbers and odds and Canadian laws pertaining to lotteries.
The research has translated into a lawsuit that contends Loto-Québec is engaged in “illegal and nefarious lottery practices,” in regard to its popular Extra lottery. The suit, which is seeking $40,000 in damages for the two lottery enthusiasts and $20 million in punitive damages, is being contested by the lottery corporation. The legal challenge is just beginning to make its way through the justice system, but it does raise provocative questions, especially concerning the randomness of the Extra numbers tendered to Loto-Québec consumers.
Amar, a former salesman and father of two who is waiting for the fall to seek employment, and Ullah, an entrepreneur currently out of work, contend that the software program used to generate the Extra combination was designed to “remove the randomness factor which is both the trademark of fairness and a fundamental characteristic” of all lotteries.
It’s not the first time that Quebec’s gambling monopoly has been publicly challenged about the “randomness factor.”
In 1994, Daniel Corriveau, a computer consultant with little more than a CEGEP education, cracked the electronic keno game at the Casino de Montréal. He found a pattern in winning keno numbers, predicted the outcome of three keno games and won $600,000 before the keno operations were shut down pending police and regulatory inquiries. In terms of sales, Extra is the third most popular lottery in the province. In Loto-Québec’s 2011 fiscal year, it generated almost $144 million in sales.
It is also a lottery that is pushed by the corporation. “Do you want Extra with that?” is an oft-heard question in Quebec because terminal operators are instructed to ask that when consumers purchase a Lotto 6/49 or Lotto Max or the other lottery products that carry the Extra option.
In documents submitted to the Quebec Superior Court, Amar and Ullah compare Loto-Québec’s Extra with the Ontario Lottery and Gaming Corp.’s Encore lottery, a lottery strikingly similar to the Extra in style, prize structure and published odds. Copies of Encore combinations purchased by the men and submitted to the court show that first and last digits are repeated when multiple Encore combinations are bought. The marked contrast between similar lotteries operated by sister corporations is among the factors raised by the men to question the integrity of the Quebec game. Loto-Québec’s rendition of Extra combinations, they contend, is designed to lower a player’s odds. They contest the lottery payoff rate promoted by the corporation.
Two Montreal university professors considered some of the points raised in the lawsuit at the request of The Gazette. The intent was not to weigh the merits of the men’s legal case or speculate about which side would win should it go to trial.
Proffesor Louigi Addario-Berry of McGill’s Department of Mathematics found the matter intriguing. Of interest was the lineup of the 10 Extra combinations generated by Loto-Québec.
“The odds of that happening with one ticket – the probability of no repeats in the first or last column – is something like one out of every 7.5 million tickets,” Addario-Berry said. “Being able to find many tickets like that seems like overwhelming proof that the numbers aren’t completely random and independent of one another.”
Before launching their lawsuit, Amar and Ullah formally quizzed Loto-Québec about many things, including how Extra numbers are generated.
Extra “numbers are generated by a computerized number-generation algorithm within Loto-Québec’s central computer system,” Lynne Roiter, the corporation’s vice-president responsible for Access to Information requests, wrote in a Nov. 30, 2010, letter, now an exhibit in the case. “As such, Extra numbers are generated by use of an algorithm, which, by definition, is a sequence of operations to be performed by the central computer system every time a ticket is purchased at a terminal.” While a single Extra selection may be, in and of itself, a random number, when there are 10 of them, a clear pattern emerges.
Addario-Berry and Professor Yogendra Chaubey, chair of Concordia University’s mathematics and statistics department, note that computers rely on programs.
“You start with a random number generator, but (one) can fudge it,” Chaubey said. It is easy to create a computer program that will not repeat first or last digits in a sequence of numbers, he said.
On the crucial question of whether Loto-Québec has given the Extra number generator a script to follow, the gambling corporation is silent.
“We think we made all the efforts (required) to try to explain the way we do things, but obviously to no avail, so we will see (Amar and Ullah) in court in due time,” Loto-Québec spokesman Jean-Pierre Roy said.
Loto-Québec responded to the men’s first access request and met with them to discuss their concerns, he noted. As to Extra’s random number generation and its program, “we will make our position known to the judge,” Roy said. “It’s part of the suit, so I cannot comment at this time.” The two lottery enthusiasts contend that the corporation is violating provisions of Canada’s criminal code, which prohibits predetermined outcomes in lotteries and games of chance.
The winning Extra numbers are determined by ball machines, a method widely accepted as being random and based on chance. It’s the numbers proffered to the customers that will probably be the focus of the case.
Should the matter go to trial, much will probably depend on how well Loto-Québec’s claims to consumers stand up under scrutiny. The randomness of the Extra numbers and the payout rates can only be assessed if Loto-Québec supplies large samples of its lottery numbers and game outcomes, Chaubey said.
Whether Loto-Québec lives up to its published odds for the Extra draws will probably “boil down to a fight between statisticians” for each side, he predicted. The final analysis, according to Addario-Berry, may show that Quebec’s method has “essentially no impact on the odds of winning the big prize once (although) it basically makes it impossible to win the big prize twice on the same ticket.”
Should the matter go to trial, the judge will almost certainly be subjected to varying views of randomness. “There are different notions of what randomness means, but one very natural or intuitive idea is that if you have a sequence of random numbers, they should be unpredictable,” Addario-Berry said. “You shouldn’t be able to tell something about the next one in the sequence given the ones you have already seen.”
Numbers with patterns are most common picks
Consumers can choose their own numbers with some Loto-Québec lottery products.
The corporation found that popular selections are often based on:
- Series of consecutive numbers
- Numbers in a logical sequence
- Graphic forms created by numbers on the selection sheet
- Numbers that garner public attention
On its website, Loto-Québec illustrates its findings by showing the most popular selections in Quebec for the Lotto 6/49 draw of Jan. 30, 2010.
7-14-21-28-35-42 (multiples of 7): 824 wagers
1-2-3-4-5-6 (consecutive numbers): 424 wagers
4-8-15-16-23-42 (mentioned in the TV series Lost): 377 wagers
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