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Updated December 8, 2013

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December 8, 2013 update:
The $1 million guaranteed prize was won in Alberta for the December 7 Lotto 649 draw ending the 23-draw losing streak for the Western Canada region.

December 6, 2013 update:
Turns out Western Canada accounts for about 17.1% of national sales for the Lotto 649 game - not as much as the 17.9% assumption based on population. The 17.1% figure was reported by Western Canada Lottery Corporation in response to an inquiry on Lotto 649 sales since the launch of the $3 version of the game. Using the 17.1% number, the probability of no $1 million guaranteed prize winner in the Western Canada region in 23 draws is 1.34%.


Statistical Anomaly or Programming Error?
Nov 24, 2013

With the launch of the $3 Lotto 649 game, a guaranteed $1 million prize is awarded with every draw. With every ticket sold, a unique 10-digit number is printed along with the selection of 6 Lotto 649 numbers. After the regular Lotto 649 draw, a computer is used to select one, and only one, winning 10-digit number.

The draws are held in Toronto and the collection of the 10 digit numbers come from the 5 lottery regions across Canada. Before the winning 10-digit number is selected, all the numbers that were sold across Canada are sent to the Interprovincial Lottery office in Toronto.

One would expect, over time, winning tickets would come from all regions in Canada with the highest numbers in the most populous regions. But the distribution is not quite as even as expected and there appears to be a statistical anomaly.

As of November 24, there have been 20 Lotto 649 draws. The $1 million guaranteed prizes have been won in all regions except one - Western Canada. To calculate the probability of no winning tickets being awarded to Western Canada in 20 draws, a basic assumption has to be made - that is, Lotto 649 tickets sales are evenly distributed across Canada on a per capita basis. That is, since Ontario has 38.4% of the population, then Ontario accounts for about 38.4% of Lotto 649 sales and approximately 38.4% of the winning tickets.

The Western Canada region includes Alberta, Saskatchewan, Manitoba and the 3 territories and represents 17.9% of Canada's population as of the 2011 census. If one assumes that 17.9% of Lotto 649 sales occur in the Western Canada region, then the probability of no winning $1 million tickets being selected in 20 draws is 1.9%. To put that number in perspective, the odds of correctly guessing a single random card from a 52-card deck is 1.9%.

This is not to say an event that has a 1.9% probability of occurring will never happen. But this situation is somewhat curious since every Lotto 649 draw to date is being used to calculate the probability. That is, there has not been a single winning ticket from Western Canada and it is possible there is another reason for the statistical anomaly - a programming error.

Picking a single 10-digit number from the complete set of numbers sold is not a trivial programming task. If all the numbers were consecutive, it would be relatively easy. But since the numbers are sold all across Canada using 5 separate and independent central computers, there are gaps. The first digit indicates the region in which the ticket was sold (0 & 1 for BC, 2 & 3 for Western, 4 & 5 for Ontario, 6 & 7 for Quebec, 8 & 9 for Atlantic). The last 2 digits indicate the number of selections purchased on a ticket. A customer who purchases a single Lotto 649 selection on a ticket always have a 10 digit number ending in "01." If the ticket contains multiple selections, the player receives multiple 10 digit numbers - the first eight digits are the same for all entries; the two-digit number following the hyphen starts at 01, and increases by one for each additional selection on the ticket.

Creating a computer program to randomly select a single 10-digit number from a set of numbers that are not consecutive is not trivial. On the other hand, it is not extremely difficult and a skilled programmer should be able to accomplish the task and a skilled testing team should be able to determine the program works accurately.

Nonetheless, there are thousands of real world examples where much easier programming tasks have been implemented with flaws. One would counter that most programs do not go through the same rigor that occurs for lottery programs. That is certainly true but there have been a number of cases where flaws in lottery programs slipped though the testing process and were implemented. Some examples are described below.

So the question remains. Does the fact there have been no winners in the Western Canada region of the $1 million guaranteed prize a statistical anomaly or does a programming error exist in the selection process making it impossible for any ticket that begins with the number 2 or 3 to win?

The following are some examples of computer programming errors involving lottery corporations in the US and Canada.

The Kansas Lottery encountered a problem in December 2005, when the winning numbers announced for the Pick 3 game were identical three nights in row. By the third night, so many people picked the apparently lucky number that the lottery had to pay out nearly twice what it made in ticket sales. Officials determined that a computer problem caused the repetition. They offered coupons for free tickets to players who bought losing tickets for the three games.

In July 2007, the Tennessee Education Lottery replaced its mechanical draws using numbered ping pong balls with a computer to generate random numbers. For the next three weeks, each winning number contained no two digits alike, which appeared to defy probability. Lottery officials said a vendor had inadvertently programmed the computer not to duplicate any numbers. They offered a double refund to all players who picked numbers that couldn't win, provided they saved their losing tickets.

In July 2008, Kansas lottery officials said another problem had occurred, resulting in three winning numbers in the Pick 3 game being incorrectly reported. Players were allowed to collect prizes for both the correct numbers and the numbers reported in error.

In October 2008, the Virginia Lottery experienced a computer error. The error caused the incorrect printing of 609 winning tickets each worth $7,777 - a total value of close to $5 million. Virginal lottery officials reported the programming error was made by an employee at GTECH. At the time, GTECH was the largest lottery technology company in the world and had contracts with 27 state lotteries and a 70 percent market share worldwide.

In May 2012, Illinois Lottery officials discovered a computer error was producing duplicate tickets. A lottery spokesman reported the error occurred after new software was being uploaded to the quick-pick machines. About 3,000 tickets were affected by the error. In August 2013, the Arizona Lottery discovered there was an issue in the Pick 3 programming code that prevented the numbers eight and nine from being drawn in certain positions between June 10 and August 3. This error resulted in 92.3 percent of tickets purchased having a better chance to win, and caused 7.7 percent to have no chance of winning. Unfortunately, the lottery only provided replacement tickets for those players who kept the original tickets purchase. For many people who commonly discard losing lottery tickets, there was no remedy for the tickets they purchased without any chance of winning.

In September 2013, Western Canadian Lottery Corporation advised customers to recheck their tickets following a computer problem. Officials said a delay in the draw results may mean that winning tickets weren't correctly identified. Results were not released until 10:35 in the morning after the draw instead of releasing the results as soon as stores were open and able to redeem tickets.