Sunday, January 28, 2007

Do you want to win the Lotto 6/49? Better brush up on your stats. Ok, I’ll do it for you.

One evening this week I was stuck at work babysitting a contractor, and when I ran out of work things to do my thoughts turned to dreams of winning the lottery. It might help if I actually played, but I know the odds are stacked heavily against me, and I pay enough in taxes as it is.

I recently read a book about the MIT blackjack team who, in their heyday, frequently fleeced Las Vegas casinos through a complex system of card counting, statistics and codes. When I went to university (Acadia is roughly the Canadian equivalent to MIT), I was forced to take a few stats courses that I was sure would never come in handy. Recently I got to refresh my knowledge while helping Joan through the last course in her masters program, econometrics. I decided I would finally apply my stats knowledge to something productive, analyzing all the draws in the 6/49 ever to see which numbers come up most often, and if they are statistically significant.

I found on the BC Lotto Corporation website that I could download the results of all draws since the very first 6/49 draw in 1982. There have been 2402 draws in total, up to last nights (January 27, 2007). I pasted these numbers into a table in Excel and then used a countif function to ascertain how many times each of the numbers has been drawn. The average number has been drawn just over 343 times in the 25 years of 6/49 draws. Now comes the fun part, are there numbers that come up more often? (Excel required to view this link)

The standard deviation of occurrences of numbers in draws is very close to a whopping 20, indicating a pretty wide spread in what is supposed to be a purely random process. I used Excel to tell me which numbers appeared more than 1 standard deviation from average. There were 7 numbers (27, 31, 34, 43, 45, 46, 47) that appeared more than 1 standard deviation from average. Nothing too exciting here, but what if we go out 2 standard deviations, 40 more occurrences than average? There are 4 numbers (31, 34, 43, 47) that fall into this category. Kind of makes you wonder if some of those balls are a little heavier than others?

So then I took the 4 number that seem to come up most often and paired them up with 2 of the 3 numbers that come up next most often. I found that over the years these numbers would have paid out in 60 draws, or about 2.5% of the time. Sadly if you had played these numbers twice a week since 1982 you would still not be a millionaire. Despite the fact that they come up more often than others, the 4 numbers that occur more than 2 standard deviations from average have never appeared together in the same draw. Further analysis shows that playing these numbers in every draw is most likely to net you only $10 or $50 when you win. If you play every draw in the year and win 2.5% of the time with my scheme you will likely win about $45/year. It will cost you $208 to win that $45 though, so you may be better off putting that cash in your savings account. That being said, it is only a matter of time before the stars align, and all these significant digits show up in the same draw, and you would be an instant millionaire. If you apply my stats and win, please give me a cut.


Sharon B said...

Do you know how many people have become millionaires through Lotto 6/49? Or how many have even won over a hundred thousand dollars? Because they hit the numbers bang on!! It's mind-boggling that with such low odds of winning, and with so many possible combinations of numbers, people still win!!! That's what keeps people buying tickets - if they really thought of the low odds of winning, they wouldn't bother - I agree with you - if you keep buying lottery tickets and not winning (as most people do) you are really just paying more taxes than the rest of us who are already forking out more than our fair share to Revenue Canada :)

7:20 PM, February 06, 2007  
Anonymous said...

Acadia is roughly the Canadian equivalent to MIT

Acadia is Canada's 'arsenal of brains'???

4:43 AM, February 11, 2007  
sharon b said...

You KNOW it, Anonymous! We're just very modest :)
Signed, Acadia Grad.

2:24 PM, February 11, 2007  

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