I suppose that mathematics is not everyone’s favourite subject, and I suppose a vast number of people consumed enough about it at school to pass exams and use an even smaller amount in their daily lives. However, it struck me the other night, whilst watching my numbers tumble around in the big glass ball and not get drawn to make me an instant millionaire in this week’s draw, that the two concepts of probability and statistics are so mistakenly confused.
The announcer gave each number as it was drawn and then went on to tell me how many weeks it had been since it was last drawn and how many times it had been drawn in total. I had visions of dedicated lottery players digesting this information, maybe even cataloging it so that they could make the best estimate of the likelihood of a certain draw next week. Except of course that this is flawed.
I said to my partner, “that’s it, we’ll just pick 1,2,3,4,5,6 next week.” Of course the instant reply was “hmph .. how likely is that. “6,776,934,060 to 1, was my instant reply”. Well, ok I had to work it out but you get the point. Oddly enough exactly the same odds as 34,12,7,40,2,16. I wasn’t done yet.
“Even if we win we’ll just keep playing those numbers forever”.
“But if we win with 1,2,3,4,5,6, they’ll never come up again”.
Another common mistake. Of course the likelihood of 1,2,3,4,5,6 coming up twice in two draws is exactly the same as any set of six numbers being drawn twice in two weeks; or in fact any two different sets of numbers being drawn in two weeks.
The probabilities are the same. Statistically over time you can look back and say it doesn’t happen very often, in fact it may never have happened, but that’s a completely different analysis.
I used to run a lottery syndicate where I worked and there were about 6 of us that picked six numbers each and we played those six games, each chipping in a pound each week. If any game won we split the winnings. Most people picked favourite numbers, birthdays etc, but one guy picked all of his numbers between 31 and 40. When I asked him why he said that if they came up there would be few winners because there aren’t any birthdays in that range. And of course he’s right.
Finally just to give a real world example, I worked in a shop in Australia and my boss (the general manager) and his boss (the managing director) used to play each week. One week the GM forgot to put the numbers in and, yes you guessed it, their numbers came up. They missed out on about 3.5 million Australian dollars and to make matters worse, no one won that week so they would have swept the lot. Needless to say the mood was grim.
After a few weeks they got back on speaking terms and decided they would start playing again. The GM says “same numbers”. The MD replies “hmph, they’ll never come up again. We’ll pick some new ones”.
And yes, they missed again as their old numbers returned within a matter of months. A couple of million missed that time. The GM resigned and to the best of my knowledge they never spoke again.
Now I should qualify that they were playing a systems entry where they picked 9 numbers and hoped for six to come up, but the point was that they got 6 numbers from 9 twice in 8 weeks. What’s the probability of that? Exactly the same as any other two winning combinations, same numbers or different.
Statistically, how often does it happen? And no the answer isn’t every 8 weeks :)