On Random Numbers

The nation of South Africa has gone completely tonto after its weekly national lottery drawing, sparking an investigation and widespread allegations of fraud. Why? The winning numbers were 5, 6, 7, 8 and 9 and the powerball turned out to be... you guessed it: 10. Twenty people won 5.7 million rand and another six dozen - who had the numbers 5-9 but for some reason failed to guess the powerball - pocketed a few thousand.

Hmm... fishy? Nope. Absolutely 100% ordinary.

Counterintuitive as it may seem when you're glued to a TV screen watching a machine juggle dozens of numbered balls until you're dizzy, there's no reason why that particular sequence of numbers shouldn't come up. Yes, it's fantastically unlikely - but that's the whole point of lotteries. It would be just as fantastically unlikely if the numbers had been, say, 6, 11, 25, 29, 36 and 44. Or any other six-number combination. This one only seems suspicious because of the way we deal with numbers.

When you, I or everyone else except perhaps some odd savant Rain Man-type people tackle numbers, we organize them in our heads into ascending order: 1, 2, 3 etc. There's no law of nature that dictates we have to do this: it's just for convenience. We're pattern-seeking animals and the sequence 1, 2, 3... is an easy pattern to keep track of. It's the way we were taught to count at school. Rain Person, on the other hand, who thinks of school as a big box-shaped building where people talk about things that make no sense but you get a sandwich part way through the day, might count 15, 3, 77, 268, 29, 4,000,000,002... and he or she wouldn't be wrong.

Maybe it helps if you look at it this way: lottery balls aren't actually numbers. They're balls with symbols written on them. The symbols happen to be numbers - again, for convenience - but they could just as easily be like the ones you get when you use the shift key and the top row of your keyboard. You wouldn't think it the slightest bit dubious if your lottery picks were %, ^, &, *, (, ) and then the machine drew the balls marked %, ^, &, *, (, ). Mind you, you might find the drawing on TV a bit bewildering because, as we've established, your brain is trained to think in terms of numbers, not special characters.

Aha, you say, but if all this is just random, how come there were so many winners? Well, that one's simple. Plenty of lottery players just pick an ascending series of numbers, either because they're lazy or because they're just as shrewd as anyone who plays the lottery - i.e. not very - and they figure, correctly, that those ones are as likely to come up as any others. In this case, 20 South Africans happen to have picked 5, 6, 7, 8, 9 and 10. As for the 79 who didn't get the powerball, they probably had 4, 5, 6, 7, 8, 9 or they chose some other bonus number. For what reason I don't know. Maybe a number that had some sort of personal significance, because why not. If you're still not convinced, may I draw your attention to an example from the early days of the United Kingdom's national lottery. On 14th January 1995, 133 players all picked the winning six numbers. Let's convert that into different symbols for emphasis - one hundred and thirty-three. The numbers that week were 7, 17, 23, 32, 38 and 42. Knock yourself out to try to discover some pattern or special significance to that sequence if you like: you won't find one. 133 people just happened to pick those numbers that week and those just happened to be the ones that were drawn.

No, still not sketchy. I guarantee you that in many, many other weekly drawings in many, many lotteries, hundreds of players have picked the same six numbers that were not drawn. Those 133 Brits didn't have any inside information. They just got lucky.

Or maybe not all that lucky, considering they had to divide the jackpot equally between them and ended up walking away with a bit over a hundred thousand quid each.

Can you believe it? I'm sure they all said to each other. I mean, shoot. What are the chances?