# Norwegian family astounded by third lottery win

Every time Hege Oksnes has a child, someone in her family wins the lottery. The odds against this are daunting – are these million dollar babies? Or is there another explanation?

The probability of winning the Norwegian lottery is roughly one in five million. If you bought a ticket once a week for the next hundred thousand years (that’s almost as long as modern humans have existed), you could reasonably expect to win precisely once.

So this week, when Tord Oksnes became the third member of his family to hit the jackpot in just six years, his reaction was total disbelief. If picking one winner is so desperately unlikely, what could possibly explain three?

The family themselves superstitiously point out that every victory has coincided with the birth of an Oksnes child. And given the odds reported in some newspapers, it would be tempting to agree. The probability of choosing the right combination of numbers three times in a row, some calculate, is one in five million cubed – a mind boggling 125 million trillion to one (or, as most would say, ‘impossible’).

Luckily for rationalists, this is the wrong calculation to make. They did not win three times in three attempts, but over a period of years in which several family members bought regular tickets. But while this makes the odds considerably shorter, the case is still one of the most remarkable in gambling history.

Many find it hard to believe that such events can be explained by chance alone. But eye-catching strokes of luck are actually fairly common. Just this week, for instance, a British man won over £100,000 in the lottery for the second time this year.

The logic behind freak events can be understood using dice. The probability of rolling ten sixes in a row on a six-sided die is about one in sixty million. If we rolled the die ten thousand times, seeing that combination at some point would be much more likely – though still surprising.

But what if, instead of looking for sixes, we simply scan the numbers for interesting patterns? Ten consecutive sixes, nine consecutive ones or a series in which dice seem to repeatedly count to six: countless such sequences might be randomly generated. The vast majority will not; but we do not tend to notice that. We simply note the patterns that do exist, and treat them as weird coincidences – even though we are practically guaranteed to find some striking sequence.

And this is just how it works in reality. In a world full of outlandish possibilities, bizarre coincidences are positively certain to occur.

## A world of possibilities

So behind every fantastical event lies the impersonal churning of probabilities. For some, that simply robs the world of its magic.

But as statisticians object, these events are still spectacularly unusual. The fact that they occur at all should make us marvel at the dazzling wealth and variety of possibilities that our world has to offer.

## You Decide

1. Given that it is very close to certain that you will never win, is there any good reason to play the lottery?
2. Does statistics deprive the world of mystery and marvel?

## Activities

1. a) What is the probability of flipping a coin five times and getting only heads? b) If you last four flips have been tails, what is a probability that the next flip will be the same?
2. A famous puzzle: imagine a quiz show in which you must choose between three closed boxes. Two are empty, one contains a fabulous prize. You pick one box, and the host (who knows where the prize is) opens one of the others to reveal that it is empty. You now have a chance to change your choice. Do you stick, or switch?

## Some People Say...

“The lottery is a tax on the stupid.”

What do you think?

## Q & A

Is the lottery worthwhile?
Some people do it for the thrill, or to feed a fantasy of winning. But if you want to make a rational investment, the lottery is not it. To be confident of winning, you’d have to spend far more than you will gain.
Okay. Does this kind of probability have any other useful applications?
Oh, thousands. Several years ago a woman was convicted of murdering her two children based on a simple misunderstanding of statistics. She was saved by the intervention of academics. In World War Two Britain spent huge amounts of time and money investigating why German planes were heavily bombing particular residential areas – until a great mathematician wrote a paper explaining that these ‘clusters’ were exactly what a random distribution of bombs should produce.

## Word Watch

One in five million
(Or 0.00002%). There are 34 numbers available and players must pick seven. The formula for calculating this probability is (7!27!)/34!, where ‘!’ is an instruction to multiply the number before it by every lower number down to one. 5!, for instance, is 5x4x3x2x1, or 120.
One in five million cubed
Winning the lottery once has no effect on the likelihood of it happening again. That makes these two events ‘independent’. When calculating the probability of two or more independent events, you multiply them together. In this case, that is 5 million times five million times five million – or five million cubed.
Considerably shorter
With so many different variables, this calculation is unbelievably complicated. Professional mathematicians are currently on the case of working it out, but so far no figure is available.
Randomly generated
Genuine randomness is actually very hard for humans to recognise, because it throws up far more ‘coincidences’ than most people expect. On early iPods, for instance, the ‘shuffle’ function used a method that produced a truly random sequence; but when the results clustered around certain bands or genres, so many users were convinced that Apple were picking favourites that the company altered the function to produce a more even distribution of songs.