Editor of the Royal Statistical Society's Significance magazine
Could a computer programme predict who will win Euro 2004?
It may be an evolutionary advantage to be able to spot patterns, but often we could be fooled into looking for something that isn't really there.
Imagine. It's Sunday night in front of the big game.
One - nil to England going into extra time.
I'm on the edge of my seat. If my husband wasn't tee total he'd be on his eighth bottle of lager. An England victory in sight and even I - you'll have noticed the accent - can't resist the tide of hope and excitement.
Three minutes left to play, who can predict the result?
Well, actually, you may not believe it, but me. I can and I have.
I have similarly predicted the result of England v Switzerland and England v Croatia.
You see, I've devised a computer program, based on complex statistical algorithms, which is 100% accurate every time, and I'm willing to sell one of a limited number of copies to you for the modest sum of £1000.
Just think how easily you could win it back. To prove it, I'll send you one free prediction every week for the next five weeks, and when you see I'm 100% accurate I can guarantee you'll be praying there is still a copy of the program left.
Imagine you received this email from me at the start of Euro 2004. Would you have taken up my offer?
Of course not. But what if I got it right, not once, but five times in a row? Tempted now?
If you say yes, you've just thrown away £1,000. Because there is no software, no statistical method. In fact, there isn't even luck. Just quantity.
What you don't know is that I emailed a million people.
I split them into three groups, told one group that one team would win, one group that the other team would win, and the third that the match would be drawn.
Afterwards, I ignored the two-thirds I'd got wrong, and sent new predictions to the third of a million I got right. After game 2, one third of those people have had two correct predictions. I stick with these and ignore the failures.
After game 3, we're down by two thirds again, and the same after game 4, but after game 5 there are still around 4,000 people who've received only correct predictions.
But these 4,000 are dead impressed! And if even only a few percent decide to pay up, I'll make around £100,000!
Why would anyone fall for such a scam?
If you're congratulating yourself for resisting, I'm afraid the fact is that we fall for similar things all the time, victim not of fraud, but our own perceptions.
We notice the one extraordinary event, the occasional collision, but not the hundreds of thousands of near-misses
Think about the times you've been impressed by astounding coincidences, without stopping to think just how many opportunities for coincidence there are in each of our lives?
We notice the one extraordinary event, the occasional collision, but not the hundreds of thousands of near-misses. Those near misses are like the emails I sent that were wrong. You don't think about them. And so instinct tells us the hits must mean something. But our instinct is wrong.
One reason why is that we seem to be constituted to find patterns in things. And there was a pretty impressive pattern here - our readiness to believe perhaps encouraged by greed.
We've evolved to be noticing animals. Every observation contains an opportunity: maybe a new source of food, early warning of a predator, or just some regularity or change we could exploit.
We notice first and reason later - if ever. The result is that we are biased in favour of something rather than nothing, pattern rather than randomness, certainty rather than uncertainty, predator in the bushes rather than random pattern of leaves and shadows. And when we see a pattern, we intuit a cause, we think there's something here for us.
We've evolved to be quick to jump to conclusions, quick to spot - even invent - patterns.
What if you shuffled a pack of cards thoroughly and turned over the top 10 cards and they were all red? What if you tossed a coin ten times and got 8 heads? What would you expect to get if you tossed again? Or is your head just spinning?
We're easily bamboozled by randomness, chance and coincidence because we didn't evolve to be good at probability.
But if we're to understand the challenges of today's world, there are times when we need to check our instinct with something else.
And sometimes what that extra something amounts to is that we also need to count.
More or Less was broadcast on Thursday, 17 June 2004, at 1500 BST on BBC Radio 4.