With odds like these the money's in the bag

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was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

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I wish it would rain, and then I could be rich. Well, not really rich, but at least win £10 in the rain-forecasting competition currently being run by a Walkers Crisps. For those not yet addicted, you enter a code found on each packet of crisps onto a website which allows you to choose one of 21,000 2km by 2km squares covering Great Britain and Ireland where you think it will rain over the next couple of days. If it rains in your square in your chosen 3-hour period then you get £10.

My partner and I have become obsessed with this competition, especially since we won £30 between us last week. Only one bet a day is allowed and so nobody is going to win a packet. But Walkers have so far given away around £430,000 based on 360,000 bets. These are good odds: around 1 in 8 entries is winning £10, and so an entry has an expected return of £1.20 while a packet of crisps is only about 40p. So let’s hope that Walkers have done their risk assessment and even a wet November will not mean a repeat of Hoover’s disastrous 1992 free flight offer that ended up costing them £50 million.

I was at first surprised that the first squares to go are in the English cities, which is where people live rather than where it rains – southern Ireland is always the last area to be picked, even though in my experience it suffers an almost continuous downpour. Then I realised that this picking of familiar areas might be an example of what is known in psychology as the ‘availability heuristic’, which is a fancy scientific way of saying that people judge events as more likely if they can easily conjure up images of them occurring, regardless of the real odds. Which is fine by me, as it improves the chances of finding a good square for those of us who are willing to use the Met Office forecast.

Of course another explanation is that nobody trusts the Met Office, which has tended to get a bad press after last year’s unfortunate ‘barbecue summer’ claim. What was forgotten in the subsequent July deluge was that the forecast only claimed a 65% chance of above-average temperatures and below-average rain, and the first prediction turned out to be correct. But the media coverage put the dampers on seasonal forecasts, now abandoned.

But it’s exactly such numerical chances that I could do with to improve my odds of winning. The Met Office does produce probabilities for rain over the next few days, which they sell to their corporate customers but unlike in the US are not currently handed out to ordinary mortal consumers. One of the problems is how to communicate uncertainty about future weather – should it be through language (‘might be a hurricane’) or numbers (‘30% chance of snow’) or charts and pictures? People vary hugely as to what the want and what they understand, and so there is no single answer.

Meanwhile at home we spend hours discussing strategy. Is it best to bet before 8am on, say, Monday, when you can use the latest forecast to predict for Tuesday but when most of the squares have gone, or wait until after 8am when you can bet on Wednesday or Thursday, which gives you more choice but a less accurate forecast? We cackle with glee when the Met Office predicts a huge bank of rain coming in over the west coast, gloating as we pick a juicy square in the middle of the sodden Welsh countryside.

The returns are even greater if you don’t buy the crisps in the first place. My partner does not even like the things and so finds her entry codes by searching the gutters and rummaging through bins for packets by the non-obsessed. At the weekend we stood on a platform transfixed as a child solemnly shovelled cheese-and-onion crisps into his mouth, waiting for the delicious moment when he would fling the empty packet onto the platform, behaviour that would until recently have driven me into a rage. But no, his nice neat mother tucked it into her bag. We suspected that beneath her smug civilised exterior she was planning to use it to feed her gambling addiction, and all at the expense of her innocent child’s future health. Perhaps the Met Office will get blamed for that too.