“Tails you win: the science of chance”, a Wingspan Productions programme for BBC Four, presented by Professor David Spiegelhalter, Winton Professor of the Public Understanding of Risk, Cambridge University was broadcast on 18 October.
‘Tails you win’ tracked chance back to its roots. In the 1500s, when trying to crack the secrets of gambling, Dr Cardano found that the results of dice rolling can be seen as fractions. In the late 1600s Edmund Halley‘s analysis of data on the ages at which people died found that as we get older we are more likely to die. At the time, people thought death was a strange mystical happening that befell people at any age (as all statisticians know – there is valuable information in data!).
We went on a journey around the mysterious workings of chance in our lives, stopping off to look in on related mathematical and statistical concepts: chance, probability, risk, randomness and uncertainty.
The old adage ‘if you can’t beat them, join them’ seems to apply to our dealings with chance. We fear it “when chance seems cruel some call it fate”, we can be thrilled by it “when chance is kind we call it luck”. Others try to deny its existence (until they are proven wrong) but overall, we have befriended chance, and we have begun to learn how to turn blind uncertainty into computable probability. But there is still more to learn.
So, can understanding chance help us to gauge risks, make us safer, more efficient and maybe even less risk-averse (or at least less averse to taking a calculated risk)?. In brief, yes.
We enjoy trying to beat chance in gambling or in investments. The programme looked at both Premium Bonds, an example of the 1950s British public putting its faith in random selection of bond numbers, and our current National Lottery.
We use our understanding of probability to make our lives ‘safer’ and more efficient, e.g. attempts to earthquake proof San Francisco, predict the weather, plot the future economy. But somehow we know that we can only get so far. We can predict probabilities within a given, often broad range with built-in uncertainty but even with the best know-how, we can’t engineer chance out of system and are never 100% certain.
So why do we struggle with concepts of randomness and uncertainty? and see coincidences as spooky when they can often be explained and ’quantified’ ? well, we seem to be hard wired to see patterns and don’t easily accept that we are not in control of the world we live in. This need to see patterns has, however, enabled us to understand chance better. We learnt that even chaotic randomness has structures, rules and patterns. It has its’s own shape too. National lottery draws generate prize winning numbers randomly, but in plotting the frequency with which numbers arise, you can see that they fit a bell-shaped curve. And yet, remain entirely unpredictable.
David took risks. Whilst punting on the River Cam (probability of falling in whilst punting 1/200 or 0.005/0.5%), he explained that, as a mathematician (and a chartered statistician), it is his job to use the mathematics of chance to calculate probabilities even on things which seem chaotic and unpredictable. Later, he took what he termed a rational risk: a skydive.
Having a measured sense of risks, including the risk of death can, he argued, make you less risk averse. And perhaps it makes more sense to take risks as you get older. After all, we are all doing a deal with chance every day via the lifestyle, health and risk-taking choices we make.
The best way to compare the risk attached to experiences is to use a ‘cheery little unit’ called a micromort, something he developed to explain the risk of death. A micromort is a 1 in 1,000,000 chance of death, for example. for every day that we are 5 kg over weight or drink 3 beers, or smoke 2 cigarettes a day we smoke, we can expect to lose half an hour of life. And so, he rationalised that. given a 7,000 micromorts risk of a 58-year old man dying on any given day anyway, what’s an extra 7 micromorts for a skydive (much the same risk as running a Marathon or going 40 miles on a motorbike). Go David.
As the programme continued, it felt as though we had befriended chance and our minds had been opened to new ways of thinking about everything…from the workings of the universe and our own everyday experience such as whether to carry an umbrella.
We learnt that the applications of probability are leading to new approaches in new areas all the time. What statisticians term the Monte Carlo Method, something akin to rolling a dice over and over again, until you have a substantial set of possible variations on the future, is being used in many different spheres and sectors. During the Cold War, the Los Alamos physicsts used it to develop a nuclear bomb. To find out when an atomic chain reaction might occur, they chose an outcome at random and calculated what the result would be…then another, each time, calculating a new result until they had hundreds of different but equally likely results …and combining them all, they got a likely picture of what would happen. The outcome? their bomb did, in fact, work.
This ability to look at an array of possible futures to compute problems, is being used in a number of areas, not least in meteorology where precise deterministic forecasts are becoming a thing of the past. Meteorologists know that small errors at the beginning of a forecast can grow into huge differences within a matter of a few days and so they forecast using probabilities. Professor Palmer and colleagues at the European Centre for Medium-term Weather Forecasts in Reading compute 50 different 3-day forecasts – 50 different futures – each with slightly varying starting points to reflect the uncertainty involved. Whilst they might all indicate the same direction of winds, they might indicate different strengths. Over 50 possible futures, 30% of them may suggest rain.
In Britain the forecasts we see don’t yet incorporate this information. But it sounds as though things might be changing and that, in future we may all need to develop a new relationship with uncertainty. Saying that there is a 30% chance of rain might sound like weather forecasters will be hedging their bets. But can we really demand certainty from our weather forecasters (think back to Michael Fish’s deterministic weather forecast of the UK storms in 1987) and is it not better to quantify the weather’s uncertainty in a more precise way. As David says “Better a reliable probability than a wrong prediction”.
Ultimately, we learnt that the world is too complex to fully control. Revealing his inner-philosopher, David advised us that “uncertainty is an essential part of being alive”. And so, we cannot blame banks and weather forecasters for not anticipating the meltdown of the economy or devastating storms… the fault, if there is one, is in the nature of chance. There is no use in looking for absolute certainties…we can never rely on 100% predictions. Putting numbers on chance is a good way of getting a handle on the future….but things are only as good as the numbers we have to hand.
For a programme that was filmed in the Winter and included some quasi-Gothic scenes, including a graveyard at night, David’s wit and the subject matter shone brightly throughout, Lots of interesting odds were dispersed throughout and the programme was liberally injected with a humour and accessibility which made a difficult subject seem easy. Thanks Wingspan, thanks David and thanks BBC Four. We loved ‘Tails you win…’.