The unbearable lightness of expected utility

In chapter 8 of my book, Risk Intelligence, I discuss the concept of expected utility.  To calculate the expected utility of a course of action, the first step is to estimate – separately – the probability of success, and the potential gains and losses that success and failure would entail.  Next, one does a little math, multiplying the probability of success by the potential gains, and multiplying the probability of failure by the potential losses.  Finally, we adding these two figures together to end up with the expected utility of that course of action.  After doing this for each possible action, the rational choice is to pick the action with the highest expected utility.

Expected utility is an abstract concept. It doesn’t refer to any actual win or loss: it’s the average amount you would win or lose per bet if you placed the same bet an infinite number of times. But this ethereal figure takes on an almost physical nature for the expert gambler, looming even larger in his consciousness than the actual profit or loss that hypnotises the rest of us. Expert gamblers see something different when they look at a poker table or a roulette wheel. Most people see a range of prizes; they see a single abstract figure.

This was brought home to me one night when a highly successful gambler invited me to accompany him to a casino. This particular gambler made all his money betting on horses. He shunned casinos, and only ventured in on this occasion because he wanted to give me and his other companions the thrill of seeing someone playing for high stakes. We followed him over to the craps table.

Craps is a dice game in which players place wagers on the outcome of the roll of two dice. My gambler friend proceeded to show off by placing bets of 1000 US dollars on the pass line, one after the other. A pass line bet is won immediately if the first roll is a 7 or 11. If the first roll is a 2, 3 or 12, the bet loses (this is known as “crapping out”). If the roll is any other value, it establishes a point; if that point is rolled again before a seven, the bet wins. If, with a point established, a seven is rolled before the point is re-rolled, the bet loses (“seven out”). A pass line win pays even money; in other words, my friend stood to win or lose a thousand dollars on each bet.

However, as he told me later over cocktails in the casino bar, it wasn’t this figure that was at the forefront of his mind. Instead, he just treated each bet as a bit of fun that cost him fourteen bucks. Although not a casino gambler, he was familiar enough with craps to know that the expected value of a pass line bet is -0.014. And this meant that, on average, each bet of a thousand dollars would leave him fourteen dollars less well off. The actual profit or loss at the end of an hour on the craps table could be anything from plus fifty thousand dollars to minus fifty thousand, and my friend would be aware of this figure too. But the figure that mattered most for him was the expected value of minus fourteen bucks per bet. That’s not a good-value bet, of course. Which is why, in any other circumstance, my gambler friend would never play craps.

Breaking in and sneaking over: why placehacking is risk intelligent

Would you illegally climb the Shard, Europe’s tallest building, currently unfinished, just for fun? Maybe that’s not your idea of amusement. But what if you were itching to leap over a walkway, sneak past the security guard, sprint up the Shard’s seventy internal flights of stairs and then scale an external crane ladder to possibly the best night views of London… and just couldn’t let yourself?

Would you walk past the Shard each day on your way to work and regret it forever? Blame society for making you too fearful and law-abiding? Or would you conclude that your abstaining from such behaviour was for the best? After all, scaling a ladder-like structure at the top of a crane blowing in the wind at great height with no ropes, crampons or climbing aids is not risk intelligent, right?

Or is it? Dr Bradley Garrett, urban explorer, anthropologist and geographer, scratched that itch some weeks ago and survived. While he agrees there were obvious elements of physical and legal danger, he understood the risks involved perhaps better than anyone else, for he is a professional ‘placehacker’: someone who physically trains and mentally prepares to sneak into forbidden public spaces. He is more than a tourist, however – he is an academic (his PhD thesis is titled ‘Place Hacking: Tales of Urban Exploration’) and a social campaigner. His aim, by scaling the Shard, is to demonstrate that we live in a risk-averse society under a nanny state obsessed with safety – as demonstrated by our shocked reactions. Dr Garrett argues that our natural desire to explore and wander our own neighbourhood, if not the entire world, is suppressed. The other message he can’t help but send is that the ‘most secure site outside of the Olympic Park’ is, or was, incredibly easy to break into. It makes you wonder what we are in store for with the Olympics.

Of course not everyone should take on the Shard or even something smaller. Knowing your personal limits is part of having good risk intelligence. It’s worth observing that while Dr Garrett displays formidable risk intelligence, the risks he takes are directly physical, unlike, for example, the risk of choosing which stock to buy or whether to trust a new nanny with your child. A directly physical risk carries the challenge that no matter how much analysis you’ve put in, when it comes to the actual moment of placing your body onto the single ladder at the top of the Shard, you might face instant death due to a whim in the weather or a momentary glitch in your own bodily instincts. This is a very different risk outcome from the instant ruin of your business or the death of someone close. You might go through hell and back rebuilding your business or suffer great stress through grief but we still live in an era where medicine is unlikely to save you if you fall from the Shard. If you fall, that is most probably the end of your risk-taking.

So what place do directly physical risks have in the realm of risk intelligence? Is placehacking worth potentially dying or suffering major injuries for? Our preconceptions of placehackers, Dr Garrett argues, are usually prejudiced, like the way homeless people are often taken for scavenging drunks or the way the Beat writers were considered mad for going ‘on the road’. The urban explorer is usually perceived as an angry, off-grid anarchist rebel who sees the world as a playground and life as expendable. But an intelligent and dedicated placehacker such as Dr Garrett (and he is far from being the only one) will consider whether it’s worth dying for their profession the same way a firefighter, a soldier posted to a warzone or certain types of athlete would consider it. Young US recruits who can’t afford a college education often see being drafted into the army as a career-saver. They are thinking ‘it is unlikely to happen to me’. Not only is that statistically true, it allows them to get on with the job and worry instead about making the rent, supporting their families and all the other day to day things most people worry about.

Like people who work in warzones or burning buildings, Dr Garrett’s preparation for his place-hacking is tantamount to being ‘trained’. His whole life, whether he planned it or not, has lead up to his ‘Shard moment’. Before climbing it he had broken in to the Barcelona subway system, spent five years on archaeological digs in thirteen different countries and spent three years working for the US Bureau of Land Management. Add to that his teenage skateboarding (which he pursued so fully it became a business before he sold up and switched to academia) and you have a man who is highly attuned to buildings and the societies that govern them from a viscerally anthropological perspective. He is physically embodying his intellectual ideas. We need more Garretts in the world, not less. We might not climb the Shard at night ourselves, but it’s good for our risk intelligence to know that a skater-turned-PhD can do it, survive, and have a blast. We all have our Shards.

New “risk intelligence test” is a disappointment

Imagine my surprise, last week, when I read a report announcing that researchers in Germany had created “the first quick test for establishing an individual’s risk intelligence.” After all, I created an online risk intelligence test back in 2009, and I was simply following in the tracks of many researchers before me. What was so special about the new test from Germany, I wondered.

The answer, as I soon found out, is … nothing! In fact the test doesn’t measure risk intelligence at all. To be fair, the authors of the test do not pretend that it does. They claim, instead, that the test measures what they call “risk literacy.” It seems the journalists used poetic license when they described it as a risk intelligence test.

The test is certainly quick. There are only four questions, and it takes only a couple of minutes to answer them. But the questions are the same old probability puzzles that have been the mainstay of books about risk for decades.

For example, one of the questions is as follows:

Out of 1,000 people in a small town 500 are members of a choir. Out of these 500 members in a choir 100 are men. Out of the 500 inhabitants that are not in a choir 300 are men.

 What is the probability that a randomly drawn man is a member of the choir?

Many books that purport to help people think more clearly about risk focus on such analytical puzzles. But although these puzzles can be fun to explore and their solutions are often pleasingly counterintuitive, mastering probability theory is neither necessary nor sufficient for risk intelligence. We know it is not necessary because there are people who have very high risk intelligence yet have never been acquainted with the probability calculus. And mastering probability theory is not sufficient for risk intelligence either, as is demonstrated by the existence of nerds who can crunch numbers effortlessly yet show no flair for estimating probabilities or for judging the reliability of their predictions.

Risk intelligence is not about solving probability puzzles; it is about how to make decisions when your knowledge is uncertain. Outside of some highly structured risk-taking activities, such as are found in casinos and financial markets, dealing with uncertainty is a more useful skill than probability analysis. It is also much easier to learn, primarily because it depends on common sense and simple logic rather than abstract mathematics.

It is depressing to find people still confusing these two things. The journalists who have been waxing lyrical about the German test would do well to read Agatha Christie. Fifty years ago, in The Mirror Crack’d from Side to Side, she showed her disdain for the kind of probability puzzles that the German test regurgitates, when she has Dr Haydock complain: “I can see looming ahead one of those terrible exercises in probability where six men have white hats and six men have black hats and you have to work it out by mathematics how likely it is that the hats will get mixed up and in what proportion. If you start thinking about things like that, you would go round the bend. Let me assure you of that!

Risk intelligence and negative capability

The term risk intelligence or RQ has only emerged in recent years. Although the phrase is new, however, the concept is prefigured in Keats’ idea of negative capability – how much mystery uncertainty or doubt a person can handle without getting an irritable reaction.

From a psychoanalytic perspective, these irritable reactions are the unleashed by the unconscious to protect the ego from emotional shock when it is too weak to deal with reality. Like anger, which blows out the light in the mind, these tremors also disrupt the flow of light in the mind.

This alternative reality presented by the ego then distorts the person’s ability to assess the extent of their knowledge and therefore to estimate probabilities.

It could be argued that selflessness or egolessness all else being equal should improve a persons risk intelligence. However, this is rather simplistic and misses the positive elements of high risk intelligence such as determination – not taking setbacks personally, but seeing how they can be overcome to reach the goal. 

Risk intelligence is not just about avoiding the negatives; it’s also about embracing the positives.  Risk intelligence is the new and natural arena for the bringing together and merging of numerous concepts. By drawing on both contemporary and historical approaches, we may not only to better understand astute risk takers, but will also become more astute risk takers ourselves.

Friday 13th and the “Hound of the Baskervilles effect”.

Oh dear, it’s Friday 13th today! Whether you are superstitious or not, you can’t help but notice this combination of day and date because it is so marked in cultural consciousness as being unlucky. You might not care about the number 13, black cats or any other superstition but as a risk intelligent person are you wondering whether drivers will be just a little more anxious than normal today? Or if important meetings will sour halfway through if the collective mood of the nation is punctuated with unease?

Perhaps, however, you are in China as you read this, where no one cares it’s Friday 13th. But did you notice any malaise in the ether on the fourth day of this month if you were there? Or in Japan? In Mandarin, Cantonese and Japanese the words “four” and “death” are pronounced almost identically. So despised is the number 4 in these countries that mainland Chinese omit the number 4 in designing military aircraft and some Chinese and Japanese hospitals do not list a fourth floor or number any rooms with 4. Multiply that dislike by nearly 1.5 billion people and it becomes worth asking what noteworthy effects the fear of number 4 might have. Can believing in superstition even be dangerous enough to hasten a stress-related death, such as the heart attack that kills Charles Baskerville in Sir Arthur Conan Doyle’s classic novel The Hound of the Baskervilles?

A group of Western and Chinese academics undertook research to ask precisely this question. Their objective was to determine ‘whether cardiac mortality is abnormally high on days considered unlucky’ and they did this by examining the numbers of cardiac and non-cardiac mortalities on or around the fourth of each month in groups of Chinese and Japanese people based in the US. Interestingly they found that cardiac deaths for Chinese and Japanese people peaked on the fourth of each month – the peak being particularly large for those with chronic heart disease. The study was done in the US with a non-Asian control group but the peak on the fourth of each month was particularly noticeable in California which has a high Asian and American-Asian population. Of course the number 4 itself isn’t dangerous the way a heart attack is but believing it to be gives it an indirect but quantifiable power, which is what these academics are suggesting.

The risk intelligent course of action would be to rationally acknowledge that numbers, even ones that sound like words, are just numbers and must be used as such. But to do away with superstition is to do away with deep-rooted parts of our cultural psyche, wherever we are from. Plus we may not be able to shrug them off at all. You can emigrate to a new life in the US but you can’t leave your fear of the number 4 neatly behind in China – as the cardiac statistics indicate. Also there are good traditions that would have to be thrown out if we treated all numbers the same, such as the Chinese belief that 8 is a lucky number and that cheques given as wedding gifts should contain as many eights as possible, ie £88.88. My guess is that our feelings about certain numbers are here to stay in some form or another, at least for the time being. Just don’t put a 4 on the cheque you give your Chinese friend on their wedding day.