Statistical risk assessment

By Prof. Christian Hesse and Frederic Friedel

As described in part one of this series, we will try to assess the risk of playing chess using a unit developed by Ronald Howard in the 1970s. It is called micromort – 'micro' stands for one millionth, and 'mort' is the French word for death. So one micromort is one millionth statistical death. If a million people are exposed to a risk of this size, then on the average one of them will die. Statisticians and mathematicians use the micromort to quantify the concept of risk. 

In terms of understanding this tiny portion of risk, it is better to break it down to the level of a single person: one micromort is the risk of a 25-year-old male in Central Europe of getting up in the morning and not surviving the day, for whatever reason. That happens to one in a million 25-year-olds. For 25-year old women the risk is slightly lower. And in other parts of the world it is different too – slightly higher or lower, depending on where you are.

This daily risk for a 25-year-old male in Central Europe doubles every seven years. At the age of 32 it is two micromort, at age 39 it is four micromort. At age 60 it is roughly 30 micromort. At 90, you are facing 500 micromort and at age 100, you have 1500 micromort against you, every day. Interestingly, that is almost exactly the risk that a newborn baby faces the very first day of its life (again in Central Europe). If the newborn survives this first day, then the risk drops dramatically at first, and then more slowly, until it reaches a minimum of a quarter of a micromort at age ten. After that age, it starts to rise again.

You can also measure the risk of certain activities on the micromort scale in a data-based fashion. Smoking three cigarettes adds one micromort to your daily risk. And smoking 30 cigarettes daily for 40 years shortens your life expectancy on the average by about ten years. If you break down the statistics of cigarettes to a single cigarette, then every cigarette shortens your life by about 10 minutes. So with 30 cigarettes a day over 40 years starting at age 17 you move your life expectancy to where it was in the last century.

Today the global life expectancy averaged over the world population is 73.2 years according to WHO data. That is an enormous 25% increase from 1975 when it was only 59 years globally. In Africa an increase of almost 25% was even achieved between the years 2000 and 2023.

Statistically, the following activities increase your risk by one micromort:

• Air travel for 7000 miles
• Travel by train for 6000 miles
• Driving a car for 300 miles
• Riding a motorcycle for 25 miles
• Riding a bike for 10 miles
• Spending 3 hours in a coal mine
• Drinking Miami water for one year
• Living within 20 miles of a nuclear reactor for 15 years
• Eating 100 charcoal-broiled steaks

Other risks that lead to an increase in the micromort score are:

• Running a marathon: 8 micromort
• Parachuting (per jump): 7 micromort
• BASE jumping (per jump): 430 micromort
• Giving birth by Caesarean section: 170 micromort
• Having a bypass operation: 16.000 micromort
• Climbing Matterhorn: 2840 micromort
• Attempting to ascent Mount Everest: 38.000 micromort
• Marrying Henry the VIII : 500.000 micromort

So in terms of micromort, how dangerous is a game of chess?

Since we do not want to merely do some guesswork, but use a statistical model as well as data for a data-based approximation, we first focus on grandmaster games. We do this because the best data for our purposes are available for “slow” grandmaster games. No bullet, rapid, blitz or internet games are considered, but only those with long time controls. Let us assume that such games have an average length of four hours.

Furthermore, in 1950 there were 27 grandmasters, currently there are 2065 grandmasters. Let us assume that the increase in the number of grandmasters over these 75 years was linear rather than polynomial or exponential.

Let us further assume that most GMs play between 50 and a 100 slow games per year and hence take the midpoint of 75 as the average number of slow games played by GMs per year. Let us also assume that this average of 75 slow games per year for an average GM is valid over the entire period of 75 years from 1950 until 2024.

And finally, let us assume that 90 percent of the games that a GM plays are against other GMs and only ten percent against IMs or lesser rated players.

For a layperson these seem to be a lot of assumptions, each one of which is error-prone and hence will be off by a certain amount. And some might even be off by a large amount. Hence one could be led to think that the computations based on all of these inaccurate assumptions will be even more inaccurate in view of error-propagation with error-intensification or even error-explosion.

This, however, will not the case, since some of the given estimates underestimate the true value and others are likely to overestimate them. Hence, most likely there will not be an error-superposition but an error-compensation and error-reduction. 

We assume that there were five Grandmasters having died during a game of chess (or the aftermath), namely, Bogoljubow, Simagin, Purdy, Bagirow, Gipslis, all of which died by a heart attack or a stroke during a game or shortly thereafter. With these assumptions the risk of a GM playing a slow game and dying comes out to 0.9 micromort which we round to 1 micromort.

We compare this to the risk of the general public to die of a heart attack or stroke. For Germany, this risk is 2.4 micromort per day. For the entire population of the European Union, it is 6.6 micromort. For the US-population it is only 1.9 micromort.

Assuming furthermore that for an International Master and even for amateur players, the emotional and hence also the physical strain on the body (especially the heart and the brain) during a slow game is roughly comparable to that of GMs, one might take this risk approximation of 1 micromort also for non-GM chess players. At least we can assume it is probably not larger than that.

Put differently, one may conclude for Germany and the US that the risk of dying from heart attack or stroke induced by a slow game of chess is less than half compared to spending the corresponding time not at the chess board, but living an average day with its corresponding everyday risks for heart attack and stroke. So in this respect chess is good for us and clearly risk-reducing.

In the third part of this series we will examine how playing the game of chess regularly will affect your life expectancy. We also speculate how the statistical results we obtain might explained by factors that are present in chess players as opposed to a non-chess population.

Christian Hesse holds a Ph.D. from Harvard University and was on the faculty of the University of California at Berkeley until 1991. Since then he is Professor of Mathematics at the University of Stuttgart (Germany). Subsequently he has been a visiting researcher and invited lecturer at universities around the world, ranging from the Australian National University, Canberra, to the University of Concepcion, Chile.

Some years ago Christian authored “Expeditionen in die Schachwelt”, a collection of about 100 essays that the Viennese newspaper Der Standard called “one of the most intellectually scintillating and recommendable books on chess ever written.” The book has appeared in English with the title The Joys of Chess. It has a foreword by by Ex-World Champion Vishy Anand:

"A rich compendium of spectacular highlights and defining moments from chess history: fantastic moves, beautiful combinations, historical blunders, captivating stories, and all this embedded into a plentitude of quick-witted ideas and contemplations as food for thought."

Christian Hesse has written or contributed to many dozens of articles for ChessBase