"Beware of false knowledge; it is more dangerous than ignorance.” – George Bernard Shaw
Question: You are in Las Vegas and are offered a $1 bet in which you have 99.9% chance of winning $10 and a mere 0.1% chance of losing $11,000. Would you take it?
The odds suggest that if you were to take the bet one thousand times you would win $10 a staggering 999 times. The wise choice, however, would be to refuse. Why? Because the expected gain from your victory is less than your expected loss. In more practical terms, for every ten dollars you bet you would gain $9.99 but lose $11.
This is an important point because the world is ripe with such asymmetrical situations and it is important to unlearn that it is not the frequency of correctness that matters, it is the magnitude of correctness which is most important.
I personally experienced such a situation on January 1, 2008. My family and I were staying at a friend’s lake cabin in Northern Wisconsin and after celebrating New Year’s Eve with one too many libations, my wife and I decided we were in need of a little exercise. My friend suggested we go snowshoeing across the lake.
My wife, having noticed a thin layer of slush above the ice on the lake, was concerned the ice wasn’t safe. My friend, after drilling through the ice to create an ice-fishing hole, assured her that there were eight solid inches of ice and offered the numerous snowmobilers gliding across the lake on their heavy sleds as further visual evidence of the lake’s ability to withstand our weight.
Bearing these common-sense points in mind, we confidently proceeded toward a small island ensconced in the middle of the lake. Once there, we continued across a marshy area until we heard a crack. Before we could stop to assess the situation, my wife had broken through the ice.
Luckily, I was standing on solid ground and she only plunged up to her waist before grabbing hold of the ice edge. After a fearful minute, I was able to assist her out of the water and onto solid ground. We then hastily made a beeline back across the lake careful to follow our precise tracks back to the warmth and safety of the cabin.
In retrospect, everyone involved in the situation made the mistake of confusing the probability of falling through the ice (which was admittedly small) with the magnitude of the consequences of falling through the ice. (Had my wife and I both been just a few feet farther to the left the outcome could have been fatal.)
In his book, “Think Twice” – which cleverly and appropriately has the double entendre of “Thin Ice” in the title – Michael Mauboussin encourages people to focus on process and not outcomes when making a decision that involves probability.
Returning to the opening question, a focus on outcome leads a person to take a $10 bet with a chance of winning 999 out of 1000 times because they will win an overwhelming percentage of the time. A focus on process suggests the decision is still a poor one because the magnitude of the rare possibility outweighs the benefits.
In other words, even if the thickest of ice has a remote chance of being thin somewhere it behooves you to think twice about crossing it because the result could be a cold dose of reality.
(Please note that this habit of focusing on process versus outcome is not inherently conservative, nor does it eschew risk taking. Quite to the contrary, if the odds were reversed so that you lost $10 99.9% of the time but won $11,000 just 0.1% of the remaining time, it would be a good bet.)
Homework Assignment: Nine of your ten board members believe your company’s sales will grow a modest 3 percent this year, but one estimates sales will plummet 50 percent. How do you modify your strategic plans to account for this possibility?