In a terrific book by William Poundstone, Fortune’s Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street, is the story of a 1968 dinner meeting between mathematician Edward Thorp and fund manager Warren Buffett.
Poundstone casually mentions that Buffett and Thorpe discussed their shared interest in nontransitive dice.
“These are,” writes Poundstone, “a mathematical curiosity, a type of ‘trick’ dice that confound most people’s ideas about probability.”
A nice description of nontransitive dice by Ivars Peterson at the Mathematical Association of America’s website:
The game involves four specially numbered dice. You let your opponent pick any one of the four dice. You choose one of the remaining three dice. Each player tosses his or her die, and the higher number wins the throw. Amazingly, in a game involving 10 or more throws, you will nearly always have more wins.
Here’s what the dice look like:
The trick is to always let your opponent pick first, and then you pick the die to the left of his selection (if he picks the die with the four 4s, then circle round to the die with the three ones). It’s just like playing Rock, Paper, Scissors — only you get to see what the other guy picks in advance.
With these dice, you always have a 2/3 probability of winning — what a great sucker’s bet!
Knowing when you’ve made a mistake and learning from that experience can be a very rewarding and profitable undertaking.
If you can admit your mistake, you can learn from it. However, an inability to learn from mistakes can mean you make the exact same mistake again.
Consider Steve Feinberg, the onetime owner of Chrysler, and CEO of Cerberus Capital Management reflecting on his ‘mistake’
…even now, Mr. Feinberg, a man who can play a decent game of chess while blindfolded, is hard-pressed to pinpoint many mistakes. Sitting in his office on Park Avenue, far away from the detritus that surrounds Detroit, he grows pensive when asked what he has learned from his audacious — and failed — effort to privatize and resurrect the legendary and deeply troubled auto giant. “I don’t know what we could have done differently,” he says, crossing his arms on his chest. “From the day we bought it, we worked hard to improve it.” He pauses, pondering, as the clock ticks away. Then he shakes his head. “We were too optimistic on timing,” he says. “Maybe what we should have done was not bought it.”
Compare that with Warren Buffett talking about his oft-cited U.S. Airways purchase in hindsight:
I liked and admired Ed Colodny, the company’s then-CEO, and I still do. But my analysis of USAir’s business was both superficial and wrong. I was so beguiled by the company’s long history of profitable operations, and by the protection that ownership of a senior security seemingly offered me, that I overlooked the crucial point: USAir’s revenues would increasingly feel the effects of an unregulated, fiercely-competitive market whereas its cost structure was a holdover from the days when regulation protected profits. These costs, if left unchecked, portended disaster, however reassuring the airline’s past record might be.
Words matter. To learn more about decoding CEOs read Investing Between the Lines: How to Make Smarter Decisions By Decoding CEO Communications.