Dice tails

Maxim two, from Richard Zeckhauser, is “when you are having trouble getting your thinking straight, go to a simple case.” This maxim came to mind listening to Michael Mauboussin and the Acquired duo discuss business valuation and the difference between tangible and intangible assets.

“(Intangible assets like brand, code, etc.) also makes you vulnerable. If your product or service does not work there’s not much there left. If you think of pushing out the tails relative to traditional business, that’s the way I think about it. There are more extreme good things and more extreme bad things than we’ve witnessed in the past.” – Michael Mauboussin, Acquired, October 2021

We’ve thought about this idea before, in the complex world and in the increasing returns economy. But it’s a big idea and like the lead in a story, we need to fill out this character a bit more.

Here’s the distribution of results of one, two, three, and four dice rolls. For one, the results are equally likely. For two, as anyone who has played Catan knows, seven comes up the most.

one two three four dice distributions

Though it’s a basic Google chart, it is simple enough for Zeckhauser and satisfactory for Mauboussin. For a die, the chance of rolling the highest score is ~16%. In the case of two the chance is ~3%, for three it’s ~0.5% and for four it’s ~0.1%.

Different parts of life are more or less similar to different amounts of dice. Businesses with lots of intangible value are closer to the end of fewer dice, because those kinds of distributions have fatter tails. Business with more tangible capital are more like rolling many dice.

Now, dice distributions offer no mechanistic or explanatory approach about what kind of system a case may be. There’s nothing about “brand building” that makes it more like rolling two dice relative to something like pool construction. But the metaphoric fit is just fine.

Thanks to Michael Mauboussin for this post and all the others. He was one of the early podcast guests who was going around explaining things that seemed like really big ideas in a really basic way. He was so good at it I thought, hey, I should write some of this stuff down. Well, I’m still writing.