Today in his excellent new newsletter “The Magnet,” Mark Frauenfelder discusses “transitive dice” - D6s with the weird property that while Die A has an advantage over Die B and Die B has an advantage over Die C, Die A LOSES to Die C on average.
That is to say, if you give an opponent the choice of any of the three dice, one of the remaining two dice will always beat it. This is some pretty eldritch probability stuff (and an example of how counterintuitive propability can be).
The key is in understanding the probability distributions. Die A has five “4” sides and one “6” side. Die B has five “3” sides and one “6” side. Die C has three “5” sides and three “2” sides.
That means: “A beats B 25 out of the 36 possibilities. C beats A 21 out of 36. C beats A 21 out of 36.”
Frauenfelder notes that Warren Buffet is obsessed with nontransitive dice, which makes sense. After all, Buffet has repeatedly, publicly proclaimed that he only invests in companies that are in noncompetitive markets.
For example, here’s why he bought a huge stake in Moody’s: “I know nothing about credit rating. The only reason I bought it is because there are only three credit rating agencies and they serve the whole country, and they have pricing power.”
His ideal company is one with a monopoly so secure, “even your idiot cousin could run it.” Presumably, you could teach that same idiot cousin to memorize which die beats each of the others, too.
