A set of dice is nontransitive if it contains three dice, A, B, and C, with the property that A rolls higher than B more than half the time, and B rolls higher than C more than half the time, but it is not true that A rolls higher than C more than half the time. In other words, a set of dice is nontransitive if the binary relation – X rolls a higher number than Y more than half the time – on its elements is not transitive.
It is possible to find sets of dice with the even stronger property that, for each die in the set, there is another die that rolls a higher number than it more than half the time. Using such a set of dice, one can invent games which are biased in ways that people unused to nontransitive dice might not expect.
Themes for the next decade: Cannabis, 5G, and EVs
A lot changes in 10 years, and many changes are expected by the time 2030 rolls around. Some key themes have already emerged, and we expect them to continue to impact investing decisions. At the recent Morningstar conference, several panelists joined a discussion about several major themes for the next decade, including cannabis, 5G and Read More
Warren Buffett On How He Tried To Trick Bill Gates With Non Transitive Dice