The concept of a set of three dice where the relation “will beat probabilistically” is non-transitive was first explored by Martin Gardner. Expanding on this concept, I spoke last year on how such a set of dice can be constructed having an arbitrary number of sides, and how it may be done such that all of the “victorious probabilities” can be made equal. I will now describe constructing sets where the number of dice is also arbitrary, and on modifying such sets to mimic the outcome of a tournament.

Attendance of the previous talk is not necessary to follow this one.