Reciprocal relations are an interesting generalization of complete relations covering both an important class of preference relations studied in fuzzy set theory, as well as the class of winning probability relations studied in probability theory. Due to their intrinsic nature, reciprocal relations that are not weakly transitive can be considered to be cyclical. Most attention so far has gone to cycles of lengths three, using the metaphor of the Rock-Paper-Scissors children game, triggered by evidence from nature and society.

In this lecture, I will focus on winning probability relations associated with random vectors and point out the link with the underlying dependence structure. Interesting prototypical settings, such as dice games, mutual rank probability relations and graded stochastic dominance, will be discussed.

I will also initiate the study of cycles of length four, introducing the Rock-Paper-Scissors-Lizard metaphor. Although the picture is still incomplete, it already offers some interesting insights.