Chains of White and Black arrangements beating one another in the rock—paper—scissors way

[Alexander Poddiakov]

I am looking for those who may find the topic of chains of White and Black arrangements according to the rock—paper—scissors principle interesting.

Intransitive dice (such that the probabilities of die A winning against die B, B against C, C against D, and D against A are all the same) are well known
https://mathworld.wolfram.com/EfronsDice.html
“Intransitive” means beating one another in the rock—paper—scissors way: A≻B, B≻C, C≻D, D≻A.

I study not stochastic intransitive dice but deterministic intransitive chess pieces’ arrangements.

A short post with examples


A popular text with diagrams (нou need to wait a few seconds to see its English translation):
White and Black positions based on the Rock—Paper-Scissors principle
https://trv--science-ru.translate.goog/ ... r_pto=wapp

Full-text scientific article
Intransitively winning chess players’ positions
https://arxiv.org/pdf/2212.11069

I will be happy to receive feedback on the idea of White and Black arrangements beating one another in the rock—paper—scissors way.