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.

[FireDragon761138]

Conventional, shallow understandings of game theory might make Chess sound like a "simple" game, but chess has these kinds of positions where structures with nonlinear features can emerge.

[towforce]

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

At first glance, it looks as though the usual "works in an example, but doesn't scale up" issue will apply. There are a huge number of squares/pieces permutations, even for just one colour of piece.

Chess is not designed like an encryption algorithm in which good mathematicians have worked hard to minimise the occurrence of patterns which could be uncovered by somebody who is trying to crack the encryption: I therefore believe that chess almost certainly contains such usable patterns, and this is my approach to the evaluation problem.