Intransitively winning chess players' positions

Chess players' positions in intransitive (rock-paper-scissors) relations are considered. Namely, position $A$ of White is preferable (it should be chosen if choice possible) to $B$ Black, Black $C$ White, $D$ but White. Intransitivity winningness chess considered a consequence complexity the environment - contrast with simpler games transitive only. Perfect values impossible. Euclidian metric cannot used describe space relations. The Zermelo-von Neumann theorem complemented by statements about possibility vs. impossibility building pure winning strategies based on assumption transitivity positions. Questions other positional raised.