Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to position C of White, position C of White is preferable to position D of Black, but position D of Black is preferable to position A of White. Intransitivity of winningness of positions of chess players is considered to be a consequence of complexity of the chess environment -- in contrast with simpler games with transitive positions only. The space of relations between winningness of positions of chess players is non-Euclidean. The Zermelo-von Neumann theorem is complemented by statements about possibility vs. impossibility of building pure winning strategies based on the assumption of transitivity of positions of chess players. Questions about the possibility of intransitive positions of players in other positional games are raised.

翻译：考虑国际象棋手在透明关系中的位置。 也就是说, 白方的A位更可取( 如果可以选择,应该选择), 以B为B为B位, 黑方的B位优于白方的C位, 白方的C位优于黑方的C位优于黑方的D位优于白方的D位优于白方的A位。 象棋选手职位获胜的不透明被视为国际象棋环境的复杂性 -- -- 与仅具有中转位置的简单游戏不同。 象棋选手职位的胜出空间是非欧裔的。 Zermelo- von Neuumann 论调得到了关于可能性和不可能在假定国际象棋手职位的过渡性的基础上建立纯胜出战略的声明的补充。 提出了关于其他运动手的对手是否具有透明位置的问题。