백단 is a kind of exaggeration to discribe someone's East Asian board game skill level. This expression is same as 20,000 rate point in chess. Haha. As you know, a champion of chess competition can read opponents' mind very well. So if someone's 눈치 is 백단, this one can read other's mind very well like a champion of a chess competition.

백단(100단; 바둑이라는 동양의 게임/스포츠의 최고 등급이 10단. 그보다 아주 높은 수준). 눈치: wits, sense '눈치가 백단이다'; Someone really catches on fast. A colloquial idiom. "영어도 못 하면서 미국에서 살다 보니, 눈치가 백단이 되었어요." "쟤는 눈치가 백단이야. 정말 여우 같아."