Too late to edit, but I felt there was something wrong with this comment and I figured out what: the Cantelli bound is 1/(1+k²). This means as little as 50% ca

Too late to edit, but I felt there was something wrong with this comment and I figured out what: the Cantelli bound is 1/(1+k²). This means as little as 50% can be less than one standard deviation, as little as 80% below two standard deviations, etc.