Example: three (non-standard) dice A, B,C, such that on average B beats A and C beats B, yet A beats C!
Really defeats intuition. Deeply unsettling, maybe because dice feel familiar and safe?
Recently I've been prototyping some video game ideas involving dice, so this felt like a very important discovery. I'm not sure yet whether I can use it directly, but if nothing else, it's encouraging to learn that dice hold such deep mysteries