For background (if you care), see this post (which links to the first one as well).
I have proven that balanced, non-transitive n-sided dice exist for every n>2 (and the proof is quite slick, I think). The trick to this is a particular kind of labeling followed by concatenation. I have also proven several nice things (if a set is balanced, all 3 dice add to the same total!) on top of my original thoughts. My task now is attempting to find an upper bound for the victorious probability. My conjecture is 2/3. I also conjecture this is unattainable, that is, it is asymptotic.
I’m going to be writing a lengthy paper on this topic, so it’ll be easier to link to that once it’s done (in April or so).
That’s enough on dice. Back to your regularly scheduled blogramming.
Thanks for reading.