Otherwise -- cool subject. I know about non-transitive voting (it was fairly relevant to what I did in academia for a while). But I hadn't heard much before about the dice. ;)
The prescriptivists lost a long, long time ago: language is defined by usage.
You can be "correct" according to some prescriptivist definition of the english language, or you can be understood by the people who actually use the language to communicate. Since nearly everyone uses "dice" for both the singular and plural form, and most people will never even have heard "die" being used in this context, dice is the correct form.
Otherwise -- cool subject. I know about non-transitive voting (it was fairly relevant to what I did in academia for a while). But I hadn't heard much before about the dice. ;)