>Does anyone have a description and analysis of such a set of dice
>(or some equivalent problem)? It could be a useful didactic tool.
>Or perhaps it is simply a hoax.
No, not a hoax... In fact, it can be done with as few as three dice.
Consider:
A: 333333 B: 222266 C: 115555
Now, A clearly beats B iff B rolls 2 : probability 2/3
C beats A iff C rolls 5: probability 2/3
And B beats C if B rolls 6 [P=1/3] or B rolls 2 and C rolls 1
[P = 2/9]. Thus P(B beats C) = 5/9.
Of course, for the purposes of gambling^H^H^H^H^H^H^H^H informal
lectures in probability theory, you would use more values and mix them
up a little, to make the principle less obvious...
As for why it works, the real question is why people [myself
included] find it surprising. We seem to think that there "ought" to
be a one-parameter ranking of "fitness" - and there isn't.
-Robert