  Intransive dice $D^{(1)}, \ldots, D^{(\ell)}$ are dice such that $D^{(1)}$
has advantage with respect to $D^{(2)}$, dice $D^{(2)}$ has advantage with
respect to $D^{(3)}$ and so on, up to $D^{(\ell)}$, which has advantage over
$D^{(1)}$. In this twofold work, we present: first, (deterministic) results on
existence of general intransitive dice. Second and mainly, a central limit
theorem for the vector of normalized victories of a die against the next one in
the list when the faces of a die are i.i.d.\ random variables and all dice are
independent, but different dice may have distinct distributions associated to,
as well as they may have distinct number of faces. From this central limit
theorem we derive a criteria to assure that the asymptotic probability of
observing intransitive dice is null, which applies for many cases, including
all continuous distributions and many discrete ones.

Probability