  We settle a version of the conjecture about intransitive dice posed by
Conrey, Gabbard, Grant, Liu and Morrison in 2016 and Polymath in 2017. We
consider generalized dice with $n$ faces and we say that a die $A$ beats $B$ if
a random face of $A$ is more likely to show a higher number than a random face
of $B$. We study random dice with faces drawn iid from the uniform distribution
on $[0,1]$ and conditioned on the sum of the faces equal to $n/2$. Considering
the "beats" relation for three such random dice, Polymath showed that each of
eight possible tournaments between them is asymptotically equally likely. In
particular, three dice form an intransitive cycle with probability converging
to $1/4$. In this paper we prove that for four random dice not all tournaments
are equally likely and the probability of a transitive tournament is strictly
higher than $3/8$.
