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

Intransitive dice tournament is not quasirandom