3 problems

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Hur–Kim conjecture on the winning probability of balanced nontransitive dice triples
A balanced and nontransitive (BN) triple of dice is a triple $(A_1,A_2,A_3)$ whose cyclic winning probabilities are equal and greater than $\frac{1}{2}$ ; its winning probability is…
Conjecturerefutedcombinatorics nontransitive-dice probabilityarXiv posted 2 days ago
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Conrey–Gabbard–Grant–Liu–Morrison conjecture on transitivity of random dice
Let a random $n$ -sided die in the multiset model be a uniformly chosen multiset of $n$ positive integers between $1$ and $n$ whose sum is $n(n+1)/2$ . Let $A$ , $B$ , and $C$ be indep…
Conjectureopencombinatorics nontransitive-dice probabilityarXiv posted 2 days ago
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Corey et al.'s asymptotic equidistribution conjecture for tournaments from dice
Let $n$ be fixed, and consider the tournaments on $[n]=\{1,2,\dots,n\}$ that are induced by comparing independent, proper $N$ -sided dice, where $N$ tends to infinity. Corey et al.'…
Conjectureopennontransitive-dice probability tournamentsarXiv posted 2 days ago

Hur–Kim conjecture on the winning probability of balanced nontransitive dice triples