6 problems

Equal-likelihood conjecture. For any fixed $k$, all tournaments on $k$ dice are equally likely.

Let $k$ random dice determine a tournament on $k$ alternatives by orienting each pair according to the beats relation: an edge points from die $\mathbf a$ to die $\mathbf b$ when…

Let an $n$-sided die be a multiset of $n$ integers from $1$ through $n$, and sample such dice uniformly subject to the face-sum condition … A finite collection of dice is called ch…

Intransitive-function conjecture. With an appropriate measure on this space of functions, if three such functions are chosen at random, the probability that they form an intransiti…

Uniform-comparison conjecture. As $n\to\infty$, the probability of each of these assignments is equally likely.

Intransitive-dice conjecture. The probability that the chosen triple is intransitive approaches $1/4$ as $n\to\infty$.