  In the present paper we show that for any given digraph $\mathbb{G} =([n],
\vec{E})$, i.e. an oriented graph without self-loops and 2-cycles, one can
construct a 1-dependent Markov chain and $n$ identically distributed hitting
times $T_1, \ldots , T_n $ on this chain such that the probability of the event
$T_i > T_j $, for any $i, j = 1, \ldots n$, is larger than $\frac{1}{2}$ if and
only if $(i,j)\in \vec{E}$. This result is related to various paradoxes in
probability theory, concerning in particular non-transitive dice.
