  We study the generic tropical initial ideals of a positively graded
Cohen-Macaulay algebra $R$ over an algebraically closed field $\mathbf{k}$.
Building on work of R\"omer and Schmitz, we give a formula for each initial
ideal, and we express the associated quasivaluations in terms of certain
$I$-adic filtrations. As a corollary, we show that in the case that $R$ is a
domain, every initial ideal coming from the codimension-$1$ skeleton of the
tropical variety is prime, so "generic presentations of Cohen-Macaulay domains
are well-poised in codimension-$1$."
