  Nora and Wanda are two players who choose coefficients of a degree $d$
polynomial from some fixed unital commutative ring $R$. Wanda is declared the
winner if the polynomial has a root in the ring of fractions of $R$ and Nora is
declared the winner otherwise. We extend the theory of these games given by
Gasarch, Washington and Zbarsky to all finite cyclic rings and determine the
possible outcomes. A family of examples is also constructed using discrete
valuation rings for a variant of the game proposed by these authors. Our
techniques there lead us to an adversarial approach to constructing rational
polynomials of any prescribed degree (equal to $3$ or greater than $8$) with no
roots in the maximal abelian extension of $\mathbb{Q}$.
