  In 2023, Defant and Li introduced the Ungar move, which sends an element $v$
of a finite meet-semilattice $L$ to the meet of some subset of the elements
covered by $v$. More recently, Defant, Kravitz, and Williams introduced the
Ungar game on $L$, in which two players take turns making Ungar moves starting
from an element of $L$ until the player that cannot make a nontrivial Ungar
move loses. In this note, we settle two conjectures by Defant, Kravitz, and
Williams on the Ungar games on the Young-Fibonacci lattice and the lattices of
the order ideals of shifted staircases.
