  A strong placement game $G$ played on a board $B$ is equivalent to a
simplicial complex $\Delta_{G,B}$. We look at weight games, a subclass of
strong placement games, and introduce upper bounds on the number of positions
with $i$ pieces in $G$, or equivalently the number of faces with $i$ vertices
in $\Delta_{G,B}$, which are reminiscent of the Kruskal-Katona bounds.
