  Dots-and-Boxes is a popular children's game whose winning strategies have
been studied by Berlekamp, Conway, Guy, and others. In this article we consider
two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize
the same lattice game board structure as Dots-and-Boxes. The nature of these
variations along with this lattice structure lends itself to applying Pick's
theorem to calculate claimed area. Several strategies similar to those studied
in Dots-and-Boxes are used to analyze these new variations.
