Dots-and-Polygons
Jessica Dickson, Rachel Perrier

TL;DR
This paper explores two new variations of the Dots-and-Boxes game, applying geometric and combinatorial strategies, including Pick's theorem, to analyze gameplay and potential winning tactics.
Contribution
It introduces Dots-and-Triangles and Dots-and-Polygons, extending game analysis methods to new lattice-based variations with geometric calculations.
Findings
Strategies similar to Dots-and-Boxes are effective in the new variations
Pick's theorem is useful for area calculation in these games
The paper provides insights into optimal play tactics
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsModular Robots and Swarm Intelligence · Advanced Materials and Mechanics
