Variations on Narrow Dots-and-Boxes and Dots-and-Triangles

Abstract

We verify a conjecture of Nowakowski and Ottaway that closed $1 \times n$ Dots-and-Triangles is a first-player win when $n \neq 2$. We also prove that in both the open and closed $1 \times n$ Dots-and-Boxes games where $n$ is even, the first player can guarantee a tie.