An update on domineering on rectangular boards

TL;DR

This paper reviews the game of Domineering on rectangular boards, establishing outcome classes for various dimensions and summarizing previous research to deepen understanding of the game's strategic complexity.

Contribution

It provides new outcome class results for specific rectangular board dimensions and consolidates existing knowledge on Domineering's strategic outcomes.

Findings

Outcome classes established for several rectangular board dimensions

Previous work on Domineering summarized and extended

Restricted outcome classes identified for additional board sizes

Abstract

Domineering is a combinatorial game played on a subset of a rectangular grid between two players. Each board position can be put into one of four outcome classes based on who the winner will be if both players play optimally. In this note, we review previous work, establish the outcome classes for several dimensions of rectangular board, and restrict the outcome class in several more.