High Temperature Domineering Positions

TL;DR

This paper investigates the maximum temperature in Domineering, a combinatorial game, by developing a parallel search program to analyze positions with high temperatures near 2.

Contribution

The authors created a parallel exhaustive search tool to analyze high-temperature Domineering positions, addressing the conjecture about the maximum temperature being 2.

Findings

Identified positions with temperatures close to 2

Provided computational evidence supporting the conjecture

Enhanced understanding of game temperature in Domineering

Abstract

Domineering is a partizan game where two players have a collection of dominoes which they place on the grid in turn, covering up squares. One player places tiles vertically, while the other places them horizontally; the first player who cannot move loses. It has been conjectured that the highest temperature possible in Domineering is 2. We have developed a program that enables a parallel exhaustive search of Domineering positions with temperatures close to or equal to 2 to allow for analysis of such positions