Date Presented

Spring 4-27-2023

Document Type

Thesis

Department

Environmental Science

First Advisor

Randy Ribler, PhD

Second Advisor

M. Zakaria Kurdi, PhD

Third Advisor

Edward G DeClair, PhD

Abstract

This thesis improves a process that analyzes all the states of a game of Dots and Boxes. We use retrograde analysis and simulations to create a solution that provides significant performance improvements over our previous best solution. Expanding upon a previous 4x4 solution using rotations, reflections, better optimization, and cloud computing to limit the processing time and gather more data efficiently. We compute a file and the number of states associated with each file and process every state starting with a completely filled board. We optimized the data for cloud computing by running simulations to find the most efficient number of processors and assess potential bottlenecks. The data produced from the results will be able to provide solutions and optimal play for dots and boxes games of different dimensions.

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