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Saturday, June 1
Computational Statistics
Computational Statistics E-Posters
Sat, Jun 1, 9:30 AM - 10:30 AM
Grand Ballroom Foyer

A Computational Approach to the Structure of Subtraction Games (306252)

Bret Benesh, College of Saint Benedict/Saint John’s University 
Jamylle Carter, Diablo Valley College 
Deidra Coleman, Wofford College 
Douglas Crabill, Purdue University 
Jack Good, Purdue University 
*Kali Lacy, Purdue University 
Michael Smith, Purdue University 
Jennifer Travis, Lone Star College 
Mark Daniel Ward, Purdue University 

Keywords: Data Science, Game Theory, Subtraction Games, Combinatorics

We present a computational methodology for the structure of subtraction games. One of the oldest problems in combinatorial game theory is to characterize the structure of subtraction games. Although the structure can be analyzed recursively, at present, a methodology for explicitly characterizing the structure of a subtraction game is not (yet) known. In the last two years, our team characterized the (eventual) period lengths of the Sprague-Grundy values of subtraction games with 3 parameters. Recently, however, we greatly generalized these results, to fully characterize the complete sequences of SG-values, including both the periodic and the pre-periodic portions of the sequences. We have analyzed 72 TB of data about this problem, to verify this computational approach to the analysis of these games.