An experimental study of the game of Nim

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This study is an analysis of the game of Nim. The paper is divided into two parts. The first part is a theoretical examination of the game in which the game is solved and a method of identifying the winner is presented. Since Nim is a game with a complete mathematical solution, a strategy for optimum play is also presented. The second part of the paper presents the findings from an experimental study asking questions like: given that it is known who should win, how often does the predicted outcome occur when the game is actually played. Since Nim is a flexible game and can be constructed to be rather complicated, some inconsistency between the experimental and theoretical results is reasonable. The experimental results collected for this paper are consistent, albeit weakly consistent, with the theoretical findings. In addition, there is evidence that learning is involved; as players played the game repeatedly they improved and the experimental results became closer aligned with the theoretical predictions.