Impartial Scoring Play Games
Fraser Stewart

TL;DR
This paper explores the structure of impartial scoring play games, focusing on nim and octal games, introducing an analysis function, and discussing its properties and conjectures.
Contribution
It introduces a new analytical function for impartial scoring play games and examines their properties, providing insights into nim and octal games.
Findings
Defined a function to analyze impartial scoring games
Examined properties and conjectures of the analysis function
Provided structural insights into nim and octal games
Abstract
In this paper we will be examining impartial scoring play games. We first give the basic definitions for what impartial scoring play games are and look at their general structure under the disjunctive sum. We will then examine the game of nim and all octal games, and define a function that can help us analyse these games. We will finish by looking at the properties this function has and give many conjectures about the behaviour this function exhibits.
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Taxonomy
TopicsArtificial Intelligence in Games · Sports Analytics and Performance · Digital Games and Media
