Impartial Scoring Play Games

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.