When waiting moves you in scoring combinatorial games

TL;DR

This paper characterizes a class of combinatorial scoring games, linking them to Conway's normal-play games, and extends existing comparison theorems for scoring games involving numerical scores.

Contribution

It provides a new characterization of scoring games with pass moves and extends comparison theorems for games with numerical scores.

Findings

Characterization of combinatorial scoring games with pass moves

Embedding of Conway's normal-play games into scoring games

Extension of Ettinger's comparison theorem for scoring games

Abstract

Combinatorial Scoring games, with the property `extra pass moves for a player does no harm', are characterized. The characterization involves an order embedding of Conway's Normal-play games. Also, we give a theorem for comparing games with scores (numbers) which extends Ettinger's work on dicot Scoring games.