Depth, balancing, and limits of the Elo model

TL;DR

This paper explores the concept of game depth as a human-centered complexity measure, extending it to continuous forms, analyzing various games, and proposing methods to increase depth, with applications to specific games and rules.

Contribution

It introduces a continuous measure of game depth, provides new depth results, and presents tools to increase game depth, applying these to analyze multiple games and rules.

Findings

Extended game depth to continuous measures

Identified methods to increase game depth

Analyzed effects of rules on game complexity

Abstract

-Much work has been devoted to the computational complexity of games. However, they are not necessarily relevant for estimating the complexity in human terms. Therefore, human-centered measures have been proposed, e.g. the depth. This paper discusses the depth of various games, extends it to a continuous measure. We provide new depth results and present tool (given-first-move, pie rule, size extension) for increasing it. We also use these measures for analyzing games and opening moves in Y, NoGo, Killall Go, and the effect of pie rules.