A brief conversation about subtraction games

TL;DR

This survey reviews finite subtraction games, highlighting Flammenkamp's 1997 findings of exponential period lengths, and includes an appendix on finite excluded subtraction.

Contribution

It provides a comprehensive overview of finite subtraction games and emphasizes Flammenkamp's experimental observation of exponential period lengths, with additional insights on excluded subtraction.

Findings

Flammenkamp observed exponential period lengths in certain subtraction games.

The survey consolidates development history and key results in finite subtraction games.

Includes new discussion on finite excluded subtraction by Suetsugu.

Abstract

In this survey we revisit {\sc finite subtraction}, one-heap subtraction games on finite rulesets. The main purpose is to give a general overview of the development, and specifically to draw attention to Flammenkamp's thesis (1997), where he, contrary to other studies, experimentally observes exponential eventual period length of the outcomes, for a carefully selected subclass of games. In addition, we contribute an appendix on {\sc finite excluded subtraction} by Suetsugu.