A brief conversation about subtraction games

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.

15 pages, 2 figures, Appendix by Koki Suetsugu