The Sprague-Grundy Functions of Saturations of Misere Nim
Abstract
We consider mis\`ere Nim as a normal-play game obtained from Nim by removing the terminal position. While explicit formulas are known for the Sprague-Grundy functions of Nim and Welter's game, no explicit formula is known for that of mis\`ere Nim. All three of these games can be considered as position restrictions of Nim. What are the differences between them? We point out that Nim and Welter's game are saturated, but mis\`ere Nim is not. Moreover, we present explicit formulas for the Sprague-Grundy functions of saturations of mis\`ere Nim, which are obtained from mis\`ere Nim by adjoining some moves.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.