Geodesic
The Sprague-Grundy functions of saturations of misère Nim
Yuki Irie1
1Tohoku University
The electronic journal of combinatorics, Tome 28 (2021) no. 1
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We consider misère 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 misère 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 misère Nim is not. Moreover, we present explicit formulas for the Sprague-Grundy functions of saturations of misère Nim, which are obtained from misère Nim by adjoining some moves.
DOI : 10.37236/8916
Classification : 91A46
Mots-clés : misère Nim, Sprague-Grundy function, position restrictions

Yuki Irie  1

1 Tohoku University 
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Yuki Irie. The Sprague-Grundy functions of saturations of misère Nim. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/8916

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