@techreport{oai:ipsj.ixsq.nii.ac.jp:02002217,
 author = {Hiyu,Inoue and Shin-nosuke,Kadowaki and Shun-ichi,Kimura and Haruki,Wada and Hiyu Inoue and Shin-nosuke Kadowaki and Shun-ichi Kimura and Haruki Wada},
 issue = {10},
 month = {May},
 note = {We consider a Subtraction Nim, where two players have exactly the same options, but is partizan in the sense that at the game ending, a partizan rule is applied for the decision of the winner. The example we consider is the following: Let a set of removable numbers S be a non-empty subset of positive integers greater than or equal to 2, which is applied for both players Left and Right. At the end of the game, Left wins if the number of remaining tokens is even, and Right wins if the number of remaining tokens is odd. We computed the outcomes for many S, and found surprising phenomena that in many examples of S (more than 81% of the samples), the outcomes are L-positions for all large enough n. In comparison, R-positions appear only occasionally. Our theorem explains why that phenomena occur. We prove that n ± 1 are L-positions when n is an R-position. Weaker restrictions apply for P-positions and N-positions. Only L-positions can last forever., We consider a Subtraction Nim, where two players have exactly the same options, but is partizan in the sense that at the game ending, a partizan rule is applied for the decision of the winner. The example we consider is the following: Let a set of removable numbers S be a non-empty subset of positive integers greater than or equal to 2, which is applied for both players Left and Right. At the end of the game, Left wins if the number of remaining tokens is even, and Right wins if the number of remaining tokens is odd. We computed the outcomes for many S, and found surprising phenomena that in many examples of S (more than 81% of the samples), the outcomes are L-positions for all large enough n. In comparison, R-positions appear only occasionally. Our theorem explains why that phenomena occur. We prove that n ± 1 are L-positions when n is an R-position. Weaker restrictions apply for P-positions and N-positions. Only L-positions can last forever.},
 title = {On Ending Partizan Subtraction Nim},
 year = {2025}
}