| Item type |
SIG Technical Reports(1) |
| 公開日 |
2025-05-31 |
| タイトル |
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言語 |
ja |
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タイトル |
On Ending Partizan Subtraction Nim |
| タイトル |
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言語 |
en |
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タイトル |
On Ending Partizan Subtraction Nim |
| 言語 |
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言語 |
eng |
| 資源タイプ |
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資源タイプ識別子 |
http://purl.org/coar/resource_type/c_18gh |
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資源タイプ |
technical report |
| 著者所属 |
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Hiroshima University |
| 著者所属 |
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Hiroshima University |
| 著者所属 |
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Hiroshima University |
| 著者所属 |
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Hiroshima University |
| 著者所属(英) |
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en |
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Hiroshima University |
| 著者所属(英) |
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en |
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Hiroshima University |
| 著者所属(英) |
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en |
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Hiroshima University |
| 著者所属(英) |
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en |
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Hiroshima University |
| 著者名 |
Hiyu,Inoue
Shin-nosuke,Kadowaki
Shun-ichi,Kimura
Haruki,Wada
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| 著者名(英) |
Hiyu Inoue
Shin-nosuke Kadowaki
Shun-ichi Kimura
Haruki Wada
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| 論文抄録 |
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内容記述タイプ |
Other |
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内容記述 |
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. |
| 論文抄録(英) |
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内容記述タイプ |
Other |
|
内容記述 |
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. |
| 書誌レコードID |
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収録物識別子タイプ |
NCID |
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収録物識別子 |
AA11362144 |
| 書誌情報 |
研究報告ゲーム情報学（GI）
巻 2025-GI-55,
号 10,
p. 1-6,
発行日 2025-05-31
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| ISSN |
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収録物識別子タイプ |
ISSN |
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収録物識別子 |
2188-8736 |
| Notice |
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SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc. |
| 出版者 |
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言語 |
ja |
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出版者 |
情報処理学会 |
IPSJ-GI25055010.pdf (823.3 KB)
