2021-07-28T12:35:42Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:002088372020-12-14T15:00:00Z00581:10023:10035
Variant of Wythoff's Game-Corner Two RooksVariant of Wythoff's Game-Corner Two Rookseng[特集：離散と計算の幾何・グラフ・ゲーム] Combinatorial game theory, Nim, Impartial games, Misère gameshttp://id.nii.ac.jp/1001/00208735/Journal Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=208837&item_no=1&attribute_id=1&file_no=1Copyright (c) 2020 by the Information Processing Society of JapanKwansei GakuinKwansei GakuinKwansei GakuinNational Institute of InformaticsKai, HirokawaRyohei, MiyaderaYusuke, SakamotoKoki, SuetsuguThis article presents an impartial game, “Corner Two Rooks.” This game is a variant of “Corner the Queen” that is mathematically equivalent to Wythoff's game. In “Corner the Queen, ” a single chess queen is placed on a large grid of squares. Each player can move the queen any number of steps toward the upper-left corner of the grid, vertically, horizontally, or diagonally. The player who moves the queen into the upper-left corner is the winner. In this work, the authors use two rooks of chess instead of the queen, and a rook can jump over another rook but not onto another. There is a restriction on the distance that a rook can travel in each turn. This game can be considered as a misère game of the traditional Nim game with four piles and a restriction of the number of stones to be removed in each turn. The authors present the set of P-positions of the game using a theorem for misère games. When there is no restriction on the distance that a rook can travel in each turn, we obtain a similar result in which the set of P-positions is simpler.------------------------------This is a preprint of an article intended for publication Journal ofInformation Processing(JIP). This preprint should not be cited. Thisarticle should be cited as: Journal of Information Processing Vol.28(2020) (online)DOI http://dx.doi.org/10.2197/ipsjjip.28.970------------------------------This article presents an impartial game, “Corner Two Rooks.” This game is a variant of “Corner the Queen” that is mathematically equivalent to Wythoff's game. In “Corner the Queen, ” a single chess queen is placed on a large grid of squares. Each player can move the queen any number of steps toward the upper-left corner of the grid, vertically, horizontally, or diagonally. The player who moves the queen into the upper-left corner is the winner. In this work, the authors use two rooks of chess instead of the queen, and a rook can jump over another rook but not onto another. There is a restriction on the distance that a rook can travel in each turn. This game can be considered as a misère game of the traditional Nim game with four piles and a restriction of the number of stones to be removed in each turn. The authors present the set of P-positions of the game using a theorem for misère games. When there is no restriction on the distance that a rook can travel in each turn, we obtain a similar result in which the set of P-positions is simpler.------------------------------This is a preprint of an article intended for publication Journal ofInformation Processing(JIP). This preprint should not be cited. Thisarticle should be cited as: Journal of Information Processing Vol.28(2020) (online)DOI http://dx.doi.org/10.2197/ipsjjip.28.970------------------------------AN00116647情報処理学会論文誌61122020-12-151882-77642020-12-09