{"created":"2023-06-20T15:45:42.556759+00:00","id":213,"links":{},"metadata":{"_buckets":{"deposit":"b14251ee-29a1-408f-b779-0d3c1a51eab9"},"_deposit":{"created_by":2,"id":"213","owners":[2],"pid":{"revision_id":0,"type":"depid","value":"213"},"status":"published"},"_oai":{"id":"oai:hama-med.repo.nii.ac.jp:00000213","sets":["6:14:39"]},"author_link":["577"],"item_2_biblio_info_5":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2003-03-28","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"23","bibliographicPageStart":"1","bibliographicVolumeNumber":"17","bibliographic_titles":[{"bibliographic_title":"浜松医科大学紀要. 一般教育"}]}]},"item_2_description_30":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_2_description_9":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"This is a continuation of the author's previous papers [1] and [2], and is devoted to the study of optimal strategies arising in the card game of concentration. Suppose that two players A and B have both perfect memory and a set of cards consisting of all twin cards is used in their concentration game. In the first paper [1], we started to investigate two basic strategies, the strategies I and II. Note that the changing situation of this game is characterized by a vector (m,m - r), where the total number of the remaining twin cards is 2m , and the both players keep in memory m-r different cards including no twin cards. Now, the player having the move have to make a choice just before he turns up the second card. Indeed, he can select it randomly, either from the set of m+r-1 unknown cards or from the set of m-r memorized cards for 1≦m-r≦m-2, the former selection forms the strategy I and the latter does the strategy II. We are ready to explain our optimal strategy M. Before coming to a decision concerning the second card, the player calculate the expectation e1(m,m-r) of his points obtained if he adopts the strategy I in the present situation (m,m-r) and he also gets another expectation e2(m,m-r) based on the strategy II. Then he prefers the one giving rise to the maximum value max{e1(m,m-r),e2(m,m-r)}, which turns out to depend on the changing situation (m,m-r) in a rather complicated way. Such a strategy of selecting, in every situation of his move, the optimal one in a family of basic strategies that produces the maximum value of expectation is called the strategy M. The purpose of this paper is to give a full account of the strategy M and then to make a comparison of various strategies such as M, I , II and others. In order to exhibit an advantage of the strategy M over the other, we discuss several cases of the concentration game in which A constantly adopts the strategy M but B changes his strategy within the above-mentioned strategies. On the same line as in [1] and [2], we investigate the expectation of A's points in the situation (m,m-r) of, his own move, and succeed in proving its asmptotic behavior of the form αrm+δr+O(1/m), where m goes to ∞ for each fixed r. The detailed study of these coefficients αr and δr as sequences of r = 1,2,3, … enables us to state the following: The leading term αrm is independent of B's strategy, but the constant term δr does depend on it; if B changes his strategy from the strategy M to any one of other non-optimal strategies, then δr increases. The key point in discusions that follow in sections 2 and 3 is to show that A should select the strategy I when r is odd, and the strategy II when r is even, for sufficiently large values of m. For each value of m , on the other hand, the problem of solving the inequality e1(m,m-r) > e2(m,m-r) seems to be difficult, which one can see by checking several tables listed in the final section 4.","subitem_description_type":"Abstract"}]},"item_2_publisher_6":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"浜松医科大学"}]},"item_2_source_id_19":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"09140174","subitem_source_identifier_type":"ISSN"}]},"item_2_source_id_23":{"attribute_name":"NII書誌ID","attribute_value_mlt":[{"subitem_source_identifier":"AN10032827","subitem_source_identifier_type":"NCID"}]},"item_2_version_type_32":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Noda, Akio"}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-08-27"}],"displaytype":"detail","filename":"kiyo17_01.pdf","filesize":[{"value":"873.7 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"kiyo17_01.pdf","url":"https://hama-med.repo.nii.ac.jp/record/213/files/kiyo17_01.pdf"},"version_id":"423ae704-8ca4-459a-9843-b6aa3514baef"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"optimal strategy","subitem_subject_scheme":"Other"},{"subitem_subject":"card game","subitem_subject_scheme":"Other"},{"subitem_subject":"expectation","subitem_subject_scheme":"Other"},{"subitem_subject":"a system of difference equations","subitem_subject_scheme":"Other"},{"subitem_subject":"asymptotics","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"A Mathematical Note of Card Games ,III; on Optimal Strategies in the Concentration Game","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A Mathematical Note of Card Games ,III; on Optimal Strategies in the Concentration Game"}]},"item_type_id":"2","owner":"2","path":["39"],"pubdate":{"attribute_name":"公開日","attribute_value":"2013-08-27"},"publish_date":"2013-08-27","publish_status":"0","recid":"213","relation_version_is_last":true,"title":["A Mathematical Note of Card Games ,III; on Optimal Strategies in the Concentration Game"],"weko_creator_id":"2","weko_shared_id":-1},"updated":"2023-06-20T18:20:45.930769+00:00"}