一次洗牌，无反馈的猜牌游戏的瞬间

IF 1 Q1 MATHEMATICS

Discrete Mathematics Letters Pub Date : 2023-08-07 DOI:10.47443/dml.2023.119

Tipaluck Krityakierne, Poohrich Siriputcharoen, T. Thanatipanonda, Chaloemkiat Yapolha

{"title":"一次洗牌，无反馈的猜牌游戏的瞬间","authors":"Tipaluck Krityakierne, Poohrich Siriputcharoen, T. Thanatipanonda, Chaloemkiat Yapolha","doi":"10.47443/dml.2023.119","DOIUrl":null,"url":null,"abstract":"We consider card guessing with no feedback, a variant of the game previously studied by Ciucu in 1998. In this study, we derive an exact, closed-form formula for the asymptotic (in the number of cards, n ) expected number of correct guesses, as well as higher moments, for a one-time riﬄe shuﬄe game under the optimal strategy. The problem is tackled using two diﬀerent approaches: one approach utilizes a fast generating function based on a recurrence relation to obtain numerical moments, while the other is the symbolic approach employing the method of indicators for ﬁnding expected counts. The results obtained contribute to the existing literature on card guessing with no feedback.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Moments of the one-shuffle no-feedback card guessing game\",\"authors\":\"Tipaluck Krityakierne, Poohrich Siriputcharoen, T. Thanatipanonda, Chaloemkiat Yapolha\",\"doi\":\"10.47443/dml.2023.119\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider card guessing with no feedback, a variant of the game previously studied by Ciucu in 1998. In this study, we derive an exact, closed-form formula for the asymptotic (in the number of cards, n ) expected number of correct guesses, as well as higher moments, for a one-time riﬄe shuﬄe game under the optimal strategy. The problem is tackled using two diﬀerent approaches: one approach utilizes a fast generating function based on a recurrence relation to obtain numerical moments, while the other is the symbolic approach employing the method of indicators for ﬁnding expected counts. The results obtained contribute to the existing literature on card guessing with no feedback.\",\"PeriodicalId\":36023,\"journal\":{\"name\":\"Discrete Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47443/dml.2023.119\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2023.119","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑的是没有反馈的猜牌游戏，这是Ciucu在1998年研究过的一种游戏变体。在本研究中，我们导出了在最优策略下的一次性随机洗牌游戏的渐近(在牌数中，n)期望正确猜测次数以及更高时刻的精确，封闭形式公式。该问题采用两种不同的方法来解决:一种方法利用基于递归关系的快速生成函数来获得数值矩，而另一种方法是采用指标方法来寻找期望计数的符号方法。所得结果有助于现有的无反馈猜牌的文献。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Moments of the one-shuffle no-feedback card guessing game

We consider card guessing with no feedback, a variant of the game previously studied by Ciucu in 1998. In this study, we derive an exact, closed-form formula for the asymptotic (in the number of cards, n ) expected number of correct guesses, as well as higher moments, for a one-time riﬄe shuﬄe game under the optimal strategy. The problem is tackled using two diﬀerent approaches: one approach utilizes a fast generating function based on a recurrence relation to obtain numerical moments, while the other is the symbolic approach employing the method of indicators for ﬁnding expected counts. The results obtained contribute to the existing literature on card guessing with no feedback.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

12 weeks