{"title":"On card guessing games: Limit law for no feedback one-time riffle shuffle","authors":"Markus Kuba , Alois Panholzer","doi":"10.1016/j.aam.2024.102689","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the following card guessing game with no feedback. An ordered deck of <em>n</em> cards labeled 1 up to <em>n</em> is riffle-shuffled exactly one time. Then, the goal of the game is to maximize the number of correct guesses of the cards. One after another a single card is drawn from the top, the guesser makes a guess without seeing the card and gets no response if the guess was correct or not. Building upon and improving earlier results, we provide a limit law for the number of correct guesses and also show convergence of the integer moments.</p></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0196885824000204","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the following card guessing game with no feedback. An ordered deck of n cards labeled 1 up to n is riffle-shuffled exactly one time. Then, the goal of the game is to maximize the number of correct guesses of the cards. One after another a single card is drawn from the top, the guesser makes a guess without seeing the card and gets no response if the guess was correct or not. Building upon and improving earlier results, we provide a limit law for the number of correct guesses and also show convergence of the integer moments.
我们考虑下面这个没有反馈的猜牌游戏。一副有序的扑克牌由 n 张标有 1 至 n 的扑克牌组成，正好洗一次。然后，游戏的目标是最大限度地提高猜中牌的正确率。一张接一张的牌从最上面抽出，猜牌者在没有看到牌的情况下进行猜测，猜对与否不会得到任何回应。在先前研究成果的基础上，我们提出了正确猜测次数的极限规律，并证明了整数时刻的收敛性。
期刊介绍：
Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas.
Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.
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