On card guessing with two types of cards

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2024-02-16 DOI:10.1016/j.jspi.2024.106160

Markus Kuba , Alois Panholzer

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引用次数: 0

Abstract

We consider a card guessing strategy for a stack of cards with two different types of cards, say $m_{1}$ cards of type red (heart or diamond) and $m_{2}$ cards of type black (clubs or spades). Given a deck of $M = m_{1} + m_{2}$ cards, we propose a refined counting of the number of correct colour guesses, when the guesser is provided with complete information, in other words, when the numbers $m_{1}$ and $m_{2}$ and the colour of each drawn card are known. We decompose the correct guessed cards into three different types by taking into account the probability of making a correct guess, and provide joint distributional results for the underlying random variables as well as joint limit laws.

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用两种卡片猜牌

我们考虑的是对一叠有两种不同类型牌的纸牌的猜牌策略，例如 m1 红牌（红心或方块）和 m2 黑牌（梅花或黑桃）。给定一副 M=m1+m2 的扑克牌，当猜牌者获得完整信息时，换句话说，当数字 m1 和 m2 以及每张抽出的扑克牌的颜色都已知时，我们建议对猜对颜色的次数进行精细计算。通过考虑猜对的概率，我们将猜对的牌分解为三种不同类型，并提供了底层随机变量的联合分布结果以及联合极限规律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.