发表机构
University of the Ryukyus（冲绳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对广义扑克牌组（花色与点数可任意设定），推导随机选取牌中配对数量的均值与方差精确公式（含高斯超几何函数），并给出点数趋于无穷时的渐近行为。
AI 中文摘要
本研究分析了从一副扑克牌中随机选取的一组牌中配对（即同点数两张牌）的数量。标准扑克牌组由52张牌组成，不含王牌，有4种花色和13个点数，而我们的分析考虑了一个广义牌组，其中花色和点数的数量可以任意设定。我们推导了从该广义牌组中随机选取给定数量的牌时，配对数量的均值和方差的精确公式，并使用高斯超几何函数表示。此外，我们推导了当点数趋于无穷大时，均值和方差的渐近行为。
英文摘要
In this study, we analyze the number of pairs (i.e., two cards of the same rank) in a set of cards randomly selected from a deck of playing cards. While the standard deck of playing cards comprises 52 cards excluding the joker with 4 suits and 13 ranks, our analysis considers a generalized deck where the numbers of suits and ranks can be set arbitrarily. We derive the exact formulas for the mean and variance of the number of pairs in a given number of cards randomly selected from this generalized deck, expressed using the Gauss hypergeometric function. Moreover, we derive the asymptotic behavior of the mean and variance as the number of ranks tends to infinity.
Comments14 pages, 4 figures
