Bar Bets and Generating Functions: The Distribution of the Separation of Two Distinct Card Ranks. Issue 3 (5th February 2021)

• Record Type: Journal Article
• Authors: Saunders, Arnold; Mahmoud, Hosam
• Is Part Of: American Mathematical Monthly. Volume 128:Issue 3(2021)
• Page Start: 258
• Page End: 264
• Publication Date: 2021-02-05
• Subjects: MSC: Primary 60C05 -- Secondary 05A15 -- 97A20; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/00029890.2021.1856581
• Languages: English
• ISSNs: 0002-9890

Abstract

ABSTRACT: What is the probability two distinct ranks (say, a king and a five) will appear within a card of one another in a shuffled deck? An old bar bet is predicated on it being nearly guaranteed. By modeling the outcome using a finite automaton, we construct the probability generating function for card rank separation. We then derive the corresponding probability mass function, mean, and variance. We conclude with an unimpressive modification to make the scam a virtual lock.