Bar Bets and Generating Functions: The Distribution of the Separation of Two Distinct Card Ranks.

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. [ABSTRACT FROM AUTHOR]