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Electronic Journal of Combinatorics
Article . 2025 . Peer-reviewed
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Article . 2025
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https://dx.doi.org/10.48550/ar...
Article . 2023
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Article . 2025
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On Card Guessing Games: Limit Law for One-Time Riffle Shuffle

On card guessing games: limit law for one-time riffle shuffle
Authors: Markus Kuba; Alois Panholzer;

On Card Guessing Games: Limit Law for One-Time Riffle Shuffle

Abstract

We consider a card guessing game with complete feedback. A 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, where one after another a single card is drawn from the top, and shown to the guesser until no cards remain. Improving earlier results, we provide a limit law for the number of correct guesses. As a byproduct, we relate the number of correct guesses in this card guessing game to the number of correct guesses under a two-color card guessing game with complete feedback. Using this connection to two-color card guessing, we can also show a limiting distribution result for the first occurrence of a pure luck guess.

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Keywords

Combinatorial probability, Probability (math.PR), 05A15, 05A16, 60F05, 60C05, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, Central limit and other weak theorems, Combinatorics (math.CO), Asymptotic enumeration, Game theory, Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green
gold