Kuba, M., & Panholzer, A. (2025). On Card Guessing Games: Limit Law for One-Time Riffle Shuffle. Electronic Journal of Combinatorics, 32(3), Article P3.19. https://doi.org/10.37236/13539
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
-
Journal:
Electronic Journal of Combinatorics
-
ISSN:
1077-8926
-
Date (published):
2025
-
Number of Pages:
25
-
Publisher:
ELECTRONIC JOURNAL OF COMBINATORICS
-
Peer reviewed:
Yes
-
Keywords:
Card guessing; Riffle shuffle; Complete feedback; Limit law
en
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.
