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.
@article{10_37236_13539,
author = {Markus Kuba and Alois Panholzer},
title = {On card guessing games: limit law for one-time riffle shuffle},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/13539},
zbl = {8097647},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13539/}
}
TY - JOUR
AU - Markus Kuba
AU - Alois Panholzer
TI - On card guessing games: limit law for one-time riffle shuffle
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/13539/
DO - 10.37236/13539
ID - 10_37236_13539
ER -
%0 Journal Article
%A Markus Kuba
%A Alois Panholzer
%T On card guessing games: limit law for one-time riffle shuffle
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/13539/
%R 10.37236/13539
%F 10_37236_13539
Markus Kuba; Alois Panholzer. On card guessing games: limit law for one-time riffle shuffle. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13539
