Year: 2025
Type: article
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.
DOI: 10.37236/13539
Authors: Markus Kuba, Alois Panholzer
Institutions: University of Applied Sciences Technikum Wien, TU Wien
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413131546