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.
Keywords
Cite
@article{arxiv.2306.16079,
title = {On Card guessing games: limit law for one-time riffle shuffle},
author = {Markus Kuba and Alois Panholzer},
journal= {arXiv preprint arXiv:2306.16079},
year = {2023}
}
Comments
18 pages, 2 figures; (references updated in version 2)