No-feedback Card Guessing Game: Moments and distributions under the optimal strategy
Combinatorics
2022-09-20 v2
Abstract
Relying on the optimal guessing strategy recently found for a no-feedback card guessing game with -time riffle shuffles, we derive an exact, closed-form formula for the expected number of correct guesses and higher moments for a -time shuffle case. Our approach makes use of the fast generating function based on a recurrence relation, the method of overlapping stages, and interpolation. As for -time shuffles, we establish the expected number of correct guesses through a self-contained combinatorial proof. The proof turns out to be the answer to an open problem listed in Krityakierne and Thanatipanonda (2022), asking for a combinatorial interpretation of a generating function object introduced therein.
Keywords
Cite
@article{arxiv.2209.04276,
title = {No-feedback Card Guessing Game: Moments and distributions under the optimal strategy},
author = {Tipaluck Krityakierne and Poohrich Siriputcharoen and Thotsaporn Aek Thanatipanonda and Chaloemkiat Yapolha},
journal= {arXiv preprint arXiv:2209.04276},
year = {2022}
}