Moments of the one-shuffle no-feedback card guessing game

被引：1

作者：

Krityakierne, Tipaluck ^{[1
,3
]}

Siriputcharoen, Poohrich ^{[1
]}

Thanatipanonda, Thotsaporn Aek ^{[2
]}

Yapolha, Chaloemkiat ^{[1
]}

机构：

[1] Mahidol Univ, Dept Math, Fac Sci, Bangkok, Thailand

[2] Mahidol Univ, Int Coll, Div Sci, Salaya, Nakhon Pathom, Thailand

[3] Commiss Higher Educ, Ctr Excellence Math, Bangkok, Thailand

来源：

DISCRETE MATHEMATICS LETTERS | 2023年 / 12卷

关键词：

card guessing; higher-order moments; generating function; no feedback; combinatorics; method of indicators;

D O I：

10.47443/dml.2023.119

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider card guessing with no feedback, a variant of the game previously studied by Ciucu in 1998. In this study, we derive an exact, closed-form formula for the asymptotic (in the number of cards, n) expected number of correct guesses, as well as higher moments, for a one-time riffle shuffle game under the optimal strategy. The problem is tackled using two different approaches: one approach utilizes a fast generating function based on a recurrence relation to obtain numerical moments, while the other is the symbolic approach employing the method of indicators for finding expected counts. The results obtained contribute to the existing literature on card guessing with no feedback.

引用

页码：110 / 117

页数：8

共 20 条

[1] On card guessing game with one time riffle shuffle and complete feedback
Liu, Pengda
DISCRETE APPLIED MATHEMATICS, 2021, 288 : 270 - 278
[2] No-feedback card guessing for dovetail shuffles
Ciucu, M
ANNALS OF APPLIED PROBABILITY, 1998, 8 (04): : 1251 - 1269
[3] On card guessing games: Limit law for no feedback one-time riffle shuffle
Kuba, Markus
Panholzer, Alois
ADVANCES IN APPLIED MATHEMATICS, 2024, 156
[4] Card guessing with partial feedback
Diaconis, Persi
Graham, Ron
He, Xiaoyu
Spiro, Sam
COMBINATORICS PROBABILITY AND COMPUTING, 2022, 31 (01) : 1 - 20
[5] Guessing about Guessing: Practical Strategies for Card Guessing with Feedback
Diaconis, Persi
Graham, Ron
Spiro, Sam
AMERICAN MATHEMATICAL MONTHLY, 2022, 129 (07): : 607 - 622
[6] The card guessing game: A generating function approach
Krityakierne, Tipaluck
Thanatipanonda, Thotsaporn Aek
JOURNAL OF SYMBOLIC COMPUTATION, 2023, 115 : 1 - 17
[7] 'Learning' with no feedback in a competitive guessing game
Weber, RA
GAMES AND ECONOMIC BEHAVIOR, 2003, 44 (01) : 134 - 144
[8] Estimating depth of reasoning in a repeated guessing game with no feedback
Mariano Runco
Experimental Economics, 2013, 16 : 402 - 413
[9] Estimating depth of reasoning in a repeated guessing game with no feedback
Runco, Mariano
EXPERIMENTAL ECONOMICS, 2013, 16 (03) : 402 - 413
[10] Shuffle, Cut, and Learn: Crypto Go, a Card Game for Teaching Cryptography
Gonzalez-Tablas, Ana I.
Gonzalez Vasco, Maria I.
Cascos, Ignacio
Planet Palomino, Alvaro
MATHEMATICS, 2020, 8 (11) : 1 - 13

← 1 2 →