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Central limit theorem in complete feedback games

Part of: Stochastic processes Game theory Limit theorems

Published online by Cambridge University Press:  16 October 2023

Andrea Ottolini Open the ORCID record for Andrea Ottolini [Opens in a new window]  and
Raghavendra Tripathi
Andrea Ottolini*
Affiliation:
University of Washington
Raghavendra Tripathi*
Affiliation:
University of Washington
*
*Postal address: Department of Mathematics, University of Washington, Seattle, WA 98195, USA.
*Postal address: Department of Mathematics, University of Washington, Seattle, WA 98195, USA.
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Abstract

Consider a well-shuffled deck of cards of n different types where each type occurs m times. In a complete feedback game, a player is asked to guess the top card from the deck. After each guess, the top card is revealed to the player and is removed from the deck. The total number of correct guesses in a complete feedback game has attracted significant interest in the past few decades. Under different regimes of m, n, the expected number of correct guesses, under the greedy (optimal) strategy, has been obtained by various authors, while there are not many results available about the fluctuations. In this paper we establish a central limit theorem with Berry–Esseen bounds when m is fixed and n is large. Our results extend to the case of decks where different types may have different multiplicity, under suitable assumptions.

Keywords

Central limit theoremcomplete feedback gamescard guessing

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G70: Extreme value theory; extremal processes 91A60: Probabilistic games; gambling
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 2 , June 2024 , pp. 654 - 666
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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