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Refutation of the Bayer-Diaconis-McGrath conjecture for the riffle shuffle card guessing game with feedback

Abstract : We consider the following card guessing game with feedback, introduced in [BD92]. An initially ordered deck of cards is shuffled via one or several riffle shuffles (or more generally: one a-shuffle). The player guesses the card on top of the deck, then looks at that card. The player then guesses the next card, looks at that card etc. until there is no card left, and his goal is to get as many correct guesses as possible. The authors detail a simple guessing strategy conjectured to be optimal. We show that this strategy is optimal in the case of a single riffle shuffle but not in general. The present note was sent to Professor Persi Diaconis in June 2018 and is extracted from the Master's thesis [Gal18].
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https://hal.archives-ouvertes.fr/hal-03324629
Contributor : Florian Galliot Connect in order to contact the contributor
Submitted on : Monday, August 23, 2021 - 5:38:31 PM
Last modification on : Sunday, August 29, 2021 - 3:20:55 AM

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Note to Persi Diaconis 2021.pd...
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  • HAL Id : hal-03324629, version 1

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Florian Galliot. Refutation of the Bayer-Diaconis-McGrath conjecture for the riffle shuffle card guessing game with feedback. [Other] Sorbonne Université / Université Pierre et Marie Curie - Paris VI. 2018. ⟨hal-03324629⟩

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