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

Abstract

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.