No Feedback? No Worries! The art of guessing the right card

Abstract

In 1998, Ciucu published "No-feedback card guessing for dovetail shuffles", an article which gives the optimal guessing strategy for $n$ cards ($n$ even) after $k$ riffle shuffles whenever $k>2{\log }_2\left(n\right)$. We discuss in this article the optimal guessing strategy and the asymptotic (in $n$) expected number of correct guesses for any fixed $k\ge 1$. This complements the work achieved two decades ago by Ciucu.