No-feedback Card Guessing Game: Moments and distributions under the optimal strategy

Date: September 10, 2022

This is our third take on the card guessing game, riffle shuffle version. After finding the optimal guessing strategy (maximize the expected number of correct guesses) of the decks of n cards after k riffle shuffles (no feedback version) in the previous paper, we now look at the distributions of these number of correct guesses. The techniques that have been used are recurrence relations, the method of overlapping stages and some interpolations. The paper is a little bit long (36 pages) as we want to spell out all the details. The first time reader could skip the appendices (8 pages long!). Enjoy!

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Paper: No-feedback Card Guessing Game: Moments and distributions under the optimal strategy

Accompanied Maple program: GenMoment

Sample Input-Output: Commands that were mentioned in the paper