On Card guessing games: limit law for no feedback one-time riffle shuffle

TL;DR

This paper analyzes a card guessing game with no feedback after a single riffle shuffle, establishing a limit law for the number of correct guesses and demonstrating convergence of moments.

Contribution

It provides a new limit law and moment convergence results for the number of correct guesses in a no-feedback card guessing game after one riffle shuffle.

Findings

Established a limit law for correct guesses

Proved convergence of integer moments

Improved upon previous results in the field

Abstract

We consider the following card guessing game with no feedback. An ordered deck of n cards labeled 1 up to n is riffle-shuffled exactly one time. Then, the goal of the game is to maximize the number of correct guesses of the cards. One after another a single card is drawn from the top, the guesser makes a guess without seeing the card and gets no response if the guess was correct or not. Building upon and improving earlier results, we provide a limit law for the number of correct guesses and also show convergence of the integer moments.