Shuffling Cards (with a flip)

April 2023

Introduction–The Shuffling Problem #

Card shuffling is an important part of playing any card game. When a card deck isn’t shuffled properly, it leads to uneven and unfair distribution of cards. It would certainly help if you knew what cards other players had!

Suppose we have a specified shuffling algorithm. Is it possible for us to guess the outcome of the card shuffling? Is it possible that the card deck will at some point return to its original configuration? In a previous article we explored ways of trying to guess the outcome of a specific type of card shuffling, known as the riffle shuffle. In this article, we modify the shuffling algorithm to introduce a flip that introduces some interesting complexities.

Card Shuffling

February 2022

An Interesting Card Trick #

The Problem #

Suppose you have a deck of $52$ cards. You perform a riffle shuffle on these cards. Can you say what the new position of the first card in the deck is, after the shuffle? What about the second card in the deck? The third? In general, is it possible to predict the new position of the $k$th card in the original deck after a new deck is produced through a riffle shuffle?