Keywords
Markov Chain, Card Shuffles, Interactive

Technologies
Python, Dash, Plotly, Manim

A study of the Random-to-Top card shuffling scheme, a simple list shuffling scheme wherein an item is selected at random and moved to the top of the list. This often arises as the Move-to-Front rule for cache maintenance in computer science.

Building upon the results of the work done by Persi Diaconis, and others, to produce a Markov Chain that models Random-to-Top shuffling. The Markov Chain can then be used to assess convergence speeds for a number of variations of the shuffle.

The main output of this project is a Python based Dash application that provides a walkthrough of the mathematics behind the Markov Chain, while allowing users to explore the properties of the shuffle in particular. It makes use of Plotly visualisations and Manim animations to create an interactive educational environment.