Fredrik Sköld: Kortblandningar, Markovkedjor och Simulering av Doyle's patiens

Abstract

The GSR model (Gilbert-, Shannon and Reed) is a mathematical model of the common riffle shuffle method of shuffling playing card. This paper examines the mathematics of the GSR model and card shuffling in general. The main mathematical theory used in this paper is the theory about Markov chains. This paper describes the GSR model and how it can be used to determine when a deck of cards is sufficiently shuffled. In addition, this paper examines the requirements for a card shuffling method for it to converge to the uniform distribution over all possible orderings of the card deck. This paper also shows that the requierement for a sufficiently shuffled card deck may vary depending on the intended use of the card deck, i.e. the game to be played. Therefore, this paper looks at examples of card games when the necessary distance to the uniform distribution varies. To measure the distance to the uniform distribution after a certain amount of GSR shuffles, the Total Variation distance is used. The paper also includes simulations of playing a specific card game, New Age solitaire, using GSR shuffles and other shuffling methods.

Zoom notes: Password required, contact arias@math.su.se