A Mechanistic Model of the Wash Shuffle and Monte Carlo Exploration of its Impact on Card Shuffling in Texas Hold’em

In casino games using a standard deck of cards, a wash shuffle is sometimes performed prior to the rest of the card shuffling procedure. Unlike other methods of shuffling, the wash shuffle has not yet been well studied. To this end, we first develop a mechanistic model of the wash shuffle based on our observation of how cards tend to move when a wash shuffle is being performed. Then, we use this model to simulate the card shuffling procedure used in casino poker rooms, and explore the resulting impact on where the cards are dealt in the context of Texas Hold’em poker. We find that while the addition of the wash shuffle does produce probabilities in line with what would be expected from a perfect shuffle in terms of where individual cards will end after the shuffling is performed, it still shows deficiencies in terms of breaking up clumps of cards that have started next to each other, which has significant implications in games like Texas Hold’em in which several cards are dealt face up.