When is a deck of cards well shuffled?
R. Tebbens (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Mathijs Joosten – Mentor
Mark C. Veraar – Mentor (TU Delft - Analysis)
B. van den Dries – Mentor (TU Delft - Analysis)
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Abstract
When is a deck of cards shuffled good enough? We have to perform seven Riffle Shuffles to randomize a deck of 52 cards. The mathematics used to calculate this, has some strong connections with permutations, rising sequences and the L1 metric: the variation distance. If we combine these factors, we can get an expression of how good a way of shuffling is in randomizing a deck. We say a deck is randomized, when every possible order of the cards is equally likely. This gives us the cut-off result of seven shuffles. Furthermore, this gives us a window to look at other ways of shuffling, some even used in casinos. It turns out that some of these methods are not randomizing a deck enough. We can also use Markov chains in order to see how we randomize cards by ”washing” them over a table.