Riffle shuffles of decks with repeated cards. (English) Zbl 1099.60007

This paper considers the problem of shuffling cards: How many shuffles mix a deck of cards? It deals with riffle shuffling, which is the most common way of shuffling cards. In many instances, not all cards in the deck are distinct and only the sets of cards dealt out of players, and not the order in which they are dealt out to each player, need to be random. The authors derive transition probabilities under riffle shuffles between decks with repeated cards to cover some instances of the type just described. They focus on decks with cards all of which are labeled either 1 or 2 and describe the consequences of having a symmetric starting deck of the form \(1,\dots,1,2,\dots,2\) or \(1,2,\dots,1,2\). Finally, mixing times for common card games are considered.


60C05 Combinatorial probability
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)


mixing times
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