Improved Mixing Time Bounds for the Thorp Shuffle

DOI10.1017/S0963548312000478zbMATH Open1263.60066arXiv0912.2759OpenAlexW2054037105MaRDI QIDQ4903266

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Publication date: 21 January 2013

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Abstract: E. Thorp introduced the following card shuffling model. Suppose the number of cards $n$ is even. Cut the deck into two equal piles. Drop the first card from the left pile or from the right pile according to the outcome of a fair coin flip. Then drop from the other pile. Continue this way until both piles are empty. We show that if $n$ is a power of 2 then the mixing time of the Thorp shuffle is $O(lo{g}^{3}n)$. Previously, the best known bound was $O(lo{g}^{4}n)$.

Full work available at URL: https://arxiv.org/abs/0912.2759

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