在這篇論文中我們研究n張牌要洗幾次才會均勻的問題.Aldous (1983) 證明當n很大時,大約要洗8.55次(n=52時).而Bayer和Diaconis (1992) 使用 variation distance的方法,說明當n為52張撲克牌時,洗7次就足夠了.然而前述的結論皆需用較深的數理統計理論去推導,這裡,我們提供一個簡單的方法去探討洗牌的隨機性,這個方法結合了適合度檢定與簡單的模擬步驟.模擬的結果說明了我們的結論與Bayer和Diaconis的結論是相似的.

In this paper we analyze how many shuffles are necessary to get close to ran- domness for a deck of n cards. Aldous (1983) shows that approximately 8.55 (n=52) shuffles are necessary when n is large. Bayer and Diaconis (1992) use the variation distance as a measure of randomness to analyze the most commonly used method of shuffling cards, and claim that 7 shuffles are enough when n=52. We provide another idea to measure the distance from randomness for repeated shuffles. The proposed method consists of a goodness of fit test and a simple simulation. Simulation results show that we have a similar conclusion to that of Bayer and Diaconis.

1 Introduction ...1
2 The riffle shuffle ...2
3 A measure of randomness: the variation distance ...5
4 A statistical method of measuring randomness ...7
4.1 A chi-square goodness of fit test ...7
4.2 Simulation procedure ...9
4.3 Example ...13
4.4 Simulation results ...14
5 Conclusion ...17
Reference ...18

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