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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0719106-131107 |
| Date | 19 July 2006 |
| Creators | Lin, Chia-Hui |
| Contributors | Mong-Na Lo Huang, Chin-San Lee, Mei-Hui Guo, Fu-Chuen Chang |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0719106-131107 |
| Rights | off_campus_withheld, Copyright information available at source archive |
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