This paper reports what the author believes to be the most thorough experimental examination to date of the randomization of shuffled cards, using statistical tests previously employed in nuclear physics to search for violations of physical laws by testing different radioactive decay processes for non-randomness. ![]() Not only mathematicians and scientists, but the general public as well have shown much interest in the card randomization problem, as reported in popular science periodicals and major news media. random walk diffusion theory theory of phase transitions), quantum physics, computer science, and other fields in which randomly generated data sequences are investigated. ![]() The methods employed transcend pure mathematics, and have implications for statistical physics (e.g. Proposed solutions to the problem of determining the number of shuffles required to randomize a deck of cards have drawn upon concepts from probability theory, statistics, combinatorial analysis, group theory, and communication theory. Introduction: The Card Randomization Problem Whereas mechanical shuffling resulted in significantly fewer rising sequencesġ. Number of manual shuffles matched very closely the theoretical predictionsīased on the Gilbert-Shannon-Reed (GSR) model of riffle shuffles, Number of shuffles and 4) the mean number of rising sequences as a function of Sensitive to different patterns indicative of residual order 2) as aĬonsequence, the threshold number of randomizing shuffles could vary widelyĪmong tests 3) in general, manual shuffling randomized a deck better than mechanical shuffling for a given Manually and by an auto-shuffling device were recorded sequentially andĪnalyzed in respect to 1) the theory of runs, 2) rank ordering, 3) serialĬorrelation, 4) theory of rising sequences, and 5) entropy and information theory.Īmong the outcomes, it was found that: 1) different statistical tests were Permutations of 52-cardĭecks, each subjected to sets of 19 successive riffle shuffles executed Randomizing shuffles, and 3) whether manual or mechanical shuffling randomizesĪ deck more effectively for a given number of shuffles. ![]() Whether different statistical tests yield different threshold numbers of Which of the two theoretical approaches made the more accurate prediction, 2) This paper reports a comprehensive experimentalĪnalysis of the card randomization problem for the purposes of determining 1) Which differed in how each defined randomness, has led to statistically different The two principal theoretical approaches to the problem, Question of how many shuffles are required to randomize an initially orderedĭeck of cards is a problem that has fascinated mathematicians, scientists, and
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