College of Science and Mathematics

Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2001

This study aimed to measure the uncertainty in the two kinds of perfect faro shuffle, the in-shuffle and the out-shuffle. The method used to measure the uncertainty was entropy, which was formulated by Shannon, Wiener, and Fisher (1948 as cited by Trefethen and Trefethen, 1998). The result showed that, for the in-shuffle, as the number of cards involved in the shuffle increases, the number of states that the cards undergo also increases, thus the entropy, or the measured unpredictability, increases. The out-shuffle exhibited a more erratic behavior with the respect to the shuffle made. Nevertheless, it also showed that the unpredictability of the sequence depends on the number of shuffles required to return the cards to the original order. It was also observed that the in-shuffle was more unpredictable than the out-shuffle, based on their corresponding computed entropies. Measuring the uncertainty of sequences generated by the combination of in- and out-shuffles, different cuts of the deck, or odd quantities of cards and using a different, preferably local, measure uncertainty in determining unpredictability are probable extensions of this study.