期刊名称：American Journal of Applied Mathematics and Statistics
印刷版ISSN：2328-7306
电子版ISSN：2328-7292
出版年度：2017
卷号：5
期号：5
页码：169-174
DOI：10.12691/ajams-5-5-3
出版社：Science and Education Publishing
摘要：We present a mathematical formulation of the Multiple Dice Rolling (MDR) game and develop an adaptive computational algorithm to simulate such game over time. We use an extended version of the well-known Chapman-Kolmogorov Equations (CKEs) to model the state transition of the probability mass function of each side of the dice during the game and represent the time-dependent propensity of the game by a simple regression process, which enable to capture the change in the expectation over time. Furthermore, we perform a quantitative analysis on the outcome of the game in a framework of Average Probability Value (APV) of appearance of a side of the dice over trials. The power of our approach is demonstrated. Our results also suggest that in the MDR game, the APV of appearance of a side of a dice can be appropriately predicted independently of the number of sides and trials.
关键词：MDR Game; Chapman-Kolmogorov Equations; simulation; propensity; statistics; expectation and regression
