1Department of Applied Mathematics and Statistics, Joint Waseda University, Tokyo, Japan and American University of Afghanistan, Faculty Building 1, D-22, Po.Box 458, Central Post, Kabul, Afghanistan
2Department of Applied Mathematics, Waseda University, Tokyo, Japan
3Japan International Cooperation Agency (JICA), Head Office, Kabul, Afghanistan
American Journal of Applied Mathematics and Statistics.
2017,
Vol. 5 No. 5, 169-174
DOI: 10.12691/ajams-5-5-3
Copyright © 2017 Science and Education PublishingCite this paper: Jimbo Henri Claver, Jawad Azimi, Takeru Suzuki. New Prospective on Multiple Dice Rolling Game and Its Statistical Implications.
American Journal of Applied Mathematics and Statistics. 2017; 5(5):169-174. doi: 10.12691/ajams-5-5-3.
Correspondence to: Jimbo Henri Claver, Department of Applied Mathematics and Statistics, Joint Waseda University, Tokyo, Japan and American University of Afghanistan, Faculty Building 1, D-22, Po.Box 458, Central Post, Kabul, Afghanistan. Email:
jimbo_maths@yahoo.comAbstract
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.
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