American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2017, 5(5), 169-174
DOI: 10.12691/ajams-5-5-3
Open AccessArticle

New Prospective on Multiple Dice Rolling Game and Its Statistical Implications

Jimbo Henri Claver1, 2, , Jawad Azimi3 and Takeru Suzuki2

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

Pub. Date: December 26, 2017

Cite this paper:
Jimbo Henri Claver, Jawad Azimi and 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

Abstract

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.

Keywords:
MDR Game Chapman-Kolmogorov Equations simulation propensity statistics expectation and regression

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