New Prospective on Multiple Dice Rolling Game and Its Statistical Implications

Jimbo Henri Claver^{1, 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

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

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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