@article{ajams2017553,
author={{Claver, Jimbo Henri and Azimi, Jawad and Suzuki, Takeru},
title={New Prospective on Multiple Dice Rolling Game and Its Statistical Implications},
journal={American Journal of Applied Mathematics and Statistics},
volume={5},
number={5},
pages={169--174},
year={2017},
url={http://pubs.sciepub.com/ajams/5/5/3},
issn={2328-7292},
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.},
doi={10.12691/ajams-5-5-3}
publisher={Science and Education Publishing}
}