eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2017-12-26 5 5 169 174 10.12691/ajams-5-5-3 AJAMS2017553 article Jimbo Henri Claver jimbo_maths@yahoo.com 1 2 Jawad Azimi 3 Takeru Suzuki 3 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 Japan International Cooperation Agency (JICA), Head Office, Kabul, Afghanistan 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. http://pubs.sciepub.com/ajams/5/5/3/ajams-5-5-3.pdf MDR Game Chapman-Kolmogorov Equations simulation propensity statistics expectation and regression