I will use an imperfect dice for simplicity. Let's assume there are two factors that influence the probability of the results obtained from throwing a dice: 1) the way the dice is thrown and 2) imperfections of the dice. Let's assume that we know what is the probability distribution of the results for median values of the imperfections. We also know the probability distribution of the results assuming "normal" (i.e., known) techniques of throwing the dice. What is the probability distribution of the results considering both uncertainties? I came across the term "convolution" in my research, but it doesn't seem to make any sense in my case? What do you think? Any idea how to solve the problem without a Monte Carlo simulation?