If it's random, then the probability that the same case of output will occur forever is zero. Here the probability of hitting the terminating case occurs with p

If it's random, then the probability that the same case of output will occur forever is zero. Here the probability of hitting the terminating case occurs with p=(1 - 250/256). You aren't going to randomly roll 6/256 enough times in a row to notice within the age of the universe. This is the standard method for selecting a uniform range from a source that is not an exact multiple. The worst-case probability of having to draw again can always be kept under 0.5. For example, I want a number in the range of (0 <= n < 129).