Well, classic problems in statistical analysis deal with "overdispersion"—e.g., the ratio of boys to girls in individual families has a variance too high to be

Well, classic problems in statistical analysis deal with "overdispersion"—e.g., the ratio of boys to girls in individual families has a variance too high to be modeled as a simple binomial distribution, so you can model it as a beta-binomial. In games, the challenge is the opposite: to generate distributions that with less variance in order to convince people that the random number generator is "fair". You don't have to do this, but some games will tweak the numbers so they're not independent, to keep the sample mean close to its asymptotic value. In other words, if you have a losing streak, the software steps in and breaks it for you, so that you think the RNG is "fair".