how would you choose to analysis the next single dice roll if you have the past 100(or more) results? Any other ideas beside averaging?
edit: sorry im not sure why this is moderated and put on hold. i have search for this and read the first few pages but did not find any solutions; and also not sure what other info i should include as i think its quite clear what the question is. pls advice.
Thank you,
It really depends on what you know about the die and how much you are sure about it.
If you built the die yourself, and you are absolutely sure it is a fair die, then whatever the first 100 outcomes were, they will have been the product of pure chance, and your die remains just as a fair dice as before.
If you have a high degree of confidence that the die should be a fair one, but you saw something really very atypical in the first 100 outcomes, then the Bayesian approach would be to weight your prior feelings about the die by the likelihood ratio of what you found.
The frequentist may tell you to just suppose the probabilities for the next round are given by the relative frequencies of previous observations. Problem is, if this person goes to a Casino and sees the roulette has come 10 consecutive times heads, they will put their money on heads against tails even with a mild payoff, and soon this person will be bankrupt.
Otherwise it is hard to answer this question here. Even the experts in the field won't have consensus...