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Are there any standard ways or suggested ways one might predict the next binary digit based on a finite history and the probability of each digit?
yes, by disregarding the history and just looking at the probability of the digit. 70% chance of rolling a 0, 30% change of rolling a 1. in a truly random engine, it does not depend on the previous digit.
there is some concept in psychology where humans have a tendency to apply the ratios to small sample sizes. there's also some kind of gambler's fallacy which is under the similar umbrella.
or are you talking about pseudo-random numbers generated by a computer following some algorithm? which is a different topic altogether.
This post was edited by carteblanche on Feb 5 2017 09:53am