  Within the context of the binomial model, we analyse sequences of values that
are almost-uniform and we discuss a prediction method called the frequent
outcome approach, in which the outcome that has occurred the most in the
observed trials is the most likely to occur again. Using this prediction method
we derive probability statements for the prior probability of correct
prediction, conditional on the underlying parameter value in the binomial
model. We show that this prediction method converges to a level of accuracy
that is equivalent to ideal prediction based on knowledge of the model
parameter.
