A Natural Law of Succession

Abstract:

Consider the following problem. You are given an alphabet of $k$
distinct symbols and are told that the i-th symbol occurred exactly
n_i times in the past. On the basis of this information alone, you
must now estimate the conditional probability that the next symbol
will be i. In this report, we present a new solution to this
fundamental problem in statistics and inductive reasoning. Our
solution overcomes all practical difficulties encountered by standard
approaches without requiring any special prior knowledge.