 Primary or fundamental inductive inference consists of taking observed relative frequencies as probabilities, that is, as limiting relative frequencies. This procedure, referred to as the “straight rule”, implies that one should take the current empirical distribution to resemble the limiting distribution, and therefore behave accordingly. The justification of such taking, or “positing” in Reichenbach’s terminology, is that if there is a limiting relative frequency to a sequence, this procedure will converge to it. Reichenbach notes in The Theory of Probability (1949f) that without further assumptions nothing can be said about rates of convergence or about the warranted confidence that an empirical distribution has converged. He further acknowledges that any procedure that estimates the probability to be the relative frequency, plus any quantity that keeps the estimate between 0 and 1 and that itself converges to 0, will also converge to the limiting frequency if such exists. He there (misleadingly) treats such alternative inductive rules as producing “equivalent descriptions” to the straight rule and takes the choice as of no consequence—but of course the equivalence is only in the limit. In Experience and Prediction (1938c) he instead dismisses such alternative rules on the vague grounds that they are “riskier” than the straight rule. 