 If random sequences are taken to satisfy (at least) the conditions of the lack of aftereffect and invariance of subsequence selection under any selection rule, then Reichenbach’s restriction of subsequence selection rules to regular divisions implies that the set of normal sequences is a proper superset of that of random sequences. Reichenbach accepts this weakening to avoid some of the difficulties in characterizing a random sequence, and to broaden his earlier notions of probability to include sequences of trials, which might not be perfectly independent. In later writings, he seems to suggest that as long as the sequence converges, probability claims can be applied to the component events. 