In this postscript the authors applaud Hahn and Warren's effort in their reply to remove the ambiguity in distinguishing events such as occurrence, occurrence at least once, and nonoccurrence in Hahn and Warren (2009). Still, it appears that differences between us exist regarding the nature of waiting time and its connections to the probability of nonoccurrence and the precedence relationships. In particular, the "limited and finite nature of people's experience" (Hahn & Warren, 2010, p. 706) remains the center of Hahn and Warren's arguments in accounting for the biases in people's perception of randomness, whereas they argue that it is the overlapping property of the local subsequences--rather than the length of the global sequence N--that plays a fundamental role in these seemingly paradoxical statistics. (Contains 1 table.)