People seek for patterns and pay particular attention to streaks even when they are generated by a random process. The present paper examines statistics of pattern time in sequences generated by Bernoulli trials. We demonstrate that streak patterns possess some statistical properties that make them uniquely distinguishable from other patterns. Because of the uncontaminated continuity, streak patterns have the largest amount of self-overlap, resulting in the longest waiting time and the largest variance of interarrival times. We then discuss the psychological implications of pattern time such as in memory encoding and perception of randomness.