People are often biased in their perception of randomness in that they tend to see patterns in random distributions. This is a serious problem because the accurate perception of randomness can be important in decision-making. This research presents three experiments investigating (a) the generality of this bias in randomness perception and (b) the trainability and transfer of the ability to judge randomness. The three experiments replicated the finding that people tend to judge random sequences as systematic. However, no evidence was obtained that the same bias occurs in judging lottery outcomes, thus calling into question the generality of the bias. No evidence was found for reducing people's perception bias with a short period of training. No evidence was found for far transfer though near transfer did occur.