Conditions of low and high perceived control often lead to boredom, albeit for different reasons. Whereas, high perceived control may be experienced as boring because the situation lacks challenge, low perceived control may be experienced as boring because the situation precludes effective engagement. In two experiments we test this proposed quadratic relationship. In the first experiment we had participants play different versions of the children's game “rock-paper-scissors” in which they arbitrarily won or lost. Despite having only dichotomous conditions, participants reported experiencing a broad range of levels of perceived control. Consistent with our predictions, boredom was highest at low and high levels of perceived control. Experiment 2 tested the notion that the mere prospect of gaining control may mitigate boredom. Participants given to believe that they could gain control over the game of rock, paper, scissors were less bored than those who believed there was no possibility of winning at greater than chance levels. This suggests that beliefs concerning prospective control, rather than a given level of perceived control per se, may predict engagement and boredom.