Dunn, D. S., & Wilson, T. D. (1990). When the stakes are high: A limit to the illusion-of-control effect. Social cognition, 8(3), 305-323.

Three studies investigated a boundary condition on the illusion-of-control effect (the tendency to behave as if one can control random events). Subjects wagered poker chips on the roll of a die, either to win money or to reduce the amount of time they would have to spend on unpleasant tasks. To induce illusory control, half of the subjects were allowed to choose the face of the die on which they would bet and were told they would throw the die. In addition, each chip represented either a small or large amount of money or task time. When potential costs were low, subjects with illusory control wagered more and were more confident of winning than were subjects without illusory control. When potential costs were high, illusory control had no effect on wagers or confidence. Preliminary evidence was found for a mood interpretation of these results. The illusion of control increased positive affect in both the low- and high-cost conditions. When costs were low, this positive affect may have been responsible for the increased wagering. Raising the stakes of the wager may have dampened this desire to take risks because there was more of a potential cost of doing so.