Despite what many gamblers and sports fans think, simply believing and hoping won’t change outcomes. However, illusion of control, the belief that we have influence over random events or events in which we are powerless, is an extremely common mental heuristic. Multiple factors influence the illusion of control, making the effect stronger for some situations and individuals and negligible for others. These include the familiarity of the situation, the type of outcome, and the personalities and moods of the people. There is no clear cause of this heuristic. The consequences of this sense of control can be both positive (because it encourages us to try challenging experiences) and negative (because it can make us take unnecessary risks).
In one study, participants were shown to throw dice harder when they required a high number and softer when they required a small number. Dice velocity, of course, has no effect on the number rolled, but subjects still believed that they had control.