Oddly Wired
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control

You roll dice harder to influence the outcome.

People believe they have influence over random outcomes when they are personally involved in the process.

This is the illusion of control. In experiments, people wagered more money on lottery tickets they selected themselves versus those assigned to them, as if their choice gave them mastery over the laws of probability.

Agency is often confused with luck.

Where this comes from

Study
Langer, 1975
What the check found
The attribution to Ellen Langer's 1975 study is accurate and describes a well-established psychological phenomenon, though it is not present in the provided source material.
Confidence
Solid, with limits

Related

One of these every day, and every one names the study it came from. When a finding is contested, it says so.