Some investing-relevant conclusions in a new paper in the Journal of Gambling Studies. In essence, the subjects knew the odds, but stubbornly felt that they could perform better in games of chance than the odds dictated.
The results confirmed previous findings that problem gamblers tend to
be more irrational in their perceptions, as indicated by stronger
beliefs in the role of skilful play in chance activities, and that
gambling is a potentially profitable activity. However, counter
intuitively, problem gamblers did not appear to have any poorer
understanding of objective probabilities.