They've actually done that in a psychology study. As in real life, the people with the advantage start inventing reasons why they deserved that advantage, and that it's really fair.
I think I remember reading about this and IIRC one of the players was given more starting money than the rest, but wasn't told about it. Then when they were asked why they think they won, they would say it was because of their strategy or their skill, and I think most even doubled down when they were told about the extra money. Something along those lines. My memory is likely inaccurate as well.
