When I played The Sims I had a character who was me. And that character acted how I would act.
But every other character had their own kind of personality and so when I was playing them I made sure they stayed in their own respective character as well.
But when it's a game where you have less freedom I think Rad Link has it correct. There is a difficult to distinguish line that determines whether or not you feel it is 'you' or not.
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