I mean, suppose I do know a person who has trouble letting sunk causes go, and has probably firmly forgotten about the Bayes theorem, and uses arguments as soldiers on occasion... But she is far more active than me, she keeps trying out new things, seeking out jobs even beyond her experiences etc. Should I consider her rational? I don't know. Brave, yes. Rather smart, yes. Winning, often. But rational?

Winning = rational, rational = winning. If you define rational as something other than "the intellectual means of winning", there's no point other than a religious fetish for a theorem that's difficult to compute with.