Well, I don't think I'd fare better by thinking less rationally; and if I really needed to find a way to win, rationality at least shouldn't hurt me me in the process.

I was hoping to be pithy by neglecting a few implicit assumptions. For one, I mean that (in the absence of direct rewards for different cognitive processes) good rationalists shouldn't systematically lose when they can see a strategy that systematically wins. Of course there are Kobayashi Maru scenarios where all the rationality in the world can't win, but that's not what we're talking about.