Tyler Cowen argues in a TED talk (~15 min) that stories pervade our mental lives. He thinks they are a major source of cognitive biases and, on the margin, we should be more suspicious of them - especially simple stories. Here's an interesting quote about the meta-level:
What story do you take away from Tyler Cowen? ...Another possibility is you might tell a story of rebirth. You might say, "I used to think too much in terms of stories, but then I heard Tyler Cowen, and now I think less in terms of stories". ...You could also tell a story of deep tragedy. "This guy Tyler Cowen came and he told us not to think in terms of stories, but all he could do was tell us stories about how other people think too much in terms of stories."
I don't think you can use the birthday paradox here - since the expected values of go moves are best treated as being surreal numbers:
http://en.wikipedia.org/wiki/Surreal_number
Surreal numbers were actually originally developed to handle go move values:
http://senseis.xmp.net/?Infinitesimals
http://senseis.xmp.net/?GoInfinitesimals
But the only special value mentioned on those pages, = { 0 | 0 }, is not a surreal number. It's a combinatorial game, and every surreal number is a combinatorial game, but 0 ≤ 0, making non-numeric.
Also, while values of fragments of Go games are best treated as combinatorial games, the final value of a Go game is always simply an integer (or even an element of the set {WIN, DRAW, LOSS}), and therefore so will the maximin.