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."
The other infinitesimals listed on that page were: UP, DOWN, UPSTAR, DOWNSTAR, TINY, MINY.
The idea that you can subtract the maximin of a move with the maximin of passing to produce move values is unfortunately not correct, due to subtleties over who gets to play last.
Move values are surreal numbers. That isn't an artefact designed to cope with partial games, it's equally true of complete games.
The point is not trivial to understand - but it is relatively easy to see that the conclusion (that go move values are not integers) is correct. To do that, simply work through the whole board example given here:
http://groups.google.com/group/rec.games.go/msg/dc42f06aa5ad6bc1?hl=en&dmode=source
Who said anything about subtracting the value of passing? Passing is just another move, and has no inherent privilege over the other ~200 available moves. Ah, that's where I was confused by your terminology: you speak of the value of a board state, which must account for what happens when either player plays on it, and passing doesn't affect the board; whereas I was thinking of the value of a game state including whose turn it is, and passing transitions to a different game state. The former is more natural if you're analysing partial games, and the latter... (read more)