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pengvado comments on The Danger of Stories - LessWrong
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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 is more natural if you're brute-forcing maximin.
Auction Go is then a different game, some of whose moves are bidding in the auction rather than placing stones on the board. If you can bid fractional points, then the score is fractional, so move values can be too; and likewise for surreals or any other number system. The example you linked shows that changing the set of available bid-moves can change the outcome.