perceval wrote:
a function B(x,y) on the coordinate of the go board such as:
B(x,y)=1 if the intersection if an indisputable point for B
B(x,y)=0 if the intersection if an indisputable point for W
Whatever you define "indisputable" to be, such is too simplifying because it does not distinguish the intersection's degrees and in particular does not distinguish Black's connection status from White's connection status from Black's life status from White's life status from Black's territory potential from White's territory potential. By ignoring degrees and putting the three aspects in the same bowl, you only get a too rough approximation of the kind yes or no for "Black has non-negative and White has negative connection status there AND Black has non-negative and White has negative life status there AND Black has but White has not territory there". IOW, all that you get is a special case of my model.
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The sum of B(x,y) on the whole board gives the score difference at the end of the game[/list]
Wrong. Influence changes dynamically (at least) until the game end! You only get the score difference at the game end if the game end is already reached. For that, simpler models than yours suffice.
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This can be losely interpreted as the probability that a given intersection will be B or W at the end of the game
Who cares? Influence is relevant DURING the game and not for predicting which intersections score for whom at the game end. If you want that, then a territory definition similar to n-connected is useful: how often a player can pass while an intersection is still his territory.
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but this interpretation misses the case of a dead stone with some aji that will help make some point elsewere even if its dead.
Use my model and you get such information implicitly.
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you can disagree with that definition
The point is not that one would need to disagree with the definition but that it provides by far too little information!
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if you want but that is what i am going to talk about, it seems an interesting object as being able to compute it for all posistion would solve the game.
No. Too little information.
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As i do not have a god complex i just want to throw some ideas to compute an [u]approximation [/u]of this function.
You are too pessimistic. As a special case of my model along the thoughts outlined above, calculation is reasonably possible for human beings. Only PCs can have greater problems because they are in greater need of reducing computational complexity related to proof-play game tree exploration.
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should have the same influence than:
No. Not the same. One has a *-alive group. The other has a 2-alive group. For practical purposes, this is almost the same. Almost but not exactly.
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The algo has good properties for the issues above:
it "blocks" influence from inner stone from spilling out of a closed shape.
This is insufficient since some influence can spread from inside to outside.
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