RobertJasiek wrote:
Code:
B(-4.5)
/ \
D(1) E(-10)
/ \
F(-4) G(-13)
/ \
H(2) I(-10)
B has the tentative gote move value 5.5 and the tentative sente move value D(1) - F(-4) = 5. The tentative gote move value 5.5 is larger than the tentative sente move value 5. This condition identifies a local sente. So B is White's local sente.
This is still wrong, is it?
If indeed B is White's local sente, then B has the tentative sente count -4.
Code:
B(-4)
/ \
D(1) E(-10)
/ \
F(-4) G(-13)
/ \
H(2) I(-10)
Saying that B is White's local sente with the tentative sente move value 5 overlooks that, after the sente sequence from B to F, the follow-up gote move value at F is 6. The move value increases, that is, the tentative sente move value of B is smaller than the follow-up gote move value at F, that is, 5 < 6. Therefore, if the sente sequence from B to F is played, play does not stop but proceeds in alternation to I.
Since B is not a local sente but a traversal (that is, besides the types local gote, local sente, ambiguous and maybe local double sente, there is another type of local endgames: traversal), we discard the the tentative sente move value of B.
Code:
B
/ \
D(1) E(-10)
/ \
F(-4) G(-13)
/ \
H(2) I(-10)
B, being a traversal, has as its count the average of the counts of its followers D and I, that is, (1 + (-10)) / 2 = -4.5.
Code:
B(-4.5)
/ \
D(1) E(-10)
/ \
F(-4) G(-13)
/ \
H(2) I(-10)
We had that number for the count earlier but it was wrong nevertheless because it was associated with the wrong meaning of tentatively being a local gote. Now the count -4.5 of B is correct because it is associated with the correct meaning of being a traversal. (We must not take as a count what deceiptively looks right because of accidentally having the same number.)
***
Since B is a traversal, we may simplify the game by pruning the traversed nodes to get B':
Code:
B'
/ \
D(1) I(-10)
Note that B' does not have assigned its count yet. We determine it only now. B' is a simple gote so has the gote count -4.5.
Code:
B'(-4.5)
/ \
D(1) I(-10)
CGT tells us that B = B' from a value perspective if there are / will be no kos. Therefore, if first we determine the gote count -4.5 of B', we may then also use this value as the count of B. However, in B, this same count has a different meaning! Whilst in B' the count -4.5 is a gote count, in B the count -4.5 is a traversal count!
To recollect, suppose we are here when analysing B:
Code:
B
/ \
D(1) E(-10)
/ \
F(-4) G(-13)
/ \
H(2) I(-10)
From the count -4.5 of B', we know that this is also the count of B:
Code:
B(-4.5)
/ \
D(1) E(-10)
/ \
F(-4) G(-13)
/ \
H(2) I(-10)
From the earlier analysis of the game B (yes, B, not B'), we also know that B is a traversal so the assigned count of B is a traversal count derived from the counts of D and I.
Despite numerical equality, it would be wrong to say that the count of B could simply be calculated as the average of the counts of D and E. This would miss the meaning of the count, which is NOT a gote count but is a traversal count.
Did I say traversal was difficult? It is! :)