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BQM 127
Path: BigQuestionMark · Prev: BQM126 · Next: BQM128
Keywords: EndGame, Question
From MiaiValuesList100To199, Robert Pauli: Let me have a try. Let's first switch colors to have no negatives (Black's lead normally is positive) and switch sides to have Black increase his score by going to the right (in tree and position):
We want to know how much . / \ / a \ . 4 / \ / b \ 0 . / \ / d \ . 3 / \ / e \ . 2 / \ / f \ 0 1 Each node and leaf corresponds to a position (and the position's value). The root (top node) corresponds to the position above (with a-f being empty). The label beneath each node indicates the intersection either Black (right branch) or White (left branch) took to reach the next node (or leaf). Each leaf is labeled with the (local) score of its corresponding position (which is in the "turn doesn't matter" state). So, if White takes a as well as b, for instance, Black gets nothing (0), etc. Still missing are the node values. To find them, we average daughter values and work our way up: .------2 + 1/2 + 1/32 / \ / a \ 1 + 1/16----. 4 / \ / b \ 0 .------2 + 1/8 / \ / d \ 1 + 1/4-----. 3 / \ / e \ 1/2-----. 2 / \ / f \ 0 1 White's move in question goes from node 2 + 1/2 + 1/32 to 1 + 1/16 (minus) ---------------- 1 + 1/2 - 1/32 = 1.46875 Ok, that was that (except for some ugly rounding). But let me add a warning. It's just an incident that the branches above are labeled with one move each. In general, sente follow-ups are appended! For instance, the value of this position
is not .------4 + 3/4 / \ / a \ . 6 / \ / b \ . 5 / \ / c \ 0 4 but rather .------5 a+bc / \ a / \ 4 6 because White's bc follow-up is sente.
If a move is sente or not can be checked with the
method of multiples.
Take, say, four copies of the 5-deep 2-goodies corridor
with a white stone at a in each and treat
Then treat
Conclusion: Black should treat So, in case of sente there is no branching. The value of the 5-deep 2-goodies corridor with a white stone at a, for example, would simply be 4, as if there's no alternative. Hope that carries a while.
Robert Pauli: . . / \ a-cd / \ a \ or \ 4 . c+de / \ c / \ 3 5 (appending opposing sente follow-ups with minus)
There's a choice because after In the second case Black treats it as gote. However, White has a sente follow-up at d: 3 + 3 + 3 + 3 > 0 + 3 + 4 + 4. Path: BigQuestionMark · Prev: BQM126 · Next: BQM128 This is a copy of the living page "BQM 127" at Sensei's Library. ![]() |