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Ambiguous Position Discussion
Black has a 1 point gote (MiaiCounting) with B a - W b, B c, or a 1-point sente with B c - W a. Not sure if I can follow your counting here. If B plays c, then W will get the additional point at b, since in the given position, there's no need to defend further. Consequently, if the gote move is considered worth 1 point for B, then the sente move is worth zero (ignoring the reverse gote possibility for w, of course). --GeorgMischler 2k Let's normalize the count, so that the result if Black plays 'c' and White plays 'a' is 0. Then we may represent the position like this: {{Big | 0}, 1 | -1} ("Big" means big enough for sente. Here it is more than 5, I think. Negative numbers are White scores. Positions or scores to the left of the bar are reached by Black moves, those to the right are reached by White moves.) {1 | -1} is a 1 point gote. {{Big | 0} | -1} is a 1 point sente. Make sense? -- BillSpight Assuming that I understand your notation correctly: If the {{Big | 0} | -1} is meant to be one point sente (0 - -1 = 1), then {1 | -1} still looks a two point sente to me in comparison (1 - -1 = 2). Please don't get me wrong, I really like the discussion about chosing the "right" move here, especially considering the (still sente!) "Big" follow-up. I just don't see the ambiguity. Or maybe my real world understanding of the term "ambiguity" is too narrow to be applied here. Now if we could determine the exact point value of getting sente, things might become much more obvious... --GeorgMischler Sorry. I have amended the original to state that I am using miai counting. That's the one to use when comparing plays. You are using deiri counting, which is more common. The rule for comparing deiri plays is to multiply sente values by 2 (or, equivalently, to divide gote values by 2, which gives you miai values). So the 2-point gote and the 1-point sente are the same size. -- Bill
Ah well, even I can understand it if you explain it this way! ;-) --GeorgMischler
--Jesusin (3K): I am confused about the following position.
'a' is W sente. A B's move at 'a' is worth 1 point in anti-sente. 'f' is worth 1 point in gote (MiaiCounting). So both moves should be equivalent, but... 1. a b c d e f leads to a jigo 2. f g d a c leads to B winning by 1 point Please help me! I can not understand it! Bill: First, to address the life and death issue.
After W 2, B 3 makes ko. If W 4, B 5 and White cannot play at a.
Another way to make ko.
The players prefer different plays because they are trying to get tedomari, the last play. Getting the last (1 point) play makes a difference of 1 point, here. Getting the last 1 point play is discussed in Chilling, Infinitesimals, Playing Infinitesimals, et al. In terms of infinitesmals a is * (STAR) and b is ^ (UP). ^ has an atomic weight? of 1, while * has an atomic weight of 0. Atomic weight is similar to the count of external liberties? in a semeai. A White play at b changes the local position (c) to *, with atomic weight of 0, reducing Black's atomic weight by 1. That is like filling one of Black's liberties in a semeai. A Black play at a does not change the atomic weight. That is like not filling one's own liberty.
But you have to take miai into account. In this diagram a and d are miai. That means that Black should play at b to get tedomari.
Black wins by 1 point.
If B 1 (or 6), White gets tedomari, for jigo. --Jesusin (3K): SL's 'LordOfTheYose' is always right ;-). Thanks for the enlightment, Bill. I have been working on this and I now think 'b' in 'Diag:Which 1 pt. play?' is sente for W and is a 1/2 point gote play for B. I will try to prove it:
'a' is 1/2 point gote. If it was W turn, she would take her sente at 'b' and then 'a' to win. If it is B turn, B 'b', W atari, B connects, W 'a' is jigo. And B 'a', W 'b' B connects is jigo too.
Bill: Basically the size of a play is a local phenomenon. It is not true that, on the whole board, the largest play is always the best play, nor that two plays of different sizes always lead to different results.
W a has a miai value of 1/2, while W b has a miai value of 3/4. On this board, however, White gets the same result with either.
After W 1, W 3 gets tedomari, for jigo.
Now Black gets tedomari, but the result is still jigo.
In the first case, White gained 1/2 point, then lost 3/4 point, then gained 1/2 point, for a net gain of 1/4 point. In the second case, White gained 3/4 point and then lost 1/2 point, for a net gain of 1/4 point. All same same. In your example if Black plays the 1/2 point play first, he gains 1/2 point, as White's sente sequence gains no points. If Black plays the 1 point play first, he gains 1 point but then loses 1/2 point. That's why the result is the same. :-) This is a copy of the living page "Ambiguous Position Discussion" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |