Count Of An Approach Ko
Example of how who is komaster, or more generally the ko threat situation, affects the count of an approach ko:
elsewhere. - = ko threat and response. takes the ko. elsewhere.
If Black is komaster, White has nothing better than to make the approach move and convert this to a regular ko. Assuming that a is White's territory, the local score is 14. Since this is, in effect, White's sente, that is the count of the original position.
elsewhere. takes ko. - = ko threat and reply. takes the ko. , elsewhere.
If White is komaster she can win the ko in three net plays, for a local score of -12. Black can win the ko in 1 play at a, for a local score of 15. (Black 3 will be Black sente later. four plays make a difference of 27 points, so the miai value of the ko is 6 3/4, and this position has a count of 8 1/4. Who is komaster makes a difference of 5 3/4 points.
tderz: Could s.o. please elaborate on the values 6 3/4 and 8 1/4.
I understand that 4 x 6.75 = 27, but why is this important?
However, 3 x 8.25 does not equal 27. Should it be 8.33~ ?
From which calculation stems the value 5.75 ?
Bill: 4 moves make a difference of 27 points. Each play gains 6 3/4 points, on average. 8.25 is not how much a play gains, but how much the original position is worth if White is komaster. If Black is komaster the original position is worth 14 points. The difference between 14 and 8.25 is 5.75. :)
tapir: I put some questions on timing at tapir / fun with approach kos, in particular I ask there, what does the average value of stone in an approach ko means in practice. Because while the average value might be pretty high, the value of the approach move is pretty small, as evidenced by comparing the local count before and after playing it.
Bill: Good question. :) There are some niceties about the count of a ko, and perhaps some ambiguity.
We include the marked point as belonging to White in the count of the ko.
Since this is a regular, placid ko, we say that the count is the same, no matter who is komaster. If Black wins the ko the local score is +14, if White wins it it is -12. Each play in the ko gains 8 2/3 points, and the count is +5 1/3.
Now, we normally think of the count as the value of the position, but that is not always so. Suppose that the ambient temperature is 5. Then the ko will be in play. If Black is komaster, we need not consider the result if White wins, and we may consider the value of this position as +9. If we are at the dame stage and Black is komaster, we may consider the value as +14. This illustrates the fact that Black as komaster gains when the temperature is 8 2/3 or below, and it drops.
What matters with approach kos is not counts, but values. The reason is that approach moves raise the local temperature, but by assumption the ambient temperature is too low for the count to matter.
(I have oversimplified. What matters is not actually values, but walls. But the point is that counts do not matter unless the temperature drops enough.)
tapir: What are walls in this context? I missed it somewhere in the CGT maze... Also, what is when there is a ko exchange - as there usually is? Doesn't compensation above two gote plays elsewhere effectively reduce the size of the ko? (Not to mention that most amateurs I know are not sufficiently able to correctly count and evaluate ko threats before a ko fight to determine whether they will win it or not. Let alone without ignoring any threats.)
Bill: In this case, with Black komaster, the wall is a line between (0,14) and (8 2/3, 5 1/3), and then a vertical line upwards from that. The ko exchange depends on the temperature, which is one of the dimensions of the walls of the thermograph.
tapir: Regarding first diagram + comment: "If Black is komaster, White has nothing better than to make the approach move and convert this to a regular ko." - This sentence does not compute. Not only can Black answer by instantly (so there is no ko, if White wants to fight the ko even with the intention to lose it, White can not play the approach move first, if White plays the approach move first without capturing the ko, this is not converting it to a regular ko) - as this is what is in effect calculated it would be by far simpler to go ahead and write: "If Black is komaster, White can not win the ko, so Black captures it at some point, White can play the approach move as sente." So simplified, we would have: