Corner 1-2 connection value
HolIgor asks: As you know I don't like to defend. Quite often early in the yose I would leave this unplayed.
Assume that White stones are othewise alive. Now, how much is a is worth?
The question is not so easy because it involves ko and thus depends on the whole board position. How is this counted?
I will try to invent something myself later, but does anybody know the answer?
Yes. :-) --BillSpight
The position is unfinished. Local score 4 2/3 (Black captured a stone). Move value 1/3.
So the connection value was (10 - 4 2/3)/2 = 2 2/3.
With the ko defence the value of the ko should be determined.
If it is all or nothing: 10/2 = 5. The value of ko is 5 points.
It seems that before fighting this ko White has to have enough five-point threats.
As the result White wins something compared to the safe variation if she is ready to win a ko at with a 2.5 point ko-threat by opponent (or less). Quite tough ko conditions.
PS. I did not play costly atari today :).
Next, suppose that White is komaster. White plays the 'ko defense'. The ko is big. How do we evaluate this position, then?
White will win the ko. Does that mean that Black (the koloser) should not start the ko?
Actually, it is just the opposite. Black should start the ko as early as he can afford to do so. When White fills the ko, Black gets compensation by playing a move elsewhere. The earlier Black starts the ko, the larger that play will be.
How early can Black afford to cut and let White make the ko?
Suppose that he does so when the size of the play he gets in compensation for the ko (the ambient temperature) is three points. If White wins the ko, she protects the cut in exchange for a play worth three points. It is better to play the safe defense, and, instead of taking Black's cutting stone, play a three-point move herself.
If the ambient temperature is somewhat above 2 2/3, Black can play Black 1 with sente, even if White is komaster. Then at temperature 2 2/3 someone will take a stone here.
So White only sets up the ko when the temperature is 2 2/3 or less (as a rule). It is the 'safe defense' that determines the size of the play. That means that, even if White is komaster and makes ko, the play has a miai value of 2 2/3.
cynewulf: If Black is komaster and White plays b, Black can make a big ko with a.