aLegendWai (9k? KGS): As told by Charles, I try my best to re-organize and integrate ideas in the discussion forum. To make it concise and consistent, some minor/repetitive messages will be deleted/modified/integrated.
|Table of contents|
|Table of diagrams
W keeps chasing it - wrong!
W keeps chasing it - OK
W's cut is impossible (W1 is captured)
B's response 3a
B's response 3b
B's response 3c
B's response 3d
Throw-in, nobi 1
Throw-in, nobi 2
Throw-in, nobi 3(W8 captured by B9)
White takes gote
If B plays first - Normal [Hane]
If W plays first - Normal [Hane]
One very theoretical example (Part 1)
One very theoretical example (Part 2)
aLegendWai (9k? KGS): Correct me if wrong.
Nothing is wrong in this endgame play. Locally speaking (ie without considering the whole board), it is a typical and correct way to respond in the endgame. Since white(W) is protected by the circled white stone. Nothing black(B) can do now.
(PS: In the question, it assumes that everything to the right is White's territory.)
aLegendWai (9k? KGS): A very good question! It is another way to respond. Locally speaking, it gives the same result as the "normal hane" . But it doesn't automatically mean they are equal. Reasons:
I will try to explain how B answers the throw-in.
A ko fight over for one point. Locally speaking, B can only pass (there's no ko threat in the diagram!) and W wins the ko.
Paul Clarke: What if Black plays tenuki after ? It looks to me as though Black has gained slightly.
Bill: Yes, Black has gained 1/3 point. :-) But see below.
We know B should not be too timid.
B should fight instead of retreat.
But the question is how B should fight?
B is happy to keep extending. When B extends by 1 stone, W keeps losing 2 points ().
Note: The loss of 1-point (at second line) occurs once B plays at . Afterward the 1-point loss keeps moving by 1 point to the right. So this loss is not counted to the loss of further B extension.
Bill: OC, is bad. However, whether chasing White this way loses anything depends on what is to the right. For instance:
Suppose is on the board. Then White can run Black up to it, and because of connect and die Black cannot fill at . The local score is the same as if White had blocked more accurately, as below.
aLegendWai (9k? KGS): I couldn't agree with you more! By the way, it is no point to perform such plays in the endgame. W cannot gain any. It gains the same if W plays at instead.
Even if B makes a mistake of connect-and-die here, W gains the same when W plays at and B makes the same connect-and-die mistake.
aLegendWai (9k? KGS): After extension, how W should respond then?
W has to grasp the only chance to play at the first line now. It is no longer possible if you miss that chance (due to the lack of the support of at the third line. This keeps B's invasion group 1 liberty).
aLegendWai (9k? KGS): Simply they gets the same point/score difference.
Bill: They get the same score only at the end of the game. Normally this position will be played out before that. The throw-in is never better, almost always worse.
aLegendWai (9k? KGS): Hi, Bill. First it is out of concern in the illustration because we just concern locally (ie consider what is given in the diagram). In this sense, both plays are definitely equal as far as I know.
Even if we think globally, I'm afraid we cannot be so sure to say throw-in is never better if you consider trickiness as a valid point. It is harder to deal with throw-in comparing with the normal hane.
In a real game, players not only play the standard moves, but also trick move. Very often if the opponent doesn't get trapped, it will turn out to get a better result. Although trick moves are usually not the optimal play, we can still see trick moves in the game.
So the trick play - throw-in is still worthwhile depending on situation (although it is never tricky to advanced players like you ^^).
I think you assume both parties must play perfectly. In this case, throw-in is not preferred then.
The following illustrate why they get the same point/score difference. (Credits: HolIgor)
HolIgor: Black has 4 points while white has 3 points. The score is -1. Black ended in gote.
aLegendWai (9k? KGS) Note: -1 is caluclated by the formula (W-B = 3-4). The reverse is possible, ie B-W = 4-3 = +1. It makes no difference to the result. The +/- simply denotes:
HolIgor: Black will have to defend before connecting the ko. The score is 0. Black has 2 points plus 1 captured; white has 3 points. There is yet another possible point for white in the ko. So, white has already won a point and can add another.
Yet, this is gote for white.
ChrisSchack: Would it be a good idea for W to play a here immediately following?
aLegendWai (9k? KGS): Note:
aLegendWai (9k? KGS): One may not finish the sequence and leave it as a ko threat. Also one should respond in a way to minimize the no. of ko threats presented in its shape. A solid connection usually elminate potential ko threats.
All these has to be counted too.
Let's look at the sagari first. After , - is sente. Whether this is better than - , depends upon the value of that sente as a ko threat versus the chance that White will get the reverse sente. With no ko, dominates.
Now let's look at the throw-in. forces Black to fill eventually at a, but at what cost?
The cost is 1 2/3 points. That's how much worse this position is for White than the original position.
The play could also go - , - . The value of the position remains the same.
At this point Black can fill the ko at to reach a position worth the same as after the sagari or the hane-tsugi (minus the ko threats on both sides). Filling is worth only 1/3 point, while the other plays are worth 2 points. So White's throw-in has allowed Black to gain 1 2/3 points for free.
Since the throw-in is bad, the hanetsugi is correct, subject to the qualifications concerning ko threats.
Black has 4 points while white has 3 points. The score is -1 (=W-B). Black ended in gote.
Note: -1 is caluclated by the formula (W-B = 3-4). The reverse is possible, ie B-W = 4-3 = +1. It makes no difference to the result. The +/- simply denotes:
is used to protect the cut.
Black has 1 point while white has 4 points. The score is +3 (=W-B). White ended in gote (in case if the sequence completes).
To find the value of this endgame, we have to compare the difference between B playing first and W playing first.
I would say is the normal play here. There is still some aji at a, and usually it helps not to play out extra moves, if you are trying to leave the maximum aji.
HolIgor: I don't understand. I clearly see that if this local yose is the last yose in the game loses one point. A push at b is now 0.5 sente for black, so it is a reverse sente for white and one has to take it with a double value to compare with gote moves. Yet, since this is at the very end of the game the proper move can be found only when searching for tedomari. For example, if the remaining moves are all miai there b is a correct play here. If the maximum value of the remaining move is 1 then, perhaps, it does not matter. If there are moves with values more than 1.0 left, then is better, perhaps.
aLegendWai (9k? KGS): If 2 dead B stones () are in the W's territory...
aLegendWai (9k? KGS): It is a theoretical example showing how dead stones can be alive (supposing W wrongly plays at ).
After the sequence up to , it is likely for B to make a separate living group.
- Even if W doesn't play at , W cannot make any good ko fight (B can avoid any disadvantageous ko fight!).
- the cutting point is not a problem at all due to sufficient B liberties.
You may see a player forms a separate group (by similar skills in the endgame) from real games on the Internet although this kind of situations usually appears towards the end of another corner.
unkx80: Bill, thanks for showing me and others that the throw-in is inferior than just atari, i.e. the - - sequence in the original problem is all right.
Bill: De nada. I am so used to playing the sagari that at first I overlooked the fact that the throw-in is wrong in this case, myself. ;-)
aLegendWai After all, Bill make an very interesting issue which make this normal question so abnormal :) Throw-in is an interesting topic which we can learn a lot from analysing it.
And I know one more trick play in the endgame too. Useful in handicap game. Haha... ^o^
More credits should be given to Bill.