Tas: Probably easy to see for you strong players. Can anyone tell me the status of this one?
Bill: Without seeing the rest of the left side, it is hard to say what best play is, but I think this is right for Black when there are no ko threats. The result will be seki or 10000 year ko. Diagram 1
As Dieter points out, White to play starts with the hane at . (Later): Sorry, White to play should play to live, as explained below.
Bill: The question in this sequence is . Does Black have to play here now? If Black does not, White can play there:
threatens a double atari with . The size of that threat depends upon what is below . Diagram 2
was made possible by . Note that that was White's reply to . One reason for that was the threat of . In other variations Black plays where is. In fact, it is a candidate for Black's first move.
I know you were only asking about status, and I was addressing the question of best play, but the two are closely related. Depending on the ko threat situation Black can make a kind of 10000 year ko and kill White. But that is not normally best play.
Bill (Later): Just for fun I simplified the left side by adding to eliminate White's threat. What is best play then, when neither player has a ko threat?
elsewhere. fills at . Diagram 4
tderz " fills at ." I do not understand this, how is it possible? Wouldn't that be an illegal move?
Bill: captured the stone, so the point is open for .
Because neither player has a ko threat, Black wins the ko. However, White gets a play elsewhere. In theory, with Japanese scoring, this is very slightly superior to connecting at instead of playing . (By area scoring, because counts as a point for White in the seki, is plainly superior.)
tderz: Diagram 4a Isn't this bigger than in Diagram 4?
Here connects/saves (x? points?), Black must throw-in , which will be captured by white a, while also threatening to connect anoher stone with b (sente), thereafter threatening c?
Actually Bill commented on all of that in Diagram 2.
Compare with Bills Diagram 7a.
If White plays first lives. Diagram 5
This is gote. White to play can simply play .
tderz: The points a-e could make sense.
Bill: f too.
Black could wait with the gote capture p (if there is something bigger than 3 points reverse sente (wp saving 2 points + threatening q).
If white s then black p.
Second, this position is better for Black when there are no ko threats, because White cannot hold on to . If later Wa, Black can play Bb, and Black gets in the end, since White cannot fill the ko.
tderz: Throwing-in at looks most interesting to me for making the eye-space smaller. Diagram 8
If White later (yose) connects at in order to connect at p and threaten q, then she had to come back and reinforce with a or b, however, lacking outside liberties, both would lead to seki.
By throwing-in, Black can make it more costly (seki threatening, cf. Diagram 9) for White to play her connecting engame (, p, q).
Hence, the question is, what is wiser:
- to save one stone (with endgame continuations p-q?), or
- to ensure 6+ points in the corner?
tderz: Deriving from Diagram 8, later:
White took the endgame connection on the 1st line.
Sente seki for White?
White might want to remove the ko aji () by this (depending on game situation) Diagram 9
tderz: I now myself that it is usually a very tedious task to create the diagrams, being precise while trying to be concise.
I want to believe - I need a sign! (with the sledge hammer, if necessary)
Bill, "Black loses more than one point with the exchange, - " - in comparision to which sequence, what diagram?
(Diagram 6 above looks all the same).
This diagram is worth more than 4 points less for Black than my suggested play. True, there is a sente-gote difference of one move, but the gote gains less than 3 points.
If so, then ...
- here Black started and ends in sente, white lives
- there Diagram 6, white started and ends in sente, white lives
The end position is identical and the initiating is always answered in Diagram 9b and Diagram 8, hence sente.
Bill, if you want to say that in Diagram 1 is a better way of playing and getting a seki, I might believe you ( there is gote too), if you were comparing something concrete.
If life was worth 6+ points (I am not so sure how to calculate this, but e.g. Diagram 5 + an added white safety move), than this seems to be at least more than alleged 3 points in gote.
I admit, I am just confused, so please someone help.
- White c Diagram 6 lives in gote (Wx= 6 points, Black captured 2, protected a cutting point = y = at least 4 ; net result = z = W+2? in gote)
- Black c can make seki (Diagram 1 or Diagram 7) and capture W in gote (Wx = 0 points, B y = 3 points; net z = B+3 in gote)
... to be continued ..
First, White to play makes independent life.
Now (after ) Black has a 1.5 point gote.
This position (after ) has a local count of -2.5. Calculation below.
White has 5 points in the corner. Black has 3 points for the captured White stones, and let's count 1 point for him at , for a total of 4 points. The local score is then 4 - 5 = -1 (from Black's perspective).
TDerz: White's original gote + Black's gote => White's overall sente
After , and are miai.
White has 7 points in the corner, while Black has 3 points. The local score is -4.
TDerz: White's original gote + Black's gote => White's overall sente
Bill: White has made two local moves in a row. After White made independent life, Black played elsewhere.
The local count after White lives in Diagram 11 is the average of these scores, or -2.5.
The result will now be seki or 10000 year ko.
Now (after ) Black has a 0.75 point gote.
The local count after is +3.25.
White has no points. Black has 3 points for the captured stones plus one point at , for a local score of +4.
Now (after ) there is a 0.5 point gote for the stone.
The local count is +2.5.
Eventually Black can claim . The local score is +3.
makes seki and saves the stone.
The local score is +2.
The local count after play in Diagram 12b is thus +2.5, and the local count after play in Diagram 12 is thus +3.25. Thus the local count for the original position is the average of +3.25 and -2.5, or +0.375, and the miai value of a play is 2.875, a little less than 3.
tderz With good will, Bill, I do not understand the intermediate outcomes "+2.5" and "+3.25".
Bill: Sorry for not being clear. I hope my latest edits make things clearer.
Does simply every outcome from n diagrams get 1/n weight?
Bill: The basic idea is that each gote move or sequence from a particular position is worth the same, given that play stops when the plays become smaller.
What I am addressing is the following: we put several moves in a diagram, because we think that it would be unwise to break-off the sequence earlier - the loss would be too high. Now the diagrams 12, 12a-d have the assigned values of (with always Black as reference for the "+/-" sign, yet the value refers to dia 11, true?):
- 12 +0.75 Black ends in gote
- 12a +4.0 this diagram is after dia 12, Black moved again
- 12b -0.5 here white moved
- 12c +3.0 dias12c/12d come after 12b; here Black moves again
- 12d +2.0 here White moves again;
Now , I find it is funny that Black plays an endgame of a +0.75 value (dia 12), which white could turn into her favour by 0.5 with one move (dia 12b), preventing a black 4-pointer (12a), thus quite likely.
Mutatis mutandis from there (12b), Black faces the same situation that the difference between dias 12c and 12d is 1 point, hence bigger than the original sequence in 12. So why not taking 1 point if you initially fought about 0.75???
tderz: True, Bill. The mistake is entirely mine. I just watched the numbers 3 and (-)2 and didn't check whether it makes sense.
From these thoughts I would conclude that n diagrams do not simply get 1/n weight each (random), but that some outcomes are much more likely (e.g. 12c). (all this derives from the values as given by Bill) This is comparable to a semeai where one is usually not thinking "I take one liberty away, this is one point" rather "At the end of this sequence x>>1 points are decided".
Bill, please explain what you understand by canonical play.
Bill: I meant orthodox play. Informally, it is play that is normally correct when the local region is just barely the hottest region on the board. For instance, a losing sente is sometimes the right play, but it is not orthodox play, because it depends upon special circumstances to be right.
BTW, I corrected that term and made some other small corretions with an edit that seems not to have taken.
Also this whole - very interesting - calculation concerns only move c in diagram  for resp. Black's and White's sente.
The other moves have merits too, yet were not taken into account.
At the end of a calculation I would like to now which one is the best move and/or "how much difference is there between those moves".
We should come up with a value for a move in the coner.
I start to think that the answer might be different whether in the whole game there is only one 3-pointer left, or 2 3-pointers or an array of 5-, 4- 3- 2- and 1-pointers (perhaps that's basic endgame theory, I don't know).
Bill: This also has a score of +3. Considering that White went first, that's terrible!
Thanks for your explanations, Bill!
It is a small, overviewable problem, not difficult for problem solving at all, but it shows already how difficult it is in Go to find the best move(s).
BTW, your " miai value of a play is 2.875, a little less than 3 " means that
either colour should rather take another 3-point gote play elsewhere instead of sacrificing sente here, correct?
Bill: As a rule, yes.
Bill: The analysis with no ko threats is useful as a reference case, but not terribly realistic. In fact, such hyperactive positions generally favor the player with fewer stones at risk (Black is this case). So I thought it would be fun and worthwhile to examine the case when Black is komaster.
Informally, you can think of a player as komaster when she has just barely enough sufficiently large ko threats to win kos without allowing a ko exchange when the opponent ignores a threat. Also often unrealistic, but, again, it helps to understand this kind of situation.
Black can make a two move approach ko.
- set up the first ko.
White takes, OC, and then Black makes a threat that White answers. White plays elsewhere, and then Black makes the first approach move with . (The numbers over 3 are just to show the order of play. is really at least move 9 in the sequence of play.) Later Black plays the second approach move at , and finally Black wins the ko with .
The result is +26, counting . Black invested 4 net moves to make and win the ko. Since White can live in one move to a position worth -2.5, we can figure each play to be worth 28.5/5 = 5.7 points.
That is rather larger than the case when nobody has a ko threat -- almost twice as large.
Real life will usually fall between these conditions. Both players will have ko threats, and the position will favor Black, but not by as much as when Black is komaster.
One factor in this position, however, is that it is costly for Black to set up the ko. If Black loses the first ko, White gets 9 points (!) instead of 2.5. So maybe in this situation it would be very unusual for Black to be komaster.
Thanks, Tas! This is a very interesting position. :-)
Tas: WOW!! That lead to a lot of discussion! I had no idea that it was that interresting. No wonder I couldn't read it out. In the game I won by resign before we played out this corner, and I was just wondering.
The reason the corner wasn't played out was partly that appearently none of us could read it, and partly that it was alive until very late in the game where a white mistake alowed me to capture at the circled points, saving the squared stones. (Thereby of course also killing the, now outside, white stones.)
I'll post a little more of the surroundings when I get home to my own computer (where the sgf file is).
Bill: I now think that this is the play when Black plays first (when neither player has a ko threat). Wa does not threaten so much, and thus is smaller, and so Black does not need to prevent it right away, as a rule.
Since this is Black's sente, he will normally be able to play it, and this is the typical result here.
Tas: Added the surroundings
tderz Tas, looking at above diagram, I remark the following:
We were discussing 0.5 points, even 0.125 point differences (2.875 - 3) at some time here.
It was so incredibly big and important that Black could capture the (at least 26 points + all corner issues). I guess that a ko fight has taken place.
If you want to evaluate the size of an area in the case that it is used as a ko threat, you can count all stones ("s") which could be affected (life/death, capture), then double that number and add surrounding empty intersections ("e") which change owner.
You then compare the outcome ("z") of the formula z=2s+e with 2 moves in a row - 2 moves in case of direct ko - for the "ko loser". The possible, available ko threats of both parties have to be counted and compared in size in order to know who will run out first of appropriate ko threats. One should check who the game situation is affected by the outcomes, i.e. if you were ahead before the ko, but profiting point-wise afterwards gives you a risky position, you still might not like nor accept it.
This is the outline of an easy and rough estimation method.
According to your website your playing strength is anything between 21k and 7k IGS (3d-9H).
I think therefore that here a simple error occurred, as the white stones should not have been captured and not in this way.
Retroanalysis lets me question how came on the board:
after the capture by throw-in (which happened before or after a black stone on ) it would not have made sense (because the white ones were already captured).
But if was a ko threat before was played, then the ko should have been finished with a (saving two sente moves).
Later, white must have chosen to capture the single with b instead of capturing 4 black stones with c.
These errors have a much bigger impact than any discussion over 0.125-points.
Tas: You are rigth, it was a major blunder for white that he let me kill those stones. Sadly my computer has chrashed and the sgf is lost, so i can't show you exactly how the situation came about.