About aji-keshi

kvasir · #1

I came across this position when playing with a position from a random pro game and I am stumped why the computer is claiming one move is a -1.5 or more error. Normally one would play as in the diagram, preserving good aji and avoiding to play the one-sided block on the second line.

Click Here To Show Diagram Code: [go]$$c $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . X . . . X . . . . . X . . . | $$ | . . . O . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . X X X . . | $$ | . . . . . . . . . . . . . O O O . . . | $$ | . . . O . . . . . , . . O . . , O O . | $$ | . . . . . . . . 1 . . X X X X O O . O | $$ | . . . . . . . . . . . . . O O X X O . | $$ | . . . . . . . . . . . . . . . . . X . | $$ ---------------------------------------[/go]

What if you play the block? Does it matter objectively in this position and how much does it matter?

Click Here To Show Diagram Code: [go]$$c $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . X . . . X . . . . . X . . . | $$ | . . . O . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . X X X . . | $$ | . . . . . . . . . . . . . O O O . . . | $$ | . . . O . . . . . , . . O . . , O O . | $$ | . . . . . . . . 3 . . X X X X O O . O | $$ | . . . . . . . . . . . . 1 O O X X O . | $$ | . . . . . . . . . . . . . . . 2 . X . | $$ ---------------------------------------[/go]

Initially my b40 katago setup thinks this is almost a 2 pt. error but adjusts down to 1.6 after a lot of playouts. Besides being a move that black doesn't seem to need to play and you shouldn't, I don't understand how the computer concludes it is this big of a mistake and why in the range 1.5 - 2.0 points. It is also a large drop in percentages. Maybe someone understands these things?

I have some theories:

1. There is a large ko threat, maybe the only good threat in the position, but then there is no ko anywhere anyway.

Click Here To Show Diagram Code: [go]$$c $$ --------------------------------------- $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . X X X . . | $$ . . . . . . O O O . . . | $$ . . , . . O . . , O O . | $$ . X . . X X X X O O 3 O | $$ . . . . . . O O X X O 1 | $$ . . . . . . . . . . X . | $$ ---------------------------------------[/go]

2. Depending on how you play it there are many small, even endgame, ko threats. Maybe 1.5 pts. is a lot for just these threats, and there are still some threats anyway.

Click Here To Show Diagram Code: [go]$$c $$ --------------------------------------- $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . X X X . . | $$ . . . . . . O O O . . . | $$ . . , . . O . . , O O . | $$ . X . . X X X X O O . O | $$ . . . . . 3 O O X X O 2 | $$ . . . . . . 5 . 6 1 X 4 | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$cm7 $$ --------------------------------------- $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . X X X . . | $$ . . . . . . O O O . . . | $$ . . , . . O . . , O O . | $$ . X . . X X X X O O . O | $$ . . . . . X O O 1 2 O O | $$ . . . . . . X . O . . O | $$ ---------------------------------------[/go]

3. I had the idea that the computer was wrong and the presence of some extra stones was throwing it off. In this case it should correct itself, on the theory that it is usually right and when you add more moves it will end up in a position were it is right again. So I tried to play a few moves from the top line and then run a lot of playouts but it never changed its' mind and curiously continues the game mostly the same way compared to no bad second line block.

4. I just missed something and the bad block is bad for some other reasons :-?

Joaz Banbeck · #2

Note that the aji at 'a' remains, regardless of whether or not black plays :b1:

.

Click Here To Show Diagram Code: [go]$$c $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . X . . . X . . . . . X . . . | $$ | . . . O . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . X X X . . | $$ | . . . . . . . . . . . . . O O O . . . | $$ | . . . O . . . . . , . . O . . , O O . | $$ | . . . . . . . . 1 . . X X X X O O . O | $$ | . . . . . . . . . . . . . O O X X O a | $$ | . . . . . . . . . . . . . . . . . X . | $$ ---------------------------------------[/go]

I tend to wonder if all of those black stones in the lower right are worth defending at all. They are compromised, and at best would be a minor inconvenience to white if they were saved.

So I would play :b1:

like this:

Click Here To Show Diagram Code: [go]$$c $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . X . . . X . . . . . X . . . | $$ | . . . O . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . 1 . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . X X X . . | $$ | . . . . . . . . . . . . . O O O . . . | $$ | . . . O . . . . . , . . O . . , O O . | $$ | . . . . . . . . . . . X X X X O O . O | $$ | . . . . . . . . . . . . . O O X X O a | $$ | . . . . . . . . . . . . . . . . . X . | $$ ---------------------------------------[/go]

It really fits well with all of the other black stones on the right side.

dhu163 · #3

Yes, the aji on that side may help if W runs out of libs, but more important is if you need to make life, then hane P1, under the stones gives you both N2 and N1. So it isn't just ko threats, it noticeably damages the eyespace of a weak group, which is pretty big when living could support Bs other weak group on the right. Not defending on the lower side seems ridiculous to me as w us already blocking escape in the centre as well as with forcing moves on the weak group on the right. Even not including influence it is already around 20pts.

edit: with the 2 space, perhaps the aliveness drops from 80% to 70%. Only so low as W is strong on the right.

Shaddy · #4

before extending, block is black's sente because capturing 2 stones would stabilize the weak group

after extending, white's extend is now sente because it threatens the black group

edit: also it's not aji keshi because there's nothing interesting in the corner anyway

kvasir · #5

dhu163 explanation sounds right to me. I think he means that black could play like this to get a more solid eyeshape if necessary. That is, the black group is much stronger without blocking early and that can explain why the katago evaluation. I'll try to study it more.

Click Here To Show Diagram Code: [go]$$c $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . X X X . . | $$ . . . . . . O O O . . . | $$ . . , . . O . . , O O . | $$ . X . . X X X X O O . O | $$ . . . . . 5 O O X X O . | $$ . . . . . . 4 1 3 2 X . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm6 $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . X X X . . | $$ . . . . . . O O O . . . | $$ . . , . . O . . , O O . | $$ . X . . X X X X O O . O | $$ . . . . . X O O 3 . O . | $$ . . . . . 2 O . . 1 X . | $$ ---------------------------------------[/go]

Btw it might not be so clear but this area is one-sided (as I mentioned) in the sense that white can't easily remove the aji. For example pushing is gote as it removes white's own liberty, a liberty that is needed to capture the inside without a ko.

Click Here To Show Diagram Code: [go]$$W $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . X X X . . | $$ . . . . . . O O O . . . | $$ . . , . . O . . , O O . | $$ . X . . X X X X O O . O | $$ . . . . 2 1 O O X X O . | $$ . . . . . . . 4 . . X . | $$ ---------------------------------------[/go]

kvasir · #6

Shaddy wrote:

after extending, white's extend is now sente because it threatens the black group

I am not sure which move you mean by "white's extend".

Before I noticed the evaluation I thought it didn't matter, I thought I was never going to block before extending anyway. When I noticed that blocking first was a small mistake in the eyes of katago I tried to find the reason. Maybe you are saying the opposite, that black should block first?

Shaddy · #7

whoops, tired and misunderstood your post. agree with dhu on reread

kvasir · #8

After looking at this more closely, trying to confirm that it was the P1 aji and now I think it is not that. Instead I think it is the ko aji in the diagram because when push comes to shove it is something katago actually played. Also it is free for black, if anything it is less points this way for white than blocking directly. It is just that black needs to ignore two threats and therefore doesn't profit directly. It is different if white is trying to kill the whole black group, in this case there are local threats and the ko makes a huge difference.

Additional evidence is that when I fill the eye with a white stone (i.e. black pass, white S3) then katago doesn't care much if black plays the block first or not. Second additional evidence is that filling the eye in this way is favorable for white, W+1.6 to W+2.1, this huge considering it is -1 white territory.

Click Here To Show Diagram Code: [go]$$c $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . . . . . . | $$ . . . . . . . X X X . . | $$ . . . . . . O O O . . . | $$ . . , . . O . . , O O . | $$ . X . . X X X X O O 2 O | $$ . . . . . 5 O O X X O 1 | $$ . . . . . . . 4 . 3 X . | $$ ---------------------------------------[/go]

dhu163 · #9

In my amateur experience, not just in Go, I am often close but not quite right.

That's a much better point, and I agree with kvasir now. My under the stones idea loses points. Your diagram gains points if it works, though it is risky to spend a move. W really doesn't want to play 4, but W's group is much larger, making the ko very heavy for W. After 3, it becomes a one step ko in was favour. Using the work I did to understand these via bill's NTE (another post) the normal count of the oringal position is 1/5 of the way between w winning the ko and b winning the ko.

If B wins the ko, this is 14 1/3+L points more than just blocking, where L is the gain from weakening W's group. If W wins the ko, this is 2+M points worse for B where M is the value of B at N2

By this count, your method gains B around 6/5 + 1/15+L/5-M/5 compared to just blocking. However as L is pretty large compared to M as Ws group is larger with less eyespace being in the centre so it should be worse for W. Initially I thought this wasn't quite a normal one step ko, so I needed a different model, but I think it is completely normal.

W's group ignoring influence is around 30 points so L<=30/n where n is the number of moves required to kill. Perhaps n is around 3 in this position. M<= 20/m with m around 4. If the inequalities are tight, then this adds an extra point, so the count is around 2.2 better than blocking.

Of course, we must also consider that for now W probably has more ko threats as B has multiple weaker groups and in order for B to start this, B has to force w to retreat at 2. However it is more Bs right to start the ko at any time.

Perhaps I underestimated n because B's group on the right is weak too, but sich forcing moves already loses territory, though there might be a few ko threats.

I think it is more likely that I have underestimated M.

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