It is currently Tue Nov 29, 2022 2:04 am

All times are UTC - 8 hours [ DST ]




Post new topic Reply to topic  [ 11 posts ] 
Author Message
Offline
 Post subject: What means "approach ko" ?
Post #1 Posted: Wed Jan 05, 2022 11:35 am 
Lives in sente

Posts: 956
Liked others: 17
Was liked: 48
Rank: 1er dan
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------------------------------
$$ | . . O . . . . . X . . . . . . X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O . O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]


How do you call the result of this semeai ?

Assume black has at least two ko threats.

The best sequence (I am not quite sure it is really the best sequence ;-) ) is for me the following:

Click Here To Show Diagram Code
[go]$$W :b6: pass, :b8: pass
$$ -----------------------------------------
$$ | . . O . 5 . 2 1 X 3 . . 4 . . X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O 7 O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]


Click Here To Show Diagram Code
[go]$$Wm9 :b10: retakes ko after a first ko threat, :w13: retakes ko, :b14: retakes ko after a second ko threat, :w15: pass
$$ -----------------------------------------
$$ | . . O . O . X 1 X O . 8 X 3 4 X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O O O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]

and only now we reach a "direct ko"

Seeing that after :b6: pass and :b8: pass white cannot kill black unconditionaly my first conclusion was that the result is a "two moves approach ko".
But after :b8: pass the result is not a "direct ko" but is (another) "approach ko". In this context are we allowed to say that the proposed position leads to a "two moves approach ko"? If not what is the correct wording for this result?

Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #2 Posted: Wed Jan 05, 2022 11:54 am 
Lives in gote

Posts: 428
Liked others: 56
Was liked: 273
Rank: UK 2d Dec15
KGS: mathmo 4d
IGS: mathmo 4d
After :b16:, it is a direct ko, so I'd say that :w9: is a play in a one-move approach ko.

My understanding of terms is that n-move approach ko refers to a single direct ko locally that requires n moves by one player (more than the opponent) in order to start it.

This refers to two distinct positions depending on which side has taken the ko.

I equate this term with n-step ko.

Hence a direct ko is a 0-step ko.
An n-stage ko is something different and two nearby kos may be nonindependent though not adjacent, so they are not double kos, nor 2-stage kos but something different. Of course in theory, you might have any arrangement of kos with differing dependences but all other unnamed ones are very rare (1 in million? for each)

_________________
Give me triangles strong enough and I can measure the universe.

When Venus transits, we can align our clocks to one event. By measuring the angle to flat Earth at two places far apart on Earth, we can compute the distance to Venus and the Sun.


Last edited by dhu163 on Wed Jan 05, 2022 11:56 am, edited 1 time in total.
Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #3 Posted: Wed Jan 05, 2022 11:55 am 
Oza
User avatar

Posts: 2161
Location: Ghent, Belgium
Liked others: 324
Was liked: 948
Rank: KGS 2d OGS 1d Fox 4d
KGS: Artevelde
OGS: Knotwilg
Online playing schedule: UTC 18:00 - 22:00
At SL we call a ko resulting in another ko, a "two stage ko", and a ko that can't be resolved by winning it but needs one additional move hence another ko, an approach ko.

See https://senseis.xmp.net/?MultiStageKo and https://senseis.xmp.net/?ApproachKo

But dhu seems to disagree here.

Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #4 Posted: Wed Jan 05, 2022 11:59 am 
Lives in gote

Posts: 428
Liked others: 56
Was liked: 273
Rank: UK 2d Dec15
KGS: mathmo 4d
IGS: mathmo 4d
I think I have agreed with SL on step/approach ko, but I feel SL's definition of stage ko is slightly ambiguous.

I think GT is counting B's two passes, but forgets that B captured a stone which is like W passing once. Hence as they started with equal liberties (ignoring the ko liberties), it is a (2-1)=1 step ko.

But I see that there is ambiguity. I would call the two positions that are n approach moves from a direct ko an n-move approach ko. Bill's paper evaluating them seems to use this. This is preferable in Bill's NTE model since this allows us to say that moves to end the n-step ko (including moving to (n-1 step ko) have the same gain as ko takes in an n-step ko.

However, SL is a bit confusing in the suggestion of splitting positions by number of ko threats ignored in order to win the ko. This would mean say in a direct ko, you to play, there are two positions, one you can win immediately and the other you need to ignore a threat.

Of course, :b2: should be at :b4:.

_________________
Give me triangles strong enough and I can measure the universe.

When Venus transits, we can align our clocks to one event. By measuring the angle to flat Earth at two places far apart on Earth, we can compute the distance to Venus and the Sun.


Last edited by dhu163 on Wed Jan 05, 2022 12:19 pm, edited 6 times in total.
Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #5 Posted: Wed Jan 05, 2022 12:02 pm 
Lives with ko

Posts: 197
Liked others: 15
Was liked: 60
Rank: KGS 1k EGF 2k
KGS: Schachus12
I would call this a 1-move approach ko. I would have had both sides continuing play without passing until the ko is direct for one side. Sure black might tenuki for 6, but than white can also tenuki for 7. if we have b6 take a liberty then w7 takes the ko. Now the ko is direct for b but w needs one more approach move (7 in your variation to make a direct ko. That means b can tenuki for 9 and w needs to play the approach move if he wants to fight the local situation( if he also tenukis, he accepts any tenuki as a ko threat)

Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #6 Posted: Wed Jan 05, 2022 3:48 pm 
Lives in sente

Posts: 956
Liked others: 17
Was liked: 48
Rank: 1er dan
dhu163 wrote:
I think I have agreed with SL on step/approach ko, but I feel SL's definition of stage ko is slightly ambiguous.

I think GT is counting B's two passes, but forgets that B captured a stone which is like W passing once. Hence as they started with equal liberties (ignoring the ko liberties), it is a (2-1)=1 step ko.

But I see that there is ambiguity. I would call the two positions that are n approach moves from a direct ko an n-move approach ko. Bill's paper evaluating them seems to use this. This is preferable in Bill's NTE model since this allows us to say that moves to end the n-step ko (including moving to (n-1 step ko) have the same gain as ko takes in an n-step ko.

However, SL is a bit confusing in the suggestion of splitting positions by number of ko threats ignored in order to win the ko. This would mean say in a direct ko, you to play, there are two positions, one you can win immediately and the other you need to ignore a threat.

Of course, :b2: should be at :b4:.


I do not understand why :b2: should be at :b4:.
Could you clarify in which kind of situations the move :b2: should be at :b4: ?

Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #7 Posted: Wed Jan 05, 2022 6:07 pm 
Lives in gote

Posts: 428
Liked others: 56
Was liked: 273
Rank: UK 2d Dec15
KGS: mathmo 4d
IGS: mathmo 4d
Thanks for the exercise. Did I get it wrong?

Well B plays first with one more liberty so I expected them to win the shape unconditionally rather than getting to a ko even if it is 1 step ko. However, you are right that deciding between them is difficult.

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

This is a 1 step ko in B's hand in gote, but B's forcing moves at :b4: , :b6: have already gained something for B. The swing is 26+kotake = 7 pts? (territory). So under NTE, the gain of the next move is 27/5 = 5 2/5. If we count B's win as zero and count W's gain relative to that, the count is 5 as long as T>=5.

Note that if :w5: played elsewhere, then B could connect at :w1: to win the semeai but with 1 less point (i.e. a count of 1), but might also risk playing at :w5: themselves for 1 more local point but passing in the ko fight. So the move :w5: commits to profiting from the ko since W has already lost almost 1 point from starting the ko. This is why they say prepare (manufacture) big ko threats before starting a ko (because starting it loses you points locally if you lose).

I think that :w3: is sente on :b4: and :w5: on :b6: because they are equal liberty points and W is threatening to move to a direct ko and a count of up to 2/3(27)=18 points. Note that :w3: is not necessary and if not played, allows B to win the semeai to a count of zero. However, note that without :w1: , B could have played to a count of 2 points at best.

The average is before :w5: is a count of 3 1/5 with :w5: having gain 2 1/5.

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

B gets a 2 step (B's favour) ko in W's hand in gote.
The swing is now increased to 28+1 = 29, but the zero point hasn't shifted.
At temperatures above the ko gain 29/8 = 3 5/8, this is close to but slightly worse for B than a 1 step ko in B's hand since 2K/8 > K/5. This is 2 factors, both worse for Black.
The count is 29/4 = 7 1/4

Furthermore, W has the option of not playing :w2: , and just shorting liberties, moving to 2 directly, because B hasn't captured a stone to occupy :b6: yet.

Under NTE, when T is the gain of the first and smallest ko involved, an n-step (your favour) ko in opp's hand has the same count as an (n-1)-step (your favour) ko in your hand. I don't know how this varies with temperature. But as T goes down, smaller ko threats are required to maintain the ko since they no longer need to balance the value of sente. Local profit matters more than sente and hence winning the ko is more important.

Is there any situation where the 2 step ko is better?

last check
Click Here To Show Diagram Code
[go]$$W :b6: left of 4
$$ -----------------------------------------
$$ | . . O . 9 . 8 1 X 4 5 3 2 7 O X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O . O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]

This is like a golden chicken standing on one leg shape and doesn't look good for W initially. However, upon further inspection, B has gotten a 2 step ko (at :w7: ) in W's hand in gote. Although the zero point has been avoided since B occupies :b8: in this variation, W has made more inroads into B's position, the swing has increased to 29 2/3, so this is probably marginally worse for B than the variation above, or at best, hard to distinguish.

I almost completely concede this one. The one-step ko is better for B in the large majority of cases.

One last try: when could the 2 step ko possibly be better? W has to expect more than 2pts locally. Also, the temperature has to be low enough to change the influence of sente-gote and prioritise local variations. However, I can't see any possible way my 2 step ko could be better. Since it seems worse whichever side is to play. So the 1 step ko dominate in this case?

_________________
Give me triangles strong enough and I can measure the universe.

When Venus transits, we can align our clocks to one event. By measuring the angle to flat Earth at two places far apart on Earth, we can compute the distance to Venus and the Sun.

Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #8 Posted: Thu Jan 06, 2022 4:44 am 
Lives in sente

Posts: 956
Liked others: 17
Was liked: 48
Rank: 1er dan
dhu163 wrote:
Thanks for the exercise. Did I get it wrong?

Well B plays first with one more liberty so I expected them to win the shape unconditionally rather than getting to a ko even if it is 1 step ko. However, you are right that deciding between them is difficult.

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

This is a 1 step ko in B's hand in gote, but B's forcing moves at :b4: , :b6: have already gained something for B. The swing is 26+kotake = 7 pts? (territory). So under NTE, the gain of the next move is 27/5 = 5 2/5. If we count B's win as zero and count W's gain relative to that, the count is 5 as long as T>=5.

Note that if :w5: played elsewhere, then B could connect at :w1: to win the semeai but with 1 less point (i.e. a count of 1), but might also risk playing at :w5: themselves for 1 more local point but passing in the ko fight. So the move :w5: commits to profiting from the ko since W has already lost almost 1 point from starting the ko. This is why they say prepare (manufacture) big ko threats before starting a ko (because starting it loses you points locally if you lose).

I think that :w3: is sente on :b4: and :w5: on :b6: because they are equal liberty points and W is threatening to move to a direct ko and a count of up to 2/3(27)=18 points. Note that :w3: is not necessary and if not played, allows B to win the semeai to a count of zero. However, note that without :w1: , B could have played to a count of 2 points at best.

The average is before :w5: is a count of 3 1/5 with :w5: having gain 2 1/5.

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

B gets a 2 step (B's favour) ko in W's hand in gote.


Oops I need to go a little more slowly ;-)
In this last diagramm I do not see the two step ko. IOW how black can play two tenuki moves before playing a direct ko?

Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #9 Posted: Thu Jan 06, 2022 6:08 am 
Lives in gote

Posts: 562
Liked others: 20
Was liked: 89
Rank: panda 5 dan
IGS: kvasir
I think it is redundant to refer to approach ko as n-step ko because it is a capturing race and 'n' is not the number of liberties. In fact a group in an n-step ko will often have n+1 liberties and n-1 if there is opportunity to connect the ko early to convert into a direct capturing race. It is not very useful.

I have often seen 'step ko' used to mean what some people want to call a stage ko. I think that is because of the reason that less useful terms don't tend to stick.

Myself, I tend to count 'n' like this: "zero", "few" and "too many" approach moves.

I know it is called a "shameless ko" in Chinese when when 'n' is rather big.

Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #10 Posted: Thu Jan 06, 2022 10:48 am 
Lives in sente

Posts: 956
Liked others: 17
Was liked: 48
Rank: 1er dan
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------------------------------
$$ | . . O . . . . . X . . . . . . X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O . O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]


My initial question in this thread was :
How do you call the result of this semeai ?

To simplify my question let's take the position after the first 5 moves I proposed:

Position 1
Click Here To Show Diagram Code
[go]$$W Black to play
$$ -----------------------------------------
$$ | . . O . O . X . X O . . X . . X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O . O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]


and now the same question :
How do you call the result of this semeai ?

If I understand correctly, dhu163 and Schachus call this a "one-move approach ko".
Where is the point? According to the SL definition if this position is a "one-move approach ko" then, after a black tenuki move we should reach a direct ko.

Position after black tenuki:
Click Here To Show Diagram Code
[go]$$B :b1: tenuki
$$ -----------------------------------------
$$ | . . O . O . X . X O . a X . . X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O 2 O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]

As you can see black can follow by a move at "a" for a direct ko but after :w2: black can also choose to play tenuki without being unconditionaly killed. That means that this position is not a direct ko is it?

Strictly speaking, if you consider position 1 being a "one-move approach ko" then don't you have to modify the definition of "one-move approach ko" given in SL ?

Position 2
Click Here To Show Diagram Code
[go]$$W Black to play
$$ -----------------------------------------
$$ | . . O W O . X . X O . . X . . X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O . O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]

BTW with this new position I consider it is really a "one-move approach ko", according to SL definition

Top
 Profile  
 
Offline
 Post subject: Re: What means "approach ko" ?
Post #11 Posted: Thu Jan 06, 2022 3:59 pm 
Lives in sente

Posts: 956
Liked others: 17
Was liked: 48
Rank: 1er dan
dhu163 wrote:
Thanks for the exercise. Did I get it wrong?

Well B plays first with one more liberty so I expected them to win the shape unconditionally rather than getting to a ko even if it is 1 step ko. However, you are right that deciding between them is difficult.

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

This is a 1 step ko in B's hand in gote, but B's forcing moves at :b4: , :b6: have already gained something for B. The swing is 26+kotake = 7 pts? (territory). So under NTE, the gain of the next move is 27/5 = 5 2/5. If we count B's win as zero and count W's gain relative to that, the count is 5 as long as T>=5.

Note that if :w5: played elsewhere, then B could connect at :w1: to win the semeai but with 1 less point (i.e. a count of 1), but might also risk playing at :w5: themselves for 1 more local point but passing in the ko fight. So the move :w5: commits to profiting from the ko since W has already lost almost 1 point from starting the ko. This is why they say prepare (manufacture) big ko threats before starting a ko (because starting it loses you points locally if you lose).

I think that :w3: is sente on :b4: and :w5: on :b6: because they are equal liberty points and W is threatening to move to a direct ko and a count of up to 2/3(27)=18 points. Note that :w3: is not necessary and if not played, allows B to win the semeai to a count of zero. However, note that without :w1: , B could have played to a count of 2 points at best.

The average is before :w5: is a count of 3 1/5 with :w5: having gain 2 1/5.

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

B gets a 2 step (B's favour) ko in W's hand in gote.
The swing is now increased to 28+1 = 29, but the zero point hasn't shifted.
At temperatures above the ko gain 29/8 = 3 5/8, this is close to but slightly worse for B than a 1 step ko in B's hand since 2K/8 > K/5. This is 2 factors, both worse for Black.
The count is 29/4 = 7 1/4

Furthermore, W has the option of not playing :w2: , and just shorting liberties, moving to 2 directly, because B hasn't captured a stone to occupy :b6: yet.

Under NTE, when T is the gain of the first and smallest ko involved, an n-step (your favour) ko in opp's hand has the same count as an (n-1)-step (your favour) ko in your hand. I don't know how this varies with temperature. But as T goes down, smaller ko threats are required to maintain the ko since they no longer need to balance the value of sente. Local profit matters more than sente and hence winning the ko is more important.

Is there any situation where the 2 step ko is better?

last check
Click Here To Show Diagram Code
[go]$$W :b6: left of 4
$$ -----------------------------------------
$$ | . . O . 9 . 8 1 X 4 5 3 2 7 O X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O . O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]

This is like a golden chicken standing on one leg shape and doesn't look good for W initially. However, upon further inspection, B has gotten a 2 step ko (at :w7: ) in W's hand in gote. Although the zero point has been avoided since B occupies :b8: in this variation, W has made more inroads into B's position, the swing has increased to 29 2/3, so this is probably marginally worse for B than the variation above, or at best, hard to distinguish.

I almost completely concede this one. The one-step ko is better for B in the large majority of cases.

One last try: when could the 2 step ko possibly be better? W has to expect more than 2pts locally. Also, the temperature has to be low enough to change the influence of sente-gote and prioritise local variations. However, I can't see any possible way my 2 step ko could be better. Since it seems worse whichever side is to play. So the 1 step ko dominate in this case?


Click Here To Show Diagram Code
[go]$$B Black to move
$$ -----------------------------------------
$$ | . . O . . . a O X . . . b . . X . . . |
$$ | . . O O X X X X O O O O O X X X . . . |
$$ | . . . O . O O O X X X X X X . . . . . |
$$ | . . . O O O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]

I did some complementary works to compare a black move at "a" or "b".
The simpliest positions for these compraraisons seems not under NTE but when white has one ko threat available:

Click Here To Show Diagram Code
[go]$$B Black to move
$$ -----------------------------------------
$$ | . X O . . . a O X . . . b . . X . . . |
$$ | c X O O X X X X O O O O O X X X . . . |
$$ | X . X O . O O O X X X X X X . . . . . |
$$ | X X X O O O . . . . . . . . . . . . . |
$$ | O O O O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]
In this diagram with a white ko threat at "c" the correct move for black is a move at "a"

Click Here To Show Diagram Code
[go]$$B Black to move
$$ -----------------------------------------
$$ | . X O . . . a O X . . . b . . X . . . |
$$ | O X O O X X X X O O O O O X X X . . . |
$$ | O X O O . O O O X X X X X X . . . . . |
$$ | O X X O O O . . . . . . . . . . . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | X X O . . . . . . . . . . . . . . . . |
$$ | O O O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$[/go]
In this second diagram with a unremovable white ko threat the correct move for black is now a move at "b"

Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 11 posts ] 

All times are UTC - 8 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 1 guest


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group