Gote move vs sente move in yose

RobertJasiek · Post by **RobertJasiek** » Sun Apr 07, 2024 3:05 pm

Suppose the would-be sente option is such.

The local endgame has a gote option and a sente option. The gote option provides a tentative gote count of the local endgame. The sente option provides a tentative sente count of the local endgame. Similarly, tentative move values.

Such tentative values can be compared to characterise the local endgame as - typically behaving as - a local gote or sente. If it is characterised as a local gote, the tentative gote count is the count. If it is characterised as s local sente, the tentative sente count is the count.

Nevertheless, a local endgame with gote and sente options characterised as either local gote or local sente can exceptionally have the atypical behaviour in some global contexts.

gennan · Post by **gennan** » Sun Apr 07, 2024 11:52 pm

If I made no mistakes in post #28, I'll try to fix the mistakes my post #24 along the same lines.

As C is a sente follow-up of A for white, and sente gains nothing, A would have the same count as C: count = -5. I suppose that would be the gote count of A.
And B (with count 2) would be a reverse sente continuation for black with miai value 7.

So this partial tree ...

Code: Select all

     A
    / \
   B   C

... whould have these counts:

Code: Select all

    -5 
    / \
   2  -5

I think I can also tentatively replace D in the tree from post #28 with this partial tree from A.
So then I get:

Code: Select all

           __ F __
          /       \     
         G         A
        / \       / \
       H   J     B   C

Would root position F then keep its count of 2 from post #24, or would it get count 3.75 with local temperature 8.75?

Code: Select all

  (8.75?) _ 3.75? _
         /         \     
 (3.5) 12.5         -5
       / \         / \
     16   9       2  -5

Either way, I think white chosing A with count -5 will lead black to chose B with count 2 if the ambient temperature is < 7, because black's reverse sente has miai value 7.

Comparing F's count of 3.75 here with the count of 2 in post #24, does it mean that (given we have reached F and white will play a move there) I can assume that the ambient temperature is already < 10.5, otherwise black would have chosen G already or white would have chosen D already to prevent black from reaching G?

When we have F with white to play, is there an ambient temperature range where chosing A is better for white than chosing D? Could it be the case for ambient temperatures > 7?

RobertJasiek · Post by **RobertJasiek** » Mon Apr 08, 2024 2:01 am

Your post #28:

gennan wrote:So can we say that this position has count 2, because white has a sente sequence to reach that count

Suppose the monkey is sente indeed.

So far we can say that the initial position F has the tentative sente count 2. Whether this is the count of F we still need to determine by characterising F as a local gote, local sente or ambiguous.

and 'sente gains nothing'?

Informally.

$$B H: count 16 $$ ---------------------------- $$ . . . . . T T T T T . 7 . | $$ . . . . . T T T T 1 Q 5 6 | $$ . . . . . . . X Q 3 X O . | $$ . . X , . X . X X X 2 O . | $$ . . . . . . . . . . O . . | $$ . . . . . . . . . . O . . | $$ . . . . . . . . . . . . . | $$ . . . . . . . . . . . . . | $$ . . . . . . . . . . O . . | $$ . . . , . . . . . , . . . |
Click Here To Show Diagram Code
[go]$$B H: count 16 $$ ---------------------------- $$ . . . . . T T T T T . 7 . | $$ . . . . . T T T T 1 Q 5 6 | $$ . . . . . . . X Q 3 X O . | $$ . . X , . X . X X X 2 O . | $$ . . . . . . . . . . O . . | $$ . . . . . . . . . . O . . | $$ . . . . . . . . . . . . . | $$ . . . . . . . . . . . . . | $$ . . . . . . . . . . O . . | $$ . . . , . . . . . , . . . |[/go]

White 2 might or might not be correct. Omitting it has the advantage of the supposed follow-up White 5 being more valuable. Further analysis is needed to study both variations.

After Black 1, White 2 - Black 3 is a sente option while White 5 is a a gote option (not an alternative sente option: P18 - P19). Our master complicator Gerard Taille has woven (so far detected at least) three sente versus gote option choices in the problem position to better prove his point that value calculations are too complicated;) Or accidentally?

2 EDITs

RobertJasiek · Post by **RobertJasiek** » Mon Apr 08, 2024 2:27 am

gennan wrote: As C is a sente follow-up of A
Code: Select all
     A
    / \
   B   C

Please do not write sente trees as gote trees! Too confusing!

white chosing A with count -5 will lead black to chose B with count 2 if the ambient temperature is < 7, because black's reverse sente has miai value 7.

From A, either player might continue and has his conditions for doing so.

assume that the ambient temperature is already < 10.5, otherwise black would have chosen G already or white would have chosen D already to prevent black from reaching G?

Wishful thinking that things would be simple.

When we have F with white to play, is there an ambient temperature range where chosing A is better for white than chosing D?

What D? B? If B, yes. At low temperature, there are both options with choice depending on value conditions. (And Black to move has a more complicated choice. During the late endgame, I could construct an extremely rare example in which the following three lines are all correct due to a totally unrealistic 19.5 value drop in the environment: 1) reverse sente, 2) elsewhere and opponent chooses gote option, 3) elsewhere and opponent chooses sente option.)

1 EDIT

RobertJasiek · Post by **RobertJasiek** » Tue Apr 09, 2024 1:26 am

Click Here To Show Diagram Code: [go]$$W original problem $$ ---------------------------- $$ . . . . . . . . . . . . . | $$ . . . . . . . . . . O . . | $$ . . . . . . . X O . X O . | $$ . . X , . X . X X X . O . | $$ . . . . . . . . . . O . . | $$ . . . . . . . . . . O . . | $$ . . . . . . . . . . . . . | $$ . . . . . . . . . . . . . | $$ . . . . . . . . . . O . . | $$ . . . , . . . . . , . . . |[/go]

Click Here To Show Diagram Code: [go]$$W simplified problem $$ ---------------------------- $$ X . . . . . . . . . . . . | $$ X . . . . . . . . . O . . | $$ X . O O . . . X O . X O . | $$ X . O O . . . X X X X O O | $$ X . O O . . . X O O O O . | $$ X X X X X X X X O . . . . | $$ . . . . . . . X O . . . . |[/go]

We simplify all the time, e.g., we approximate by assuming an ideal environment. If an early endgame calculation problem is too difficult to solve using either a) exact local value calculations or b) the method of global reading and counting, we can

solve it by simplifying the problem itself!

We can make further simplifying assumptions as follows. We use a locale.

Click Here To Show Diagram Code: [go]$$W locale $$ ---------------------------- $$ X . . . . C C C C C C C C | $$ X . . . . C C C C C W C C | $$ X . O O . . . X W C X O C | $$ X . O O . . . X X X X O O | $$ X . O O . . . X O O O O . | $$ X X X X X X X X O . . . . | $$ . . . . . . . X O . . . . |[/go]

Suppose certain long alternating sequences, including certain sente sequences, are worth playing successively.

Assume that this is Black's correct local move:

Click Here To Show Diagram Code: [go]$$B assumed correct local move $$ ---------------------------- $$ X . . . . . . . 1 . . . . | $$ X . . . . . . . . O O . . | $$ X . O O . . . X O . X O . | $$ X . O O . . . X X X X O O | $$ X . O O . . . X O O O O . | $$ X X X X X X X X O . . . . | $$ . . . . . . . X O . . . . |[/go]

Now, start afresh!

EDIT: further simplified the position.

Gérard TAILLE · Post by **Gérard TAILLE** » Tue Apr 09, 2024 2:46 am

RobertJasiek wrote:
Gérard TAILLE wrote: Let's assume the ambiant temperature is high. If you decide to play in the local position that means that the value of a move in this local position is also high and more or less equal to the ambiant temperature right?
Since you do not know my theory, why have you praised it?;)

I simply assumed the quality of your theory is quite similar to Bill's one and I find this last theory quite valuable.

RobertJasiek wrote: In the case of a high temperature T, compare it to the gote move value Mgote to decide whether to play locally the gote option!

T ? Mgote

Simple, isn't it?:) The proof has been quite an ordeal though...! I have needed to exclude the sente option.

You can profit from my theorem that only the gote option matters! (If the temperature is high.)

Now, seeing this strange theorem I have serious doubt concerning your theory. Assuming it exists locally both a gote option and a sente option I cannot believe that you can ignore the sente option only on condition the temperature is high.

For me either you use another hidden assupmtion on the position or you made a mistake in your proof. I hope it is the first case!

RobertJasiek · Post by **RobertJasiek** » Tue Apr 09, 2024 4:36 am

Gérard TAILLE wrote:I simply assumed the quality of your theory is quite similar to Bill's one and I find this last theory quite valuable.

The quality is on the same level. For non-ko, non-pure-CGT endgame theory, I have written and proved ca. 6 times as many theorems, but a significant part of them would have been impossible without his prior informal, conceptual ideas. We both have studied ko theory. He has provided several times more pure-CGT endgame theory than me. So on the pure theorem count, I win hands down. Overall, our achievements play in the same league.

Now, seeing this strange theorem I have serious doubt concerning your theory. Assuming it exists locally both a gote option and a sente option I cannot believe that you can ignore the sente option only on condition the temperature is high.

For me either you use another hidden assupmtion on the position or you made a mistake in your proof. I hope it is the first case!

"We study a local endgame with one player's gote and sente options in an environment of simple gotes without follow-ups. The temperature T is high with F < T, where F is the [sente option's] follow-up move value [...] the tentative gote move value MGOTE [...]

Proposition 132
[early endgame, creator's perspective and start, high temperature]
If F < T, it is a good approximation that the creator starts
- in the environment if T ≥ MGOTE,
- locally with the gote option if T ≤ MGOTE.

[... Proof filling one printing page applying proposition 66, whose proof covers half a page, and theorem 121, whose proof refers corollary 67 and proposition 120 for the late endgame, whose proof covers more than one page ...]

Proposition 133
[early endgame, preventer's perspective and start, high temperature]
If F < T, it is a good approximation that the preventer starts
- in the environment if T ≥ MGOTE,
- locally if T ≤ MGOTE.

Proof [filling almost one and a half printing pages applying proposition 66 and theorem 125 for the late endgame, whose proof also refers to proposition 124, whose proof covers one page...]

Theorem 134 [early endgame, high temperature]
If F < T, it is a good approximation that the starting player starts
- in the environment if T ≥ MGOTE,
- locally if T ≤ MGOTE (the creator chooses the gote option).

Proof
Combine propositions 132 + 133 and their proofs.□" [22]

No surprise you have doubts before reading the proofs;)

Citation of an extract from the proof of proposition 132:

"MSENTE < F is a necessary condition for the sente option itself being a local sente. For the average (MSENTE + F) / 2 of MSENTE and F, we have MSENTE < (MSENTE + F) / 2 < F. We have assumed a high temperature, that is, F < T. The tentative conditions suggest T ≤ (MSENTE + F) / 2 as a necessary condition for starting locally with the sente option. In summary, for starting locally with the sente option, we get the conditions MSENTE < (MSENTE + F) / 2 < F < T ≤ (MSENTE + F) / 2.
Since this is a contradiction to the assumption in the tentative conditions of the existing case 'starting locally with the sente option', it does not exist." [22]

Simply speaking, in conclusion, proved by contradiction to the assumption of a high temperature!

RobertJasiek · Post by **RobertJasiek** » Tue Apr 09, 2024 7:16 am

The approximations include
- the assumption of an ideal environment,
- averaging the detail of an even or odd number of values in the environment,
- while the applied late endgame proofs presume single moves instead of longer sequences, which occur in practice in every local endgame with gote and sente options, the assumption is that this detail can be ignored during the early endgame with its still rather dense environment because any local follow-up simply "vanishes" in the environment. Practical experience confirms this but maths needs to take this as an assumption because there are counter-examples for the late endgame so, in principle, pathological counter-examples could be constructed for the early endgame as if it were a rich late endgame.

Gérard TAILLE · Post by **Gérard TAILLE** » Tue Apr 09, 2024 2:48 pm

RobertJasiek wrote:
Gérard TAILLE wrote:I simply assumed the quality of your theory is quite similar to Bill's one and I find this last theory quite valuable.

"We study a local endgame with one player's gote and sente options in an environment of simple gotes without follow-ups. The temperature T is high with F < T, where F is the [sente option's] follow-up move value [...] the tentative gote move value MGOTE [...]

Proposition 132
[early endgame, creator's perspective and start, high temperature]
If F < T, it is a good approximation that the creator starts
- in the environment if T ≥ MGOTE,
- locally with the gote option if T ≤ MGOTE.

[... Proof filling one printing page applying proposition 66, whose proof covers half a page, and theorem 121, whose proof refers corollary 67 and proposition 120 for the late endgame, whose proof covers more than one page ...]

Proposition 133
[early endgame, preventer's perspective and start, high temperature]
If F < T, it is a good approximation that the preventer starts
- in the environment if T ≥ MGOTE,
- locally if T ≤ MGOTE.

Proof [filling almost one and a half printing pages applying proposition 66 and theorem 125 for the late endgame, whose proof also refers to proposition 124, whose proof covers one page...]

Theorem 134 [early endgame, high temperature]
If F < T, it is a good approximation that the starting player starts
- in the environment if T ≥ MGOTE,
- locally if T ≤ MGOTE (the creator chooses the gote option).

Proof
Combine propositions 132 + 133 and their proofs.□" [22]

No surprise you have doubts before reading the proofs;)

Citation of an extract from the proof of proposition 132:

"MSENTE < F is a necessary condition for the sente option itself being a local sente. For the average (MSENTE + F) / 2 of MSENTE and F, we have MSENTE < (MSENTE + F) / 2 < F. We have assumed a high temperature, that is, F < T. The tentative conditions suggest T ≤ (MSENTE + F) / 2 as a necessary condition for starting locally with the sente option. In summary, for starting locally with the sente option, we get the conditions MSENTE < (MSENTE + F) / 2 < F < T ≤ (MSENTE + F) / 2.
Since this is a contradiction to the assumption in the tentative conditions of the existing case 'starting locally with the sente option', it does not exist." [22]

Simply speaking, in conclusion, proved by contradiction to the assumption of a high temperature!

I do not understand Robert.

For me if you assume one player has a gote and a sente options then, if the temperature is T <= MGOTE, it is always a good approximation to play locally and OC, at such temperature, the two options (gote and sente) must exist.
Taking the sente option that means in particular that T < F.

Assuming F < T being in contradiction with the existence of a sente option, if you assume F < T, then you assume there are no sente option.
IOW your theorem can never be applied.

Because I surely missed sommething can you simply give us an exemple of its application?

RobertJasiek · Post by **RobertJasiek** » Tue Apr 09, 2024 10:17 pm

if the temperature is T <= MGOTE, it is always a good approximation to play locally

This is another good observation. It says, however, nothing about which play is correct: local gote option, local sente option or environment.

at such temperature, the two options (gote and sente) must exist.

At any temperature, both options are on the board. For certain temperatures, the question of existence is whether playing in the sente option with the alleged value conditions exists. For this study in the proof, the comparison is F < T, that is, it is not a comparison between T and MGOTE. It is application of the theorem for F < T, when, for deciding between local play in the gote option or the environment, the comparison between T and MGOTE is used.

Taking the sente option that means in particular that T < F.

So my theorem suggests.

Assuming F < T being in contradiction with the existence of a sente option, if you assume F < T, then you assume there are no sente option.

The argument in the proof is about "non-existence of choosing to play in the sente option having, in particular, its tentative value condition T ≤ (MSENTE + F) / 2". That is, the proof does not dispute the existing sente option on the board but disputes choosing play in the sente option at high temperature.

theorem can never be applied

The contradiction is not in the theorem, which applies when F < T, but part of its proof is by contradiction, which uses this assumption in the theorem.

can you simply give us an exemple of its application?

For quite a few examples of application, see [14], [22], [23]. If somebody provides the sequences and values for an example (such as the simplified problem), I show its application. Needless to say, 42 is the answer to all questions (after I spent three days to find such examples):

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

In practice, such environments do not occur. In particular, not during the early endgame.

***

BTW, not playing sente prematurely should not surprise you. Here is the theorem for an ordinary local endgame with one player's follow-up during the early endgame at high temperature:

"Theorem 89
[early endgame, starting player's perspective, high temperature, conclusion]
If F < T, it is a good approximation that the starting player starts
- in the environment if MGOTE ≤ T,
- locally if MGOTE ≥ T." [22]

Hence, during the early endgame at high temperature, the behaviour of a local endgame with gote and sente options is essentially the same as of an ordinary local endgame with one player's follow-up.

Gérard TAILLE · Post by **Gérard TAILLE** » Wed Apr 10, 2024 8:18 am

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

OK let me try to understand the meaning of this example.
Is it a good understanding to say that a move at "a" ot "b" is a local move while a move at "c" is considered to be in the environment?
If it is true does that mean that you consider black "a" as a sente option and black "b" as gote option?

Gérard TAILLE · Post by **Gérard TAILLE** » Wed Apr 10, 2024 8:52 am

gennan wrote:

Code: Select all

Code: Select all

           2
          / \      
  (3.5) 12.5 2 
        / \
      16   9

Because FD is sente I prefer drawing the tree as follows:

Code: Select all

           _F_
          /    \      
         G      D'
        / \    / \
       H   J  D  -BIG

Code: Select all

           _2_
          /   \      
  (3.5) 12.5   x 
        / \   / \
      16   9 2  -BIG

Your calculation looks good for me.
Now what is the answer to my initial question (what is the best intitial white move : a or b?
Secondary question. How can you give the answer to this initial question with the minimum calculation?
Hint : I just want to know the best move. IOW I do not ask for the miai value of the initial position.

RobertJasiek · Post by **RobertJasiek** » Wed Apr 10, 2024 9:01 am

Gérard TAILLE wrote:
RobertJasiek wrote:
$$B Black to move $$ ----------------------------------- $$ | X X X X X . X X X O O X X X X X | $$ | X X X X X . X . . . O X O O O X | $$ | X X X X X X X X O O O X O O O X | $$ | X X X X X X X X O X X X O O O X | $$ | X X X X X X X O O X X X O O O X | $$ | . O O O O O O O X X X O O O O X | $$ | . O X X X X X X X X X O O O O X | $$ | X a X . . . . . X . X b X X X X | $$ | O X X X X X X X X c O O O O O O | $$ | O O O O O O O O O O O . . . . . | $$ -----------------------------------
Click Here To Show Diagram Code
[go]$$B Black to move $$ ----------------------------------- $$ | X X X X X . X X X O O X X X X X | $$ | X X X X X . X . . . O X O O O X | $$ | X X X X X X X X O O O X O O O X | $$ | X X X X X X X X O X X X O O O X | $$ | X X X X X X X O O X X X O O O X | $$ | . O O O O O O O X X X O O O O X | $$ | . O X X X X X X X X X O O O O X | $$ | X a X . . . . . X . X b X X X X | $$ | O X X X X X X X X c O O O O O O | $$ | O O O O O O O O O O O . . . . . | $$ -----------------------------------[/go]
OK let me try to understand the meaning of this example.
Is it a good understanding to say that a move at "a" ot "b" is a local move while a move at "c" is considered to be in the environment?

Sry, LOL!

Click Here To Show Diagram Code: [go]$$B Black to move $$ ----------------------------------- $$ | X X X X X . X X X O O X X X X X | $$ | X X X X X . X . g . O X O O O X | $$ | X X X X X X X X O O O X O O O X | $$ | X X X X X X X X O X X X O O O X | $$ | X X X X X X X O O X X X O O O X | $$ | . O O O O O O O X X X O O O O X | $$ | . O X X X X X X X X X O O O O X | $$ | X s X . . . . . X . X t X X X X | $$ | O X X X X X X X X u O O O O O O | $$ | O O O O O O O O O O O . . . . . | $$ -----------------------------------[/go]

The environment comprises T and U (I cannot put captital letters or T1 on this board).

If the preventer Black does not play local reverse sente but starts in the environment, then the creator White chooses the gote option G or the sente option S. As you should have understood by tactical reading. Now find all 42s!

RobertJasiek · Post by **RobertJasiek** » Wed Apr 10, 2024 9:13 am

Gérard TAILLE wrote:what is the best intitial white move : a or b?

But, but... this depends on the whole board!

How can you give the answer to this initial question with the minimum calculation?

What is truth, eh, calculation? Are counting a score or comparing scores of settled whole board positions "calculations", in your opinion? If not, use reading and counting with zero calculations. If yes, draw the right lottery ticket with zero calculations;)

Gérard TAILLE · Post by **Gérard TAILLE** » Wed Apr 10, 2024 10:42 am

RobertJasiek wrote:
$$B Black to move $$ ----------------------------------- $$ | X X X X X . X X X O O X X X X X | $$ | X X X X X . X . g . O X O O O X | $$ | X X X X X X X X O O O X O O O X | $$ | X X X X X X X X O X X X O O O X | $$ | X X X X X X X O O X X X O O O X | $$ | . O O O O O O O X X X O O O O X | $$ | . O X X X X X X X X X O O O O X | $$ | X s X . . . . . X . X t X X X X | $$ | O X X X X X X X X u O O O O O O | $$ | O O O O O O O O O O O . . . . . | $$ -----------------------------------
Click Here To Show Diagram Code
[go]$$B Black to move $$ ----------------------------------- $$ | X X X X X . X X X O O X X X X X | $$ | X X X X X . X . g . O X O O O X | $$ | X X X X X X X X O O O X O O O X | $$ | X X X X X X X X O X X X O O O X | $$ | X X X X X X X O O X X X O O O X | $$ | . O O O O O O O X X X O O O O X | $$ | . O X X X X X X X X X O O O O X | $$ | X s X . . . . . X . X t X X X X | $$ | O X X X X X X X X u O O O O O O | $$ | O O O O O O O O O O O . . . . . | $$ -----------------------------------[/go]

The environment comprises T and U (I cannot put captital letters or T1 on this board).

If the preventer Black does not play local reverse sente but starts in the environment, then the creator White chooses the gote option G or the sente option S. As you should have understood by tactical reading. Now find all 42s!

OK then let's assume black plays in the environment.
Now it is white to play in the followibg position:

Click Here To Show Diagram Code: [go]$$B Black to move $$ ----------------------------------- $$ | X X X X X . X X X O O X X X X X | $$ | X X X X X . X . g . O X . . . X | $$ | X X X X X X X X O O O X . . . X | $$ | X X X X X X X X O X X X . . . X | $$ | X X X X X X X O O X X X . . . X | $$ | . O O O O O O O X X X . . . . X | $$ | . O X X X X X X X X X . . . . X | $$ | X s X . . . . . X . X X X X X X | $$ | O X X X X X X X X u O O O O O O | $$ | O O O O O O O O O O O . . . . . | $$ -----------------------------------[/go]

Considering only the local position :
if black plays first at "s" we reach a position R with a count B+41
if white plays first at "g" then white is gote and we reach a position G with a count B+1
if white plays first at "s" then white gets sente and we reach a position S with a count B+2

Now, if your theorem can be applied to this position, that means that F < T.
Robert, what is the value of F and T in this example, in order to apply your theorem?

Life In 19x19

Gote move vs sente move in yose

Re: Gote move vs sente move in yose

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Re: Gote move vs sente move in yose

Re: Gote move vs sente move in yose

Re: Gote move vs sente move in yose

Re: Gote move vs sente move in yose