I begin to study thermography.
On the first examples I studied, thermograhy allowed me to have a better understanding concerning the value of a local area depending of the temperature of the environment. Really interesting indeed.

In the other hand I found examples in which I failed to find a good help from thermography and I wondering if my analysis was correct.

Black to move

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . . a . . . |
$$ | X X b . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O . O O O |
$$ | . X X X X X O |
$$ | . X . O O . O |
$$ -----------------[/go]

In the diagramm above, hesitating between "a" and "b" I tried to see if thermography can help me.
I calculated the two thermographs of the local area in the upper part of the board, under the two possibilities for black. Unfortunetly the thermographs associated to a black move at "a" and a black move at "b" seems identical. Is it true ?

In addition I built the other following diagram with the same temperature for the environment:

Black to move

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . . a . . . |
$$ | X X b . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O O O O O |
$$ | . X X X X X O |
$$ | . X . O O . O |
$$ -----------------[/go]

Maybe I am wrong but in the first diagram you must play "a" and in the second you must play "b".
Can thermography help to resolve thses two situations?

Thank you in advance for helping me.

There is only one thermograph for the top side. (Edit: Oh, it's not just the top side, because White has only one eye on the right side.) It may well be that Black should normally play at a and b at different temperatures. Which player is to move is not a condition of the thermograph.



What you have are two different whole board positions, each at temperature 0. It is probably easier to figure out correct play than to calculate the thermographs for each board.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Oops now I am lost.

Lets go slowly by considering only the first diagram

Black to play

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . . a a . . |
$$ | X X a . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

I see three local areas.
The area A for which I hesitate between the three moves marked "a"
The area B, quite simple, for which the gote move at "b" has a miai value of 2.5
The area C, also quite simple, for which the gote move at "c" has a miai value of 1

The area A is a little difficult to evaluate at least because I see three possible moves.
Let's call the areas B and C the environment.
My understanding was that the temperature of the environment is equal here to 2.5 (max of miai values in the environment) but when you mention temperature 0 it seems something is wrong in my head. Can you clarify this point Bill?

In order to know if I should play in area A rather than in the environment (B + C) I have first to calculate the miai value of area A.
Seeing that the ogeima move gains between 2.5 and 3 points, without knowing the exact value of the miai value, I know its value is greater or equal to 2.5 and I conclude it is a good idea to begin by a move in area A.

Before going further with the different possibilities for black in area A, is the beginning of the reasonning correct?

OK. Then we regard each of the moves in the top as sente, since they threaten to kill White. If White dies, the other areas of the board become moot, so they are not independent. However, we can get around that by assigning the value if Black kills as BIG. I.e., we simply assume that White must answer Black's threat and do not worry about the details. Since we are using the thermograph for heuristics, that's good enough, in general.

Now let's look at the right side of the thermograph, when White plays first. (White is associated with Right and Black with Left. Since Black scores are positive, this reverses the numbering of the x-axis that we learned in school. A quirk of combinatorial game theory (CGT).)

Click Here To Show Diagram Code

[go]$$Wc
$$ -----------------
$$ | . . . . . . . |
$$ | X X 1 . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

lives, OC, leaving the hane by either side in the top left. Now we are concerned with the left side of that thermograph.

Click Here To Show Diagram Code

[go]$$Bc
$$ -----------------
$$ | . 3 1 2 . . . |
$$ | X X W . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

Black to play plays the hane-and-connect of - , leaving a local score of +1 for Black in the top left corner and -8 for White on the top and right, for a total of -7. Since we are regarding b and c as independent, we do not count those regions. (We leave the justification for considering - as a unit for a later discussion. It is something that go players understand instinctively. )

Click Here To Show Diagram Code

[go]$$Wc
$$ -----------------
$$ | . 1 . . . . . |
$$ | X X W . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

White to play plays the hane at , leaving a local score of -9.

The position after is a gote with each side gaining 1 point. If is White's correct local play, then below temperature 1 Black answers for a local score of -7. IOW, below temperature 1 becomes a global sente, even though it is a local reverse sente. in this diagram does not show up in the thermograph, but it goes to determine the territorial value (count) after and the temperature below which Black replies to .

But White has another plausible play instead of , the jump to the edge.

Click Here To Show Diagram Code

[go]$$Wc
$$ -----------------
$$ | . . 1 . . . . |
$$ | X X . . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

If White plays we may consider the following sequence as a unit. Again, we leave why for later, but it is obvious to most go players to do so.

Click Here To Show Diagram Code

[go]$$Wc
$$ -----------------
$$ | . . 1 . . . . |
$$ | X X 2 3 . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

What about the thermograph of the resulting position?

Click Here To Show Diagram Code

[go]$$Bc
$$ -----------------
$$ | . 1 W 2 . . . |
$$ | X X B W . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

For the left wall of the thermograph after the marked stones have been played, certainly looks like sente. If so, replies for a local score of -6. This is the best that White to play can do locally if Black replies, and it is not as good as playing the second line block, which guarantees at least -7. So the jump to the edge is a mistake, at all temperatures.

Now, that fact was probably obvious, but we can demonstrate it as shown.



Actually, once we know that the result of allowing Black two moves in a row in the top is BIG, we know that Black can play there with sente. The miai value is the gain for White of playing the reverse sente. The gain for Black's first play is BIG, which is all we need to know for comparison. And by inspection we know that Black does not have to preserve a play in the top as a ko threat.

More later.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

In order to talk about thermograph let's me verify my understanding is correct:

Let's assume the best sequence for black is the sente following sequence:

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . 3 1 2 . . |
$$ | X X . 4 . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

and let's suppose the best sequence for white is the gote move:

Click Here To Show Diagram Code

[go]$$W
$$ -----------------
$$ | . . . . . . . |
$$ | X X 1 . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

Is the following thermograph correct with this assumption?

OK. To continue, let's look at Black's play on the top. We already know that Black plays with sente.

Click Here To Show Diagram Code

[go]$$Bc Variation 1
$$ -----------------
$$ | . . . . . . . |
$$ | X X 1 2 . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

First let's look at Black's crawl and White's block. At first blush, it looks like what is left is a double hane-and-connect, which is worth -5, with Black continuing at or below temperature 1. But looking a bit deeper, as I believe you have, that is not the case.

Click Here To Show Diagram Code

[go]$$Wc White first
$$ -----------------
$$ | . 2 1 3 . . . |
$$ | X X B W . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

OC, if White plays first the local score is -6, as expected.

Click Here To Show Diagram Code

[go]$$Bc Black first
$$ -----------------
$$ | . . 3 1 2 a . |
$$ | X X B W . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

The local score is not -4. Why? Because of the follow-up at a.

Click Here To Show Diagram Code

[go]$$Wc White first
$$ -----------------
$$ | . . B B W 1 . |
$$ | X X B W . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

White to play can play , for a local score of -3. What if Black plays first?

Click Here To Show Diagram Code

[go]$$Bc Black first, ko
$$ -----------------
$$ | . . B B W 1 . |
$$ | X X B W 3 2 . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

If Black plays White can make a ko with . The result will depend upon the ko threat situation and the rules.

Now, Professor Berlekamp developed komaster theory, which makes certain assumptions about who can win the ko and how, in the 1980s, and first published about it in Games of No Chance (MSRI, 1996). For non-komaster situations, Berlekamp, Bill Fraser, and I developed a theory of a Neutral Threat Environment (NTE) in the early 2000s, and I first published about it in LNCS 2883: Computers and Games (Springer, 2003). AFAICT, none of these ideas has been adopted by professional go players.

The traditional assumption, as may be inferred from the texts, is that there are no ko threats that are not shown. Assuming no ko threats, White cannot afford to make the ko, as Black kills White if she wins the ko.

If we assume that there are no ko threats, the evaluation depends upon the number of dame White has.

Click Here To Show Diagram Code

[go]$$Bc Black first, no ko, zero dame
$$ -----------------
$$ | . . B B W 1 . |
$$ | X X B W 2 . 3 |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O W O O O |
$$ | . X X X X X O |
$$ | . X B O O W O |
$$ -----------------[/go]

Again, - form a unit. The local score is +2. So the count before or is -½ and the gain for each player is 2½.

Backing up then, to before the hane-and-connect, White's hane-and-connect moves to a local score of -6, and Black's hane-and-connect moves to a count of -½ at or above temperature 2½, we get a count of -3¼ with a move gaining 2¾. And backing up again to the original position (with no dame), we get a count of -3¼ and a gain for the reverse sente of 4¾.

Click Here To Show Diagram Code

[go]$$Bc Black first, no ko, one dame
$$ -----------------
$$ | . . B B W 1 6 |
$$ | X X B W 2 4 3 |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O W O O O |
$$ | . X X X X X O |
$$ | . X 5 O O W O |
$$ -----------------[/go]

- form a unit. and are miai. The local score is -3, the same as when White plays first.

Backing up to before the hane-and-connect, the count is -4½ and each play gains 1½.

Edit: And backing up to the original position, the count is -4½ and White's reverse sente gains 3½.

That evaluation will be true with more dame, OC.

Going back to the board as given:

Click Here To Show Diagram Code

[go]$$Bc
$$ -----------------
$$ | . . . a a . . |
$$ | X X a . . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O c O O O |
$$ | . X X X X X O |
$$ | . X . O O b O |
$$ -----------------[/go]

Since the b and c regions involve White dame, we cannot just assume that they are independent of the top region.

More later.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Oops, I missed the ko you mentionned!
Let me have the opportunity to build a simpler position because this one does not reflect the issue I have in mind.

Let's make the traditional assumption of no ko threats. Then

Click Here To Show Diagram Code

[go]$$Bc Zero dame, Black first
$$ -----------------
$$ | . . B B W 2 . |
$$ | X X 1 W . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O W O O O |
$$ | . X X X X X O |
$$ | . X B O O W O |
$$ -----------------[/go]

is sente. Local score = -3.

Click Here To Show Diagram Code

[go]$$Wc Zero dame, White first
$$ -----------------
$$ | . 2 B B W 3 . |
$$ | X X 1 W . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O W O O O |
$$ | . X X X X X O |
$$ | . X B O O W O |
$$ -----------------[/go]

- form a unit. Local score = -4.

This White reverse sente will not appear in the original thermograph. The original count is -3 and the reverse sente gains 5.

Click Here To Show Diagram Code

[go]$$Wc One dame, White first
$$ -----------------
$$ | . 2 B B W . . |
$$ | X X 1 W . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O W O O O |
$$ | . X X X X X O |
$$ | . X . O O W O |
$$ -----------------[/go]

is sente. The local score is -4. OC, White will have to make a protective play.

Click Here To Show Diagram Code

[go]$$Bc One dame, Black first
$$ -----------------
$$ | . . B B W . . |
$$ | X X 1 W . . . |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O W O O O |
$$ | . X X X X X O |
$$ | . X . O O W O |
$$ -----------------[/go]

The local score is -3. is a reverse sente that gains 1 point. It will show up in the thermograph below temperature 1, since in that case Black will not stop with the sente sequence.

In this case the original count is -4 and White's reverse sente gains 4. These values will hold with more dame.

The attached thermograph is like that, but the right wall is 1 pt. off.

And we still cannot assume that the b and c areas are independent.

More later.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Bill, let me first verify with you if this new position fits my issue:

Diagramm 1
Black to play

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . . . . . O |
$$ | X X . . . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O . O O O |
$$ | . X X X X X O |
$$ | . X . O O . O |
$$ -----------------[/go]

I hope the best sequence is the following

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . 7 5 6 . O |
$$ | X X 1 2 . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O 4 O O O |
$$ | . X X X X X O |
$$ | . X . O O 3 O |
$$ -----------------[/go]

Diagramm 2
Black to play

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . . . . . O |
$$ | X X . . . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O O O O O |
$$ | . X X X X X O |
$$ | . X . O O . O |
$$ -----------------[/go]

here I hope the best sequence is the following

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . 7 3 1 2 . O |
$$ | X X 6 4 . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O O O O O |
$$ | . X X X X X O |
$$ | . X . O O 5 O |
$$ -----------------[/go]

If the above sequences are correct my basic question is the following:

Black to play

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . . a c . O |
$$ | X X b . . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O d O O O |
$$ | . X X X X X O |
$$ | . X . O O . O |
$$ -----------------[/go]

Can thermography help (I do not claim for a solution given by thermography but just an help!) to choose between "a", "b" and "c" depending of the environment (here the presence or absence of point d) ?

BTW if the environment is empty you can see that the correct black move is the ogeima at "c".

Basically, no.

Why? Because thermography works best with a rich environment of numerous alternative plays that are close in size. Both of these environments are sparse with large temperature drops.

Still, thermography offers a preference of plays to try in order. However, with so few plays on the board, it is probably easier to work out best play than to derive the thermographs.

That said, thermography's top choice of plays works for the first board.

Click Here To Show Diagram Code

[go]$$Bc
$$ -----------------
$$ | . 9 5 2 1 0 O |
$$ | X X 4 3 6 . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O a O O O |
$$ | . X X X X X O |
$$ | . X . O O 7 O |
$$ -----------------[/go]

takes ko at , at a

Result: Black +8, the same as with the sequence you found.

However, it is not as good for the second board.

Click Here To Show Diagram Code

[go]$$Bc
$$ -----------------
$$ | . 9 5 2 1 0 O |
$$ | X X 4 3 6 . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . X O O O O O |
$$ | . X X X X X O |
$$ | . X . O O 7 O |
$$ -----------------[/go]

takes ko at

The result is only +6, which is 1 point worse than the sequence you found.

However, because of the big temperature drop after F-01, you might derive the thermograph of the top region plus F-01, in which case that thermograph will indicate how to play at or below temperature 1. The combined thermograph will show that after Black takes sente she will then play at F-01, and then it will be better to leave White a sente at temperature 1 than a gote at temperature 2, even at the cost of 1 point on average. But of course you can come to that conclusion without figuring out the thermograph.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Very interesting Bill. Now I begin to understand !

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . . . . . O |
$$ | X X . . . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------[/go]

I tried to go further in order to answer the following question: under an "ideal" environment, can thermography help choosing between the gote ogeima and the sente keima?

I tried to draw the corresponding combined thermograph (choosing to ignore the point of the white eye) and the answer seems yes but I am not completly sure:
Above temperature +3 you have to choose the sente keima and under this temperature you have to choose ogeima.
In addition, in order to avoid a reverse sente white move, you would be advised to play the sente keima before you reach the +4 temperature
Is that true ?

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . . . a . . O |
$$ | X X b . . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------[/go]

Yes Bill, after a deeper analysis I understand clearly what you mean. In fact I see some interesting similarity with double sente moves analysis.
When thinking about what you call a rich environment of numerous alternative plays that are close in size it is clear that you cannot find in this ideal environment what is commonly called a double sente move.
If you cannot (or you do not want ?) read all the yose, you have to exclude from the environment all double sente moves and then you can assume the remaining environment is ideal.

Let'us take only one double sente area and assume white has just played in this area threatening a big got move g >> t. We are now in a very common situation where it exists a big gap between g and t.
Now it is black to play and, to avoid answering white threat and give her a good reverse sente move, black decides to play a sente move similar to move at "a" or "b" in the previous diagram. What move do you choose ? "a" or "b" ?
What is the difference between "a" and "b" ? They have the same miai value but "b" create a gote move with a miai value equal to +1.
As a consequence if t >= 1 the two moves "a" and "b" are equivalent.
What happens if 0 <= t < 1 ?

The key in this problem seems to be the tedomari/miai situation above t.
If black plays "a" in sente she has built a tedomari situation above t, made of only big gote move g
In the other hand if black plays "b" in sente she has built a miai situation above t, made of the big gote move g and the gote move of value +1 > t
As a consequence black must choose move "a".

Now let's take a situation with two double sente areas and assume black has taken the first one and white has answered with the second one. We have now two big gote moves g1 and g2 >> t. You can see that the tedomari/miai situation is the reverse comparing to the previous one.
As a consequence black must choose move "b".

It is exactly the situation I created in my problem with the temperature of the environment equal to zero and:
- in first diagram two gote moves => black must choose "b" to create a tedomari situation
- in second diagram only one gote move => black must choose "a" to avoid creating a miai situation.

Thank you again Bill for your help which allowed me to try to go farther (but maybe with some new mistakes ??)

Thermography does that by definition. It finds the optimal minimax result at each temperature in an ideal enviorment.

However, the large monkey jump (ogeima) is sente, too.

I tried to draw the corresponding combined thermograph (choosing to ignore the point of the white eye) and the answer seems yes but I am not completly sure:
Above temperature +3 you have to choose the sente keima and under this temperature you have to choose ogeima.
In addition, in order to avoid a reverse sente white move, you would be advised to play the sente keima before you reach the +4 temperature
Is that true ?[/quote]

I don't know what you mean by ignoring the point of the White eye.

One option not shown yet is the kosumi.

Click Here To Show Diagram Code

[go]$$Bc Kosumi
$$ -----------------
$$ | . . 1 . . . O |
$$ | X X . 2 . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------[/go]

We can compare it to the keima by means of a difference game. Let's mirror the board, except for the results of the two different sente exchanges.

Click Here To Show Diagram Code

[go]$$Bc Kosumi vs. Keima
$$ --------------------------------
$$ | . . B . . . O | X . B W W . . |
$$ | X X . W . . O | X . . B . O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

If the kosumi exchange is at least as good as the keima exchange then White to play cannot win the difference game.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Keima, White first
$$ --------------------------------
$$ | . . B 1 . . O | X . B W W 3 . |
$$ | X X 4 W . . O | X . . B 2 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

After , plays sente and then makes jigo.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Keima, White first
$$ --------------------------------
$$ | . 6 B 4 5 . O | X . B W W 3 . |
$$ | X X 1 W . . O | X . . B 2 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

If plays here, - make an obvious jigo.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Keima, White first
$$ --------------------------------
$$ | . . B 2 3 . O | X . B W W . . |
$$ | X X 4 W . . O | X . . B 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

If plays the reverse sente on the right board, - make jigo.

White to play cannot win the difference game, so the kosumi sente is at least as good as the keima sente.

But are the two equivalent? If so, then Black to play cannot win the difference game, either. Let' see.

Click Here To Show Diagram Code

[go]$$Bc Kosumi vs. Keima, Black first
$$ --------------------------------
$$ | . . B 3 4 . O | X . B W W 2 . |
$$ | X X 5 W . . O | X . . B 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

plays sente on the right and then Black makes an extra point on the left to win.

Therefore, the kosumi sente is better than the keima sente.

(N. B. We cannot conclude that if both plays are gote.)

While we are at it, let's compare the kosumi sente to the crawl sente.

Click Here To Show Diagram Code

[go]$$Bc Kosumi vs. Crawl
$$ --------------------------------
$$ | . . B . . . O | X . . . . . . |
$$ | X X . W . . O | X . . B W O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

Click Here To Show Diagram Code

[go]$$Bc Kosumi vs. Crawl, Black first
$$ --------------------------------
$$ | . 7 B 5 6 . O | X . . 3 1 2 . |
$$ | X X 4 W . . O | X . . B W O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

Black plays the hane-and-connect on the right and gets the last play on the left to win by 1 pt. If is at 5, at 4 wins, as well.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Crawl, White first
$$ --------------------------------
$$ | . 6 B 1 . . O | X . . 4 2 3 . |
$$ | X X 5 W . . O | X . . B W O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

If descends to the edge on the left, Black plays the hane-and-connect on the right for jigo. If is at 5, Black does the same.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Crawl, White first
$$ --------------------------------
$$ | . . B 4 5 . O | X . 2 1 3 . . |
$$ | X X 6 W . . O | X . . B W O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

If White plays the hane-and-connect on the right side, then Black plays sente on the left and gets the last play for jigo.

So the kosumi sente is better than the crawl sente, as well.

That's two down, one to go.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

At your peril, OC.

It was known in the 1970s that there is a problem with the idea of double sente. See Ogawa-Davies, for instance. OC, there are global double sente, but they depend upon what else is on the board. In terms of CGT evaluation or even traditional evaluation of go positions, they do not exist. Circa 1980 I submitted an article to Go World to that effect, but it was not accepted. {shrug} For more on double sente, see https://senseis.xmp.net/?DoubleSenteIsRelative .



Neither is as good as the kosumi.

If you do a difference game to compare the two as sente, you find that neither is better than the other, but they are not equivalent.

Click Here To Show Diagram Code

[go]$$Bc Crawl vs. Kosumi
$$ --------------------------------
$$ | . . . . . . O | X . B W W . . |
$$ | X X B W . . O | X . . B . O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

Click Here To Show Diagram Code

[go]$$Bc Crawl vs. Kosumi, Black first
$$ --------------------------------
$$ | . . 5 3 4 . O | X . B W W 2 . |
$$ | X X B W . . O | X . . B 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

plays sente on the right and then the hane-and-connect on the left to win by 1 pt.

Click Here To Show Diagram Code

[go]$$Wc Crawl vs. Kosumi, White first
$$ --------------------------------
$$ | . 2 1 3 . . O | X . B W W 5 . |
$$ | X X B W . . O | X . . B 4 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

plays the hane-and-connect on the left to gain 1 pt. and win.

Neither sente can be shown to be as good as the other. IOW, they are incomparable. Which is better, if either, depends on the rest of the board.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

After , I agree that the position looks better than the small jump or the crawl sente but is the move the correct one to judge the move ?

Let me try this other move:

Click Here To Show Diagram Code

[go]$$B Kosumi
$$ -----------------
$$ | . . 1 2 . . O |
$$ | X X . . . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------[/go]

At first sight, because the exchange looks like reversible play, if is correct then is sente !

I see two possible answers for black:

Click Here To Show Diagram Code

[go]$$B Kosumi
$$ -----------------
$$ | . . 1 2 . . O |
$$ | X X a b . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------[/go]

if black a:

Click Here To Show Diagram Code

[go]$$B Kosumi
$$ -----------------
$$ | . . 1 2 . . O |
$$ | X X 3 4 . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------[/go]

white can simply answer and the result is clearly a loss for black, comparing to the sequence with the small jump

if black b:

Click Here To Show Diagram Code

[go]$$B Kosumi
$$ -----------------
$$ | . . 1 2 . . O |
$$ | X X 4 3 . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------[/go]

white cut at which switch to the large jump variation

Click Here To Show Diagram Code

[go]$$B Kosumi
$$ -----------------
$$ | . . 1 a . . O |
$$ | X X . b . . O |
$$ | . X O O O O O |
$$ | . X X X O O . |
$$ | . . . X O O O |
$$ | . . . X X X X |
$$ | . . . . . . . |
$$ -----------------[/go]

This is again clearly a loss for black because by playing the kosumi instead of the large jump black offers white not only this move at "a" but also the move at "b"

[quote="Bill Spight"]
It was known in the 1970s that there is a problem with the idea of double sente. See Ogawa-Davies, for instance. OC, there are global double sente, but they depend upon what else is on the board. In terms of CGT evaluation or even traditional evaluation of go positions, they do not exist. Circa 1980 I submitted an article to Go World to that effect, but it was not accepted. {shrug} For more on double sente, see https://senseis.xmp.net/?DoubleSenteIsRelative .
[quote]

I am a little surprise to read that double sente do not exist.
As soon as you propose a defintion for a double sente it exists doesn't it ?
Inherently, I agree that defining a sente or double sente move maybe a difficulty but in the context of an environment with a temperature t it seems quite obvious:
If black plays a move and the threat after this move is greater or egal to t then the black move is sente.
If at the same time a white play creates a threat also greater or equal to t then it is a double sente.

Not necessarily.



What you are describing is a global double sente, which do exist. However, for a large enough ambient temperature a play in such a position by one player or another will not be global sente. Global double sente are relative to what else is on the board. There is no such think as an intrinsic, locally defined double sente, except those in which the sente plays do not gain anything. Seki, for example.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

So the choice for Black comes down to the kosumi or the large monkey jump. Now, we already know that these two are incomparable, but let's take a look with difference games.

There are different ways of replying to the monkey jump. Let's look at a few.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Monkey jump 1
$$ --------------------------------
$$ | . . B . . . O | X 4 1 . 3 . . |
$$ | X X . W . . O | X . 2 . . O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

is the usual reply, but here it looks passive.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Monkey jump 1, White first
$$ --------------------------------
$$ | . . B 1 . . O | X B W 3 W 5 . |
$$ | X X 2 W . . O | X . B 6 4 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

White goes first on both boards and plainly wins. Can Black do better?

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Monkey jump 1, White first
$$ --------------------------------
$$ | . . B 1 . . O | X B W 2 W . . |
$$ | X X 4 W . . O | X . B 5 3 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

fills ko.

White wins again. Obviously. Now let Black play first.

Click Here To Show Diagram Code

[go]$$Bc Kosumi vs. Monkey jump 1, Black first
$$ --------------------------------
$$ | . . B 1 2 . O | X B W 4 W 6 . |
$$ | X X 3 W . . O | X . B 7 5 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

White wins again.

Click Here To Show Diagram Code

[go]$$Bc Kosumi vs. Monkey jump 1, Black first
$$ --------------------------------
$$ | . . B 3 4 . O | X B W 1 W . . |
$$ | X X 5 W . . O | X . B 6 2 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

fills ko.

White wins yet again.

If Black is going to reply like this, plainly the monkey jump is better.

Let's look at a different reply to the monkey jump.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Monkey jump 2
$$ --------------------------------
$$ | . . B . . . O | X . 1 4 3 . . |
$$ | X X . W . . O | X . 2 . . O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

is the usual reply, but here it looks passive. OTOH, Black has , which I overlooked the other day.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Monkey jump 2, White first
$$ --------------------------------
$$ | . . B 6 7 . O | X 4 W B W 5 . |
$$ | X X 8 W . . O | X . B 1 2 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

connects.

Black has nothing better. White wins by 2 points.

Click Here To Show Diagram Code

[go]$$Bc Kosumi vs. Monkey jump 2, Black first
$$ --------------------------------
$$ | . . B 4 . . O | X 3 W B W 6 . |
$$ | X X 5 W . . O | X . B 2 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

captures two White stones to win by 1 point. White has nothing better. Black's play does not depend on winning a ko fight.

So with the replies at 2 and 4, the plays are incomparable.

What about the reply that I found the other day? How does it compare with 2 and 4?

Click Here To Show Diagram Code

[go]$$Bc Reply 1 vs. reply 2
$$ --------------------------------
$$ | . . 5 2 1 . O | X . W B W . . |
$$ | X X 4 3 6 . O | X . B . . O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

Click Here To Show Diagram Code

[go]$$Bc Reply 1 vs. reply 2, Black first
$$ --------------------------------
$$ | . 5 B 6 B 2 O | X . W B W 4 . |
$$ | X X W B W . O | X . B 1 3 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

To win, avoids a mirror image. Still, manages to make jigo. All roads lead to Rome.

White's reply on the left, sacrificing a stone, is at least as good as and on the right.

Click Here To Show Diagram Code

[go]$$Wc Reply 1 vs. reply 2, White first
$$ --------------------------------
$$ | . 4 B 2 B 3 O | X 6 W B W . . |
$$ | X X W B W . O | X . B 5 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

White plays to avoid a mirror image. fills the ko to win by 1 pt.

Click Here To Show Diagram Code

[go]$$Wc Reply 1 vs. reply 2, White first
$$ --------------------------------
$$ | . 4 B 5 B 3 O | X . W B W . . |
$$ | X X W B W . O | X . B 2 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

protects on the right, but White captures two stones on the left to win by 1 pt.

So my feeling was correct. The sacrifice is the correct reply to the monkey jump.

In case it's not obvious, let's put the icing on the cake. There is another reply.

Click Here To Show Diagram Code

[go]$$Wc Sacrifice 1 vs. sacrifice 2
$$ --------------------------------
$$ | . . B . B . O | X 8 1 5 2 7 . |
$$ | X X W B W . O | X . 6 4 3 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

is a sacrifice you see from time to time, but it doesn't look too good here, eh?

Click Here To Show Diagram Code

[go]$$Wc Sacrifice 1 vs. sacrifice 2, White first
$$ --------------------------------
$$ | . 4 B 5 B 1 O | X B W W 2 W . |
$$ | X X W B W . O | X . B B W O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner, 1 prisoner
takes back

White wins by 2 pts. Black has nothing better.

Click Here To Show Diagram Code

[go]$$Bc Sacrifice 1 vs. sacrifice 2, Black first
$$ --------------------------------
$$ | . 3 B 1 B 2 O | X B W W 4 W . |
$$ | X X W B W . O | X . B B W O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner, 1 prisoner

Black saves his two stones, but White saves his to get jigo.

Click Here To Show Diagram Code

[go]$$Bc Sacrifice 1 vs. sacrifice 2, Black first
$$ --------------------------------
$$ | . 3 B 4 B 2 O | X B W W 1 W . |
$$ | X X W B W . O | X . B B W O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner, 1 prisoner

connects, for jigo this way.

So my sacrifice is the right one.

Hmmm. Is there no other good reply?

Click Here To Show Diagram Code

[go]$$Wc Sacrifice vs. Reply 3
$$ --------------------------------
$$ | . . B . B . O | X 6 1 5 3 . . |
$$ | X X W B W . O | X . 2 . 4 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

threatens to throw in at 5 and capture . But then threatens to kill.

The right side is settled. Either player wins by playing on the left. So these plays are incomparable.

I took my bows too soon.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Just to check.

Click Here To Show Diagram Code

[go]$$Wc Sacrifice vs. Monkey jump 1
$$ --------------------------------
$$ | . . B . B . O | X 4 1 . 3 . . |
$$ | X X W B W . O | X . 2 . . O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

Click Here To Show Diagram Code

[go]$$Wc Sacrifice vs. Monkey jump 1, White first
$$ --------------------------------
$$ | . 6 B 5 B 1 O | X B W 2 W . . |
$$ | X X W B W . O | X . B 4 3 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

White wins. Black has nothing better.

Click Here To Show Diagram Code

[go]$$Bc Sacrifice vs. Monkey jump 1, Black first
$$ --------------------------------
$$ | . 3 B 1 B 2 O | X B W 4 W 6 . |
$$ | X X W B W . O | X . B 7 5 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

Black wins.

Click Here To Show Diagram Code

[go]$$Bc Sacrifice vs. Monkey jump 1, Black first
$$ --------------------------------
$$ | . 3 B 1 B 2 O | X B W 5 W . . |
$$ | X X W B W . O | X . B 6 4 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

fills the ko and wins.

So these plays are incomparable.

One more time.

Click Here To Show Diagram Code

[go]$$Bc Reply 3 vs. Monkey jump 1, Black first
$$ --------------------------------
$$ | . . B B B W O | X B W 1 W . . |
$$ | X X W . W . O | X . B 3 2 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

captures one stone and wins.

Click Here To Show Diagram Code

[go]$$Wc Reply 3 vs. Monkey jump 1, Black first
$$ --------------------------------
$$ | . . B B B W O | X B W 1 W . . |
$$ | X X W . W . O | X . B . 2 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

connects, but makes jigo.

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[go]$$Bc Reply 3 vs. Monkey jump 1, Black first
$$ --------------------------------
$$ | . . B B B W O | X B W 2 W . . |
$$ | X X W . W . O | X . B 3 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

fills the ko, for jigo.

So we can discard Reply 3, and Monkey Jump 1 is incomparable with the sacrifice.

Just one more time.

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[go]$$Bc Reply 4 vs. Monkey jump 1
$$ --------------------------------
$$ | . . . 3 1 4 O | X B W . W . . |
$$ | X X . . 2 . O | X . B . . O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

Suppose Black extends on the edge instead of jumping. It looks nuts, but let's see.

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[go]$$Wc Reply 4 vs. Monkey jump 1, White first
$$ --------------------------------
$$ | . 6 1 B B W O | X B W 4 W . . |
$$ | X X 2 3 W . O | X . B 8 5 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

connects

White wins. Black has nothing better.

Click Here To Show Diagram Code

[go]$$Bc Reply 4 vs. Monkey jump 1, Black first
$$ --------------------------------
$$ | . . 3 B B W O | X B W 4 W 6 . |
$$ | X X 1 2 W . O | X . B 7 5 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

Black wins.

The two plays are incomparable.

Well, I guess we have to check it with the sacrifice.

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[go]$$Bc Sacrifice vs. Reply 4, Black first
$$ --------------------------------
$$ | . 3 B 1 B 2 O | X B W W 6 . . |
$$ | X X W B W . O | X . B 5 4 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

Black connects, White makes jigo.

Click Here To Show Diagram Code

[go]$$Bc Sacrifice vs. Reply 4, Black first
$$ --------------------------------
$$ | . 7 B 6 B 4 O | X B W W 1 5 8 |
$$ | X X W B W . O | X . B 3 2 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

connects to win. White has nothing better.

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[go]$$Wc Sacrifice vs. Reply 4, White first
$$ --------------------------------
$$ | . 6 B 4 B 5 O | X B W W 3 . . |
$$ | X X W B W . O | X . B 2 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

Jigo.

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[go]$$Wc Sacrifice vs. Reply 4, White first
$$ --------------------------------
$$ | . 6 B 7 B 3 O | X B W W 4 5 . |
$$ | X X W B W . O | X . B 2 1 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

connects, for jigo.

Click Here To Show Diagram Code

[go]$$Wc Sacrifice vs. Reply 4, White first
$$ --------------------------------
$$ | . 6 B 7 B 1 O | X B W W 2 5 . |
$$ | X X W B W . O | X . B 4 3 O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

1 prisoner

connects, for jigo.

This may eliminate the extension.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Click Here To Show Diagram Code

[go]$$Wc Kosumi vs. Monkey jump 1
$$ --------------------------------
$$ | . . X b . . O | X c 1 d 3 . . |
$$ | X X . a . . O | X . 2 . . O O |
$$ | . X O O O O O | X X X X X O . |
$$ | . X X X O O . | . X X O O O . |
$$ | . . . X O O O | X X X O . . . |
$$ | . . . X X X X | O O O O . . . |
$$ | . . . . . . . | . . . . . . . |
$$ --------------------------------[/go]

For the time being I am still not convinced that kosumi is incomparable with the monkey jump.
Depending of the environment white must choose the correct answer between "a" or "b" and black must choose the correct answer between "c" or "d".

My reasonning is the following:
1) if the environment is such that a move at "c" is best in the right diagram then, in the left diagram, I decide with white to play "a" and black cannot win
2) if now the environment is such that a move at "d" is best in the right diagram then, in the left diagram, I decide with white to play "b" and here again black cannot win.

My conclusion is that it does not exist an environment in which the kosumi is better that the monkey jump. Where am I wrong?