OK. We know that Black first can not do better than to play the hane, with some possible but now unknown exceptions. What if White plays first and takes the ko?

Let us add this game to the corner to get the ko ensemble.

{u||||2u|0||-u|||-2u}, where 6½ > u > t > 1

Variation 1.

White first takes ko. (Written territorial values below are averages.)

Click Here To Show Diagram Code

[go]$$W White first takes ko
$$ --------------
$$ | X 1 X O X . .
$$ | 3 X O O X . .
$$ | X 5 O X X . .
$$ | . O O X . . .
$$ | 2 O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]

= u = t

s = -5 + u + t

Now let take -u. There are two variations.

Variation 2.

Click Here To Show Diagram Code

[go]$$W White takes -u
$$ --------------
$$ | X 3 X O X . .
$$ | 5 X O O X . .
$$ | X 7 O X X . .
$$ | . O O X . . .
$$ | 2 O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]

, , = u

s = - 5 + 2u

Taking the ko is better for White than variation 2 by u - t. How does that happen?

plays to {2u|0||-u|||-2u}

After plays the hane, cannot, on average, afford to play to -2u, because will kill the corner for

s = 21 - 2u > 8.

After takes the ko, plays to {2u|0||-u}. must still take the ko.

After takes the ko, plays to {2u|0}. must win the ko.

Now plays to 2u, for s = -5 + 2u.

Variation 3.

What if does not play the hane now but follows Berlekamp's Sentestrat strategy by playing to {2u|0||-u}, instead? Now let play to -u.

Click Here To Show Diagram Code

[go]$$W White takes -u
$$ --------------
$$ | X 5 X O X . .
$$ | 7 X O O X . .
$$ | X 9 O X X . .
$$ | . O O X . . .
$$ | 4 O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]

= -u, = u, = -u, , . = t

s = -5 - u + 3t

This result is worse for White than taking the ko because

s = -5 - u + 3t < -5 + u + t , that is, when

t < u , which is presumed.

But that simply means that should not play Sentestrat.

Edit: I think that Berlekamp would object to my calling in this case an example of Sentestrat, because does not actually raise the local temperature, it keeps it the same. But it is like Sentestrat in that it replies to your opponent's play instead of making your own play.

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

Visualize whirled peas.

Everything with love. Stay safe.

Oops, surely you are teasing me Bill.

Click Here To Show Diagram Code

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

I showed the white move is bad in a pure gote environment {g1|-g1}, {g2|-g2}, {g3|-g3} ....
and now you find an environment {u||||2u|0||-u|||-2u}, where 6½ > u > t > 1 and where is better than playing -u. Yes OC Bill it is possible to find a special environment (even without ko!) in which could be better.

I understood from your post https://lifein19x19.com/viewtopic.php?p=265525#p265525 (where you used the acronym "KISS") you prefer to keep things simple by avoiding adding even simple gote. Yes your are teasing me Bill don't you?

Though taking the ko by in the diagram above might be good in certain circumtances (maybe also if black has ko threats available but it is the another context), I consider that this move is in general a bad move.
Did you find an environment with only simple gote {u|-u} in which is better than playiing in the environment?

Click Here To Show Diagram Code

[go]$$ Corner ko
$$ --------------
$$ | . 2 . . X . .
$$ | 4 1 O O X . .
$$ | 3 . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]

After this sequence you studied tenuki in the environment
I am wondering if this could really by a good sequence (I mean in a simple environment, either ideal or made of only simple {u|-u} gote points.
My feelig is that both and reverses. If it is true either black has to continue in the corner or black should prefer tenuki directly instead of
What is your feeling?

It's not just better, it's thermographically better. t remains the same while the ko ensemble is played out.

I say that because you seem to be resisting the idea of including moves in the environment in the ko ensemble. I have sympathy for your approach, because it is one that I took for some 25 years.



Bad move is a strong judgement, which, IMHO, is unwarranted. You haven't even shown that there is a loss at all from playing in the ko. (Not that it is a good idea. It is obvious in general that White should wait for Black to play the hane.)



In the thermographic environment, which is composed of simple gote, the gain from White taking the ko is equal to the gain from playing in the environment. That is unusual, since we are at a lower temperature than that of the mast value, above which neither player is likely to play locally. It is a result of the inclined mast.

So we have two moves that are thermographically equal in value. Since thermography plays the averages, that does not mean that are exactly equal. We do expect that normally any difference between them will be slight, so that even if one is wrong, it may not make any difference in the final score. That is not the stuff of bad moves. It also means that we cannot say, a priori, which move is better. Now we know, as a practical matter, that it is in general better for White not to take the ko, but thermography tells us that there are potentially cases where taking the ko is better, and that often it does not matter which play is made.

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

Visualize whirled peas.

Everything with love. Stay safe.

No doubt that by adding the area {u||||2u|0||-u|||-2u}, where 6½ > u > t > 1, to the ko ensemble taking the ko gains u -t.
But the area {u||||2u|0||-u|||-2u} is in fact very subtil in order to reach this goal.
If instead you take only the simple gote {u|-u} always with 6½ > u > t > 1, then taking the ko will lose 2(u - t) and here also playing in the environment for white is not just better it's thermographically better!

That's my point : unless you add to the ko ensemble a very subtle area, playing in the environement for white is thermographically better than taking the ko.

Look at my previous calculation with an environment g1 ≥ g2 ≥ g3 ≥ g4 ...
ScoreWhiteTakesKo : g1 + g2 - g3 + g4 - g5 + g6 ....
ScoreWhiteTenuki : -g1 + g2 + g3 + g4 - g5 + g6 ....
White should prefer taking the ko if:
ScoreWhiteTakesKo < ScoreWhiteTenuki <=> 2(g1 - g3) < 0

Now I like to use all the power of thermography tool. My understanding is that an ideal environment is in fact a strange mathematical object with proporties that looks contradictory.
In one hand you can consider g1 = g2 = g3 = g4 ... but at the same time you can also wait for a drop of the temperature!
IOW you may consider 2(g1 - g3) = 0 and at the same time you can assume 2(g1 - g3) > 0 but very small.
That the reason why I claim that playing in the environment is in general better than taking the ko.
BTW by taking g1 = u and g2 = t then you have 2(g1 - g3) = 2(u - t).

It is the same thing in the following position

Click Here To Show Diagram Code

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

In one hand you can delay without harm the black hane but in the other hand you must play hane immediatly.

It just a matter of using this famous ideal environment taking into account all its power.

As far as I am concern I like to say in an ideal environment we have g1 = g2 + ε with ε equal to infinity small but ε > 0

OC, with specific environment anything may happen.

Actually, no. I studied the position after without regard to whose turn it is. OC, it arises after those 4 plays, but to analyze the position before is a big job.



Well, threatens to kill, so it is sente. And it seems like returns to the mast value of the original position. That is not a reversal, strictly speaking, because 1) sente are not, ipso facto, reversals; and 2) ko positions do not fit CGT, of which reversals are a part. Some replies are so bad that it can make sense to speak of reversals in ko positions, but that is really only informal speech, and is not the case here.

Earlier you had found that is good in no ko threat positions at low temperatures, contrary to common wisdom that the descent to a is correct. Bravo! For one thing, I was interested in whether it was also good at the temperature of the mast value.

I can't say with absolute certainty, but it appears that the throw-in is White's best play in that case, as well. That is because it yields a mast value of 1⅛, while the descent yields a mast value of 1½, which is ⅜ point worse for White. It does so at temperature 6⅝, where it appears to be neither sente nor a reversal, but gote.

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

Visualize whirled peas.

Everything with love. Stay safe.

That is true if {u|-u} with u > t is in the ko ensemble, not the environment.



Probably so.



Are g1, et al., in the ko ensemble, or in the environment? It matters when you draw the thermograph.



This is a problem of temporal logic. Logic has trouble dealing with change. This is hardly a new problem, OC. Zeno based his paradoxes upon that fact. Thermographs represent the territorial values of the mast and walls of the thermograph at all values of the temperature, t. They do not represent changes in t. But they do represent the different values at t0, before the change in temperature, and at t1, after the change.



On that we agree. Where we have disagreed is on whether taking the ko is bad.



In real life the contrast is not usually so stark. Even if you make the wrong play, if it is within ½ point of the right play the difference seldom affects the result of the game. You can see this with proessional play. If a popular joseki move is suboptimal by ½ point or so, it may remain joseki, but pros usually start avoiding it with a decade or so.



Well, yes. If you embrace thermography.



Then Berlekamp's environment based upon ε = 0.01 should appeal. If the hundredths place is even, then it is ideal. And if not, 1.99 - 1.98 + ... = 1.00, for instance, with an error of only 0.005.

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

Visualize whirled peas.

Everything with love. Stay safe.

Here is how I handled things 50 years ago, with an environment of simple gote, {g₀|-g₀}, {g₁|-g₁}, ..., such that g₀ ≥ g₁ ≥ ... ≥ 0. After all that was left was the environment, at g_i, I simply estimated g_i - g_i+i + ... as g_i/2. In effect, all of the previous gs were in the game, not the environment. I didn't play the averages with them.

That's pretty much how thermography works. Thermography plays the averages.

Edit: I do play the averages with all of the gs, in the sense that they stand in for what else is on the board. They do not represent it accurately, only approximately. But it is only with the later gs that my method played the averages in the thermographic manner.

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

Visualize whirled peas.

Everything with love. Stay safe.

Here is how I handled global sente with my old method.

Black's global sente: {2b|0||-a}, a > 0, b > g0

1) Black plays to {2b|0}, White replies to 0, then Black plays to g0 - g1 + ...

s = g0 - g1 + ...

2) Black plays to g0, White plays reverse sente to -a, then Black plays to g1 - g2 + ...

s = g0 - a + g1 - ...

Since g1 is the residual g, we estimate g1 - g2 + ... as g1/2. That makes the estimated results for the different options as follows.

1) s = g0 - g1/2

2) s = g0 - a + g1/2

So when do we estimate we should play the global sente? When

g0 - g1/2 > g0 - a + g1/2 , that is , when

a > g1

That's interesting for two reasons. First, it justifies the traditional evaluation of the value of the sente play as a. Second, we do not compare a with the largest play in the environment, but with the second largest play. That is different from what the textbooks suggested. But it is consistent with pro play. I had observed that when to play kikashi was a matter of style. This was apparent in the games between Sakata, who played kikashi early, and Takagawa, who played kikashi late. Still, I thought, and still think, that the textbooks erred by not comparing the sente with the second largest play to determine when to play it.

----

Global reverse sente: {a||0|-2b}, a > 0, b > g0

1) Black plays to a, White replies to -g0 + ...

s = a - g0 + ...

2) Black plays to g0, White plays to {0|-2b}, Black replies to 0, then Black plays to g1 - ...

s = g0 + 0 - g1 + ... = g0 - g1 + ...

So Black should play the reverse sente when

a - g0/2 > g0/2 , that is, when

a > g0

This was consistent with what the textbooks said.

Taking these two results together, we see that for a particular global sente, it is more urgent to play the sente than the reverse sente. Something that the textbooks did not say, but that pros understood.

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.

Click Here To Show Diagram Code

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

Let's try to understand the remaining misunderstanding : is white move a bad (or whatever you want) move?

Strictly speaking the answer is quite simple : we cannot say white move is a bad move because a "bad" move has simply never been defined!

Can we go further and try to define what kind of move can be said as "bad"?

Considering the position P above, we can probably try the approach used by CGT by using various environments. Lets imagine a very large ensemble of environment E = {E1, E2, E3 ...}.

a strong definition of a bad move may be the following:
If it does not exist an environment in which is one of the best move, then is a bad move for this set of environment E.
Unless E is restricted to a small set of environment (for example you may decide to put in E only the ideal environments for every t values) this defintion seems too strong:

Let's for example take as position P the following position

Click Here To Show Diagram Code

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

We certainly would like to say that a black move at "a" is bad (seeing the possibility to play at "b") but if E contains all environments made of pure {u|-u} gote points then, by taking the environment {2|-2} a black move at "a" becomes correct! With such defintion it becomes difficult to have a bad move and for me such defintion becomes completly unuseful.

Bill, do you have any idea for defining an interesting "bad" move notion or do we have to give up and forget this notion?

Well, to borrow from the chess literature, there are a range of errors from inaccuracies to blunders. I am not exactly sure what an inaccuracy is, but I expect that blunders are very bad and inaccuracies are not bad. Where the threshold to bad is, I don't know. There are tactical, strategical, and psychological aspects to the question.

For instance, if a play is strategically inferior, but the player is ahead, and the play cements the win, I would call it a safety play, not a bad play. Similarly, if the player is behind but anticipates that her play may entice the opponent to make an even worse reply, I would call it a psychological ploy, not a bad play.

I also consider the level of the player. If an amateur dan makes a DDK play, I would normally consider that a bad play, although I could be convinced that it was a desperate attempt. Looking for a place to resign, as they say.

For me, generally speaking, I would consider a play to be bad when, given what is known, it is likely to affect the result of the game.



Strictly speaking, CGT does not consider environments at all in difference games. Berlekamp introduced the idea of a universal enriched environment, and I based my redefinition of thermography upon it. I have come up with the idea of an ideal environment, but have not written any academic paper making use of it. In terms of an ideal environment or Berlekamp's universal enriched environment, taking the ko is at worst an inaccuracy. If the temperature of the environment is low, that is not an argument for playing in the environment.



I think you have to compare the play with the alternatives.



In CGT, with a non-ko environment, a play at b plainly dominates a play at a. And, even though nobody has proved it, AFAIK, experience says that it is dominated in ko environments, as well. A play at a may be correct in some circumstances, but it is still dominated. An amateur SDK who plays it instead of b is, at best, careless. For an amateur dan player I would say that it is a bad play.

By contrast,

Click Here To Show Diagram Code

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

For an amateur I think I would call a play at a an inaccuracy.

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

Visualize whirled peas.

Everything with love. Stay safe.

When reading your post it is clear that it is too difficult to define what could be a bad move.
Even if "a" dominates "b" sure you will hesitate to declare "b" as bad move because it may happen that "b" is the only best move in certain ko environment.

As an example let's take the following position:

Click Here To Show Diagram Code

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

In CGT context the environment is a non-ko one, and the point a and b are analysed as pure gote points {5|-5} and {3|-3}. No doubt that "a" dominates "b".
But even in such a simple case a ko environment may completly change the result : in the following position (the environment is at the bottom of the board)

Click Here To Show Diagram Code

[go]$$W White to play
$$ ---------------------------------------
$$ | . . X X O O O b O a O O O O O X . . . |
$$ | X X . X X X X X O X X X X X X X . . . |
$$ | O X X O O O O O O . . . . . . . . . . |
$$ | O O O O . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . O X X X . . . . . . . . . . |
$$ | . . . . . O X O X X X . . . . . . . . |
$$ | . . . . . O . . O . X . . . . . . . . |
$$ ---------------------------------------[/go]

White to play : the best move is now "b" !
You see the point? In a non-ko context a simple {3|-3} gote point is only a simple {3|-3} gote point and nothing else, full stop.
In a ko environment a simple {3|-3} gote point may create a ko threat with a completly different result!

Obviously trying to define what a bad move is, seems not a good idea!

In the last example it is because a play at a gains only 127/128 of a point, while a play at b gains 255/256 of a point, an almost always negligible difference.



Thermography explains why.

Click Here To Show Diagram Code

[go]$$W White to play
$$ ---------------------------------------
$$ | . . X X O O O b O a O O O O O X . . . |
$$ | X X . X X X X X O X X X X X X X . . . |
$$ | O X X O O O O O O . . . . . . . . . . |
$$ | O O O O . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . O X X X . . . . . . . . . . |
$$ | . . . . . O X O X X X . . . . . . . . |
$$ | . . . . . O . . O . X . . . . . . . . |
$$ ---------------------------------------[/go]

A play at a gains 5 points, a play at b gains 3 points, but makes a difference of a large White ko threat.

A play in the bottom by Black yields 6 points for Black. What about a play by White? If Black is komaster Black can reply by taking and winning the ko for a local score of 4 - t. If White is komaster White can win the ko for a local territory score of 0. Since the ko is fought at temperature 0, the ko threat makes a difference of 4 points in the bottom score when White plays first. That is, a play in the bottom gains either 3 points or 1 point. Since 3 - 1 = 5 - 3, it does not matter which play White chooses on the top side.

Click Here To Show Diagram Code

[go]$$W White to play, White takes the hottest play
$$ ---------------------------------------
$$ | . . X X O O O 2 O 1 O O O O O X . . . |
$$ | X X . X X X X X O X X X X X X X . . . |
$$ | O X X O O O O O O . . . . . . . . . . |
$$ | O O O O . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . O X X X . . . . . . . . . . |
$$ | . . . . . O X O X X X . . . . . . . . |
$$ | . . . . . O 3 4 O 6 X . . . . . . . . |
$$ ---------------------------------------[/go]

= dame or pass

s = 9 + 4 = 13

Click Here To Show Diagram Code

[go]$$W White to play, White creates ko threat
$$ ---------------------------------------
$$ | 6 5 X X O O O 1 O 2 O O O O O X . . . |
$$ | X X . X X X X X O X X X X X X X . . . |
$$ | O X X O O O O O O . . . . . . . . . . |
$$ | O O O O . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . O X X X . . . . . . . . . . |
$$ | . . . . . O X O X X X . . . . . . . . |
$$ | . . . . . O 3 4 O 8 X . . . . . . . . |
$$ ---------------------------------------[/go]

takes ko, fills ko, = dame or pass

N.B. is correct at t = 0.

s = 10 + 3 = 13

Perhaps you meant to put only 4 White stones next to a, in which case White b is the undisputed champion.

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

Visualize whirled peas.

Everything with love. Stay safe.

Yes Bill I prefer to correct my diagram with only four white stones but that is not really the point. BTW I switch "a" and "b" to fit what you said here after

Click Here To Show Diagram Code

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

In fact I was reacting to your above sentence where you questionned a domination in CGT with non-ko environement and a domination in ko environment in the case of very simple, pure {u|-u} gote points.
In my example the point is not to know if "a" is better than "b" in a ko environment (it is obvious for most go players and I have no doubt that thermography, in the ko context, explains that). The point is rather to understand what means CGT with non-ko environment.
IOW, in my exapmle, and considering we are in "CGT with non-ko environment", is it correct to say that the point "b" is a pure simple {4|-4} point, the point "a" is a pure {3|-3} point and as a consequence "b" dominates "a"?
If it is true then my example answer your question isn't it?

That statement was referring to a different diagram, which is why the letters are different.

Click Here To Show Diagram Code

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

This is the diagram, in which a play at b dominates a play at a in CGT. Neither play involves creating or destroying a ko threat. My remark had nothing to do with anything like the other diagram in this post.
.


Beside the point, as I was referring to something else.

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

Visualize whirled peas.

Everything with love. Stay safe.

Rather than edit my previous note, let me continue here.



My interpretation of a non ko environment in CGT is one in which there is no ko fight or potential ko fight.



I do not understand the relevance of your diagram, in which there is a ko fight. If the idea is to understand CGT with a non-ko environment, then don't use a ko environment to do so.

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

There is a misunderstanding Bill. In my previous post I was talking on the diagram above where I did not draw any specific environment. On contrary I assume we are in a "CGT with non-ko environment".
In this context my understanding is the following:
1)the point a is a simple {3|-3} area
2) the point b is a simple {4|-4} area
3) because I assume we are in the context of "CGT with non-ko environment" I can simply ignore that a white move at "a" create a ko threat and I am allowed to play a difference game and prove white "b" dominates "a".

Clearly the point 3) is critical and my question is the following:
in the specific context of "CGT with non-ko environment" can (must!) I ignore the creation of a ko threat and can I play a difference game showing "b" dominates "a" ?

If not, does that mean that we are not allowed to play a difference game (I am still in a "CGT with non-ko environment" context!) if a ko threat appears somewhere in a sequence?

Well, ko threats are, as a rule, sente. So, no, even in a non-ko environment a move which creates a sente is not the same as a move which does not. Edit: This ko threat costs one point to eliminate, so I think that CGT would not recognize its significance, except as a ko threat.

Edit2: I feel that I need to reiterate that I was not talking about positions with moves that create ko threats.



What has been proven about difference games has been without ko fights. Difference games can still provide useful heuristics, in general.

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

OK Bill. In general difference games can still provide useful heuristics but if a ko threat is created somewhere in a sequecnce then your are not allowed to claim that a move "b" dominates really a move "a". In my exemple above because white "a" creates a ko threat we are not allowed to play a difference game and claim "b" dominates "a".

It is not good news.

Click Here To Show Diagram Code

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

When I remember all difference games we played to prove a move dominates another in the diagram above, I realise now that most of the results of these difference games were not reliable because we forgot to look at the ko threats created against the white group. At least in the future we will be more careful.

dhu163 is right when claiming "I'm not too clear what "non-ko" environment means myself".

I apologize if I gave the wrong impression in our previous discussion. As I recall, I brought up the ko caveat and the fact that this particular case was problematic because of the lack of a dame for White and the fact that Black already has a threat with the play inside the eye. I do not recall claiming that a ko fight in the difference game meant that we could still say what best play was, regardless of the rest of the board.

Let me quote myself from #28 that discussion https://www.lifein19x19.com/viewtopic.p ... 82#p260182 . I had mentioned the ko caveat before, but here I made my approach clear, I thought. I guess not. Sorry.

(Emphasis mine.)

In that discussion I was engaging in defeasible reasoning with exceptions. That sounds fancy, but it is a very common way that people reason about things. The sente sequences I first compared with difference games had no ko fights. But with the ko fight shown in this diagram, I never claimed that the difference game yielded best play in all environments with no exceptions. I apologize if I did not make that clear.

Edit: Sorry for being defensive, but to quote myself from #31 in that discussion.



I really did try to make that point clear.

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

Visualize whirled peas.

Everything with love. Stay safe.