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 Post subject: Re: How evaluate double sente moves ? #121 Posted: Thu Oct 22, 2020 10:38 am
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RobertJasiek wrote:
The context of each proof is the proposition and its presuppositions, possibly together with applied earlier axioms, definitions and propositions. The context is the task of assigning the correct count, move value, gains and type to a local endgame (of a certain class). Now that you have possibly understood it, what do you think of my proof? Is it - for its declared scope - correct? Can you appreciate the elegant constructions of proofs by contradiction? The case "b = w" is the most difficult and beautiful part. Bill, did you want me to rediscover its beauty or have you just overlooked it?

Oops I only understand that you take into account trees like

......A......
...../.\.....
..../...\....
...B.....C...
../.\.../.\..
.l...b.w...r.

I can try to undestand your proof but you have to help me because I have first to understand your notation.

Let's take the beginning:

Remarks
CGOTE is a gote count. CSENTE is a sente count. C is a white-count.
MGOTE is a gote move value. MB,SENTE is Black's sente move value.
MW,SENTE is White's sente move value. M is a tentative move value.
FB is Black's follow-up move value. FW is White's follow-up move
value.
PA is the position of the following game tree's node A etc.
[Proposition 11 and related propositions say that Black's local sente
is characterised by these equivalent, alternative value conditions:
CSENTE < CGOTE <=>
MGOTE < FB <=> MB,SENTE < FB <=> MB,SENTE < MGOTE.

What does mean CGOTE, CSENTE, MGOTE, MSENTE? Maybe:
CGOTE = (l+b)/2 ?
MGOTE = (l-b)/2 ?
CSENTE = b ?
MSENTE ?
As soon as I understand the notation I am sure I will be able to progress quickly through your proof.

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 Post subject: Re: How evaluate double sente moves ? #122 Posted: Thu Oct 22, 2020 10:52 am
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Gerard, yes, of course, as usual. Where Csente has the context Black's sente count. And

Mb,sente = count of Black's sente follower minus count of White's reverse sente follower,

Mw,sente = count of Black's reverse sente follower minus count of White's sente follower.

White-count = count from White's value perspective = negation of the count [from Black's value perspective].

EDIT: name.

Last edited by RobertJasiek on Thu Oct 22, 2020 12:02 pm, edited 1 time in total.
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 Post subject: Re: How evaluate double sente moves ? #123 Posted: Thu Oct 22, 2020 10:58 am
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"managed to show how a double sente (with our definition) move may appear when temperature drops?"

What, please explain how it is local!

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 Post subject: Re: How evaluate double sente moves ? #124 Posted: Thu Oct 22, 2020 11:19 am
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RobertJasiek wrote:
The case "b = w" is the most difficult and beautiful part. Bill, did you want me to rediscover its beauty or have you just overlooked it?

Well, it seems to me that the common understanding of double sente assumes that b > w. Cases where b = w are usually called miai, or possibly a double ko threat. Everything I said is a theorem in CGT, proven long before I learned about it, except for the statement about double sente, which is not part of CGT , because CGT has no concept of double sente.

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 Post subject: Re: How evaluate double sente moves ? #125 Posted: Thu Oct 22, 2020 11:55 am
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It goes too far to call it common understanding that double sente assumed b > w, b = w was usually called miai, or possibly a double ko threat. There is no need to restrict b ? w. In your preliminary case examples study of double sente, you studied b>w and b<w.

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 Post subject: Re: How evaluate double sente moves ? #126 Posted: Thu Oct 22, 2020 12:04 pm
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Bill, what CGT theorem are you referring to?

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 Post subject: Re: How evaluate double sente moves ? #127 Posted: Thu Oct 22, 2020 12:09 pm
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RobertJasiek wrote:
It goes too far to call it common understanding that double sente assumed b > w, b = w was usually called miai, or possibly a double ko threat. There is no need to restrict b ? w. In your preliminary case examples study of double sente, you studied b>w and b<w.

I don't remember what I studied before submitting my double sente article to The Go World many years ago. Nowadays I just rely upon CGT. When b < w the original game is a number, which I am sure I did not consciously study way back when.

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 Post subject: Re: How evaluate double sente moves ? #128 Posted: Thu Oct 22, 2020 12:24 pm
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Please explain why the following game is a number for b<w:
Code:
......A......
...../.\.....
..../...\....
...B.....C...
../.\.../.\..
.l...b.w...r.

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 Post subject: Re: How evaluate double sente moves ? #129 Posted: Thu Oct 22, 2020 12:25 pm
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RobertJasiek wrote:
Bill, what CGT theorem are you referring to?

When w > 0 > b then neither player will play in the original game and it equals 0. Otherwise you derive the simplest number as explained in On Numbers and Games. E.g., {0|1} = ½. IIUC, b and w are each the result of an even number of plays, i.e. a sente sequence. In that case the number is 0 or the closest one to 0.

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Last edited by Bill Spight on Thu Oct 22, 2020 12:33 pm, edited 2 times in total.
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 Post subject: Re: How evaluate double sente moves ? #130 Posted: Thu Oct 22, 2020 12:30 pm
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RobertJasiek wrote:
"managed to show how a double sente (with our definition) move may appear when temperature drops?"

What, please explain how it is local!

look at Bill post : https://lifein19x19.com/viewtopic.php?p=260826#p260826

After a white play in the game {21 ||| 18 | 4 || 0 | -14} it remains {18|4||0|-14} and the thermograph drawed by Bill shows clearly it is a double sente according to our current defintion.

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 Post subject: Re: How evaluate double sente moves ? #131 Posted: Thu Oct 22, 2020 12:40 pm
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So, at least for some value cases, there are several approaches to prove non-existence of local double sente:)

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 Post subject: Re: How evaluate double sente moves ? #132 Posted: Thu Oct 22, 2020 12:45 pm
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Gérard TAILLE wrote:
look at Bill post : https://lifein19x19.com/viewtopic.php?p=260826#p260826

After a white play in the game {21 ||| 18 | 4 || 0 | -14} it remains {18|4||0|-14} and the thermograph drawed by Bill shows clearly it is a double sente according to our current defintion.

I wrote:

{18|4||0|-14}.

Let me study the latter summand.

Fb = (18-4)/2 = 7.
Fw = (0-(-14))/2 = 7.

We have these intermediate counts:

Cb = (18 + 4) / 2 = 11.
Cw = (0 + (-14)) / 2 = -7.

Tentative Mgote = (Cb - Cw)/2 = (11 - (-7)) / 2 = 18/2 = 9.

Let us verify this:

Mgote > Fb, Fw <=> 9 > 7, 7 is fulfilled. Therefore, the initial local endgame is a local gote with
M := Mgote = 9.

Local gote - not local double sente!

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 Post subject: Re: How evaluate double sente moves ? #133 Posted: Thu Oct 22, 2020 12:52 pm
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Thermography studies more in terms of environmental temperature. Such a characterisation of double sente by parallel walls in the thermograph is GLOBAL because temperature is an abstraction for available other plays elsewhere on the board. Such does not define local double sente.

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 Post subject: Re: How evaluate double sente moves ? #134 Posted: Thu Oct 22, 2020 1:10 pm
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Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote:

OK. We can write G this way, using more slashes.

G = {21 ||| 18 | 4 || 0 | -14}

I'll draw the thermograph. Be back soon.

I'm back. Here is the thermograph.

Surely you know where I encountered difficulties Bill

Starting from G = {21 ||| 18 | 4 || 0 | -14}
if use tax = 7 then the game becomes
G = {14 ||| 11 | 11 || 7 | 7}

Now what will happen with tax = 8?
I see that the games {11 | 11} and {7 | 7} are blocked and I do not know how to go to tax = 8.
Can you help me Bill?

Sure. Replace {11|11} and {7|7} with their mean (mast) values. That corresponds with using the mast instead of the lower walls. That yields.

G = {14 || 11 | 7}

When t = 8 we have

G = {13 || 11 | 9}

When t = 9 we have

G = {12 || 11 | 11} -> {12 | 11}

When t = 9½ we have

G = {11½ | 11½}

The tax method works quite well Bill.

Now what about the ideal environment method? How to proceed to analyse temperature t = 10?
When I try a white move at t=10 the move lead now to the game
{18 | 4 || 0 | -14} and with temperature t=10 I have to stop here.
How now calculate the minimax value when white plays first at temperature 10.
The point is the following : I know that when temperature will decrease this local game {18 | 4 || 0 | -14} will become double sente but I do not know which side will take this double sente.
Certainly I will replace the game {18 | 4 || 0 | -14} by the game {11|-7} but I have the feeling that I failed to take into account the real behaviour of the game {18 | 4 || 0 | -14}.
Curiously tax method seems not to have the same problem.

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 Post subject: Re: How evaluate double sente moves ? #135 Posted: Thu Oct 22, 2020 1:15 pm
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RobertJasiek wrote:
Thermography studies more in terms of environmental temperature. Such a characterisation of double sente by parallel walls in the thermograph is GLOBAL because temperature is an abstraction for available other plays elsewhere on the board. Such does not define local double sente.

I was not refering to the vertical lines but only to the fact that the conditions: M < Fb, Fw are true for the game {18 | 4 || 0 | -14}.

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 Post subject: Re: How evaluate double sente moves ? #136 Posted: Thu Oct 22, 2020 1:23 pm
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RobertJasiek wrote:
Gerard, yes, of course, as usual. Where Csente has the context Black's sente count. And

Mb,sente = count of Black's sente follower minus count of White's reverse sente follower,

Mw,sente = count of Black's reverse sente follower minus count of White's sente follower.

White-count = count from White's value perspective = negation of the count [from Black's value perspective].

EDIT: name.

......A......
...../.\.....
..../...\....
...B.....C...
../.\.../.\..
.l...b.w...r.

with the tree above I understand
CGOTE = (l+b)/2
MGOTE = (l+b)/2 - (w+r)/2
CSENTE = b
MSENTE = b - (w+r)/2
Is it true Robert?

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 Post subject: Re: How evaluate double sente moves ? #137 Posted: Thu Oct 22, 2020 1:38 pm
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"M < Fb, Fw are true for the game {18 | 4 || 0 | -14}."

You wrongly read M < Fb, Fw when I write M > Fb, Fw <=> 9 > 7, 7.

Not < but > !

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 Post subject: Re: How evaluate double sente moves ? #138 Posted: Thu Oct 22, 2020 1:51 pm
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Gérard TAILLE wrote:

......A......
...../.\.....
..../...\....
...B.....C...
../.\.../.\..
.l...b.w...r.

with the tree above I understand
CGOTE = (l+b)/2
MGOTE = (l+b)/2 - (w+r)/2
CSENTE = b
MSENTE = b - (w+r)/2
Is it true Robert?

The values are calculated afresh FOR EACH NODE!

Node B:
CGOTE = (l+b)/2
MGOTE = (l-b)/2

Node C:
CGOTE = (w+r)/2
MGOTE = (w-r)/2

Node A (tentative values):
CGOTE = (count_B + count_C)/2
MGOTE = (count_B - count_C)/2
Mb,sente = b - count_C
Mw,sente = count_B - w

EDIT:

But then in the paper I write FB and FW for the move values at nodes B and C, and CB and CC FOR their counts.

Last edited by RobertJasiek on Thu Oct 22, 2020 2:03 pm, edited 1 time in total.
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 Post subject: Re: How evaluate double sente moves ? #139 Posted: Thu Oct 22, 2020 1:55 pm
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Gérard TAILLE wrote:
Bill Spight wrote:

OK. We can write G this way, using more slashes.

G = {21 ||| 18 | 4 || 0 | -14}

I'll draw the thermograph. Be back soon.

I'm back. Here is the thermograph.

Surely you know where I encountered difficulties Bill

Starting from G = {21 ||| 18 | 4 || 0 | -14}
if use tax = 7 then the game becomes
G = {14 ||| 11 | 11 || 7 | 7}

Now what will happen with tax = 8?
I see that the games {11 | 11} and {7 | 7} are blocked and I do not know how to go to tax = 8.
Can you help me Bill?

Gérard TAILLE wrote:
Bill Spight wrote:

Sure. Replace {11|11} and {7|7} with their mean (mast) values. That corresponds with using the mast instead of the lower walls. That yields.

G = {14 || 11 | 7}

When t = 8 we have

G = {13 || 11 | 9}

When t = 9 we have

G = {12 || 11 | 11} -> {12 | 11}

When t = 9½ we have

G = {11½ | 11½}

The tax method works quite well Bill.

Now what about the ideal environment method? How to proceed to analyse temperature t = 10?
When I try a white move at t=10 the move lead now to the game
{18 | 4 || 0 | -14} and with temperature t=10 I have to stop here.
How now calculate the minimax value when white plays first at temperature 10.
The point is the following : I know that when temperature will decrease this local game {18 | 4 || 0 | -14} will become double sente but I do not know which side will take this double sente.
Certainly I will replace the game {18 | 4 || 0 | -14} by the game {11|-7} but I have the feeling that I failed to take into account the real behaviour of the game {18 | 4 || 0 | -14}.
Curiously tax method seems not to have the same problem.

Emphasis mine.

When I redefined thermography in order to handle multiple kos and superkos, for each thermograph I had to specify an environment that gave the same results as the tax method. So if the tax method is easier for you, please use it.

Quote:
When I try a white move at t=10 the move lead now to the game {18 | 4 || 0 | -14} and with temperature t=10 I have to stop here.

I suppose that at temperature 10 you stop because you know that the temperature of this position is less than 10. In that case its details are invisible at that temperature. All you can see is its mean value, which is 2. Black now replies at temperature 10, for a result of 2 + 10 = 12. (If you played on to temperature 0, you would estimate the result as 2 + 10/2 = 7, but then you have to add the correction of 10/2. As I said the easy thing is just to stop after an even number of plays at the temperature.

On the left side you move to 21 and then reply in the environment, for a result of 21 - 10 = 11. Since 12 > 11, you realize that temperature 10 is too hot for this game. The equitable temperature is the solution to

2 + t = 21 - t

t = 19/2 = 9½

m = 2 + 9½ = 11½

OC, you can do this graphically.

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Visualize whirled peas.

Everything with love. Stay safe.

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 Post subject: Re: How evaluate double sente moves ? #140 Posted: Thu Oct 22, 2020 2:35 pm
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RobertJasiek wrote:
"M < Fb, Fw are true for the game {18 | 4 || 0 | -14}."

You wrongly read M < Fb, Fw when I write M > Fb, Fw <=> 9 > 7, 7.

Not < but > !

why you did not comment my post https://lifein19x19.com/viewtopic.php?p=260758#p260758 ?
In my diagram you can see that
n = score when black plays first - score when white plays first.
For the game {18 | 4 || 0 | -14} that means n = 4 - 0 = 4
which is in line with my common go language for such situation : 4 points in double sente, the two threats 18-4 and 0 - (-14) being far bigger.

When you write
M := the move value in the initial local endgame position.
Fb := the move value in the follow-up position created after Black's start.
Fw := the move value in the follow-up position created after White's start.
if, for the environment {18 | 4 || 0 | -14}, you define M = (18-4)/2 - (0 -(-14))/7 = 9 its completly differnent and in fact you defined something that does not exist. I agree with you in that case

As I try to explain my suggestion is not to create a definition of an object which do not exist but to create a definition which could make sense to a lot of go players including the best ones.
It cannot harm to add such definition: the theory cannot change because we add a defintion can it?
I am not sure it is that difficult to find a good defintion. OC you begin by asking to go players what they call double sente move, with their go player language and then I am quite sure you will be able to find a precise defintion which fit this common understanding.
With my suggestion I only try to translate my feeling concerning a so called double sente but we have to be open to discussion.

The example I gave was really made in the context of my suggestion Robert but we can also try another defintion provided it looks like the common understanding of double sente in the go player language (not perfect of course but that's life).

In any case I am pretty sure go player will be quite satisfied to recognised such notion she knows and uses for years.
Here again, why not try if it could not harm?

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