White A might the best if
- it is correct for Black to tenuki and
- the initial white gote with the sente follow-up is better than initially White B.
Gote move vs sente move in yose
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Re: Gote move vs sente move in yose
In many cases (if not most) b is gote.Gérard TAILLE wrote:Let me show you my answer to my initial question.
The question was the following : what is the best white move, white "a" or white "b"
Let's start by the white move "b". Assumingis sente
You see the point?
White "b" is sente and lead to a position with a count +2 whitout really any choice for black
White "a" gives black a lot of options and one of them is a sequence sente for white leading to a position with count +2 without any choice for white.
Conclusion : white "a" cannot be better than white "b" because this white "a" move gives black a lot of options with one of them being equivalent to white "b". White "b" is the best choice for white. Just two counts to calculate. No need to calculate some MGOTE or MSENTE value, no need to look at other sequences.
KataGo experiment
a - winning move
b - losing move
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Re: Gote move vs sente move in yose
Sure Dany if white "b" is gote then white "a" could be the best move in the majority of cases. In that case the issue would appear completely different and it will not be the subject of this thread.dany wrote:In many cases (if not most) b is gote.
KataGo experiment
a - winning move
b - losing move
BTW Robert proposed the following position in order to assure white "b" is sente.
Let's just assume white "b" is sente and see the subtle reasonning showing that in this case white "a" cannot be strictly better than white "b".
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Gérard TAILLE
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Re: Gote move vs sente move in yose
You still did not take the point Robert. Let me explain a little more.RobertJasiek wrote:White A might the best if
- it is correct for Black to tenuki and
- the initial white gote with the sente follow-up is better than initially White B.
Let's assume an environment with only simple gote areas.
Let's call S1 the best sequence beginning by the white sente move "b" and let's call S2 the best sequence beginning withe white "a" black "c.
Locally these two sequences S1 ansd S2 are both sente for white with the same local result (count = -2). Considering the game itself (with the environment) the results of the games after S1 or S2 are the same.
Let's call S3 the sequence you proposed, beginning with white "a" black tenuki.
You said white "a" is better than white "b" => S3 < S1
and you said also that after white "a" the black tenuki is correct => S3 ≥ S2
Because S1 and S2 lead to the same result you have here a contradiction.
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Re: Gote move vs sente move in yose
Simply speaking, your proof is correct! Congratulations on the implied proposition and its suitable example!
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Gérard TAILLE
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Re: Gote move vs sente move in yose
Thank you Robert.RobertJasiek wrote:Simply speaking, your proof is correct! Congratulations on the implied proposition and its suitable example!
Sure you will now understand my two questions in my post https://lifein19x19.com/viewtopic.php?p=280542#p280542 and why in Q2 I was interested by white best moves but not black best moves!
Do you know if it already exists theorems allowing to detect such domination of a sente move against a gote one?
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Re: Gote move vs sente move in yose
Apart from the general tree simplifications, I do not know if some part of CGT implies such. Bill and I have composed a few additional theorems about simplification of specific rather simple trees, of which some can have some sente, due to reversal, see [22]. Then I have proved something related but without sente:Gérard TAILLE wrote:Do you know if it already exists theorems allowing to detect such domination of a sente move against a gote one?
"Suppose a local endgame in which only one player can make territory and the opponent's move creates two separate follow-ups that are simple gotes without follow-ups. A long sequence is not worth playing successively." [14][33]
EDIT:
Of course, there are also my and partly Bill's theorems for choice among several local endgames, which can be local sentes. [22]
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Re: Gote move vs sente move in yose
In this post the considered tree is quite simple: a depth 2 tree with only four leaves and both players have only one option.RobertJasiek wrote:"PresuppositionsGérard TAILLE wrote:a local double sente position cannot exist, providing both player have only simple follow-ups. To prove that a local double sente position cannot exist [...] first define [...] local double sente position.
We score due to a ruleset.
Let BB, BW, WB, WW ∈ ℤ,
G := {BB|BW||WB|WW},
B := (BB + BW) / 2, W := (WB + WW) / 2,
MGOTE := (B - W) / 2,
MB,SENTE := BW - W,
MW,SENTE := B - WB.
Suppose BB > BW, WB > WW, G is without reversible plays.
Suppose an environment without ko now or later.
Theorem 20 [non-existence of a local double sente]
G with MGOTE > MB,SENTE, MW,SENTE does not exist." [22]
Proof see [22]. Definition of reversible see [22] or the CGT literature.
https://www.lifein19x19.com/viewtopic.p ... 45#p143245
In your famous theorem
Theorem 134 [early endgame, high temperature]
If F < T, it is a good approximation that the starting player starts
- in the environment if T ≥ MGOTE,
- locally if T ≤ MGOTE (the creator chooses the gote option).
The tree is a little more complicated, with five leaves) and looks like the figure here under.
[img]
- double sente.jpg (28.16 KiB) Viewed 9212 times
Let's call a, b, c, ... the count of positions A, B, C, ...
We have c = (e+f)/2 and d = (g+h)/2
Now the situation is not so simple because at the beginning of the analysis you do not know if black AC and white AD are gote or sente.
In this context what do you call MGOTE to try and apply your theorem?
Is it always MGOTE = (b - d)/2 ? (even if it might happen that AD is sente ?)
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Re: Gote move vs sente move in yose
I do not understand Robert. If you need to remove G and H in order to apply your theorem then you cannot apply your theorem in the following position:RobertJasiek wrote:Even simpler: remove G and H!
After white "a" we do not reach a leave because of the remaining ko.
OC you can say that in the position above the white move at a" (move AD in my tree) is gote but in the context of the theory you must prove it is gote and it could not be so easy and it depends also on the environment.
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Re: Gote move vs sente move in yose
As I have already mentioned, the theory for local endgames with gote and sente options is for single plays or a sente sequence of exactly two plays while all on-board examples have long(er) sequences. This makes application of the related theorems for the late on-board endgame impossible and for the early endgame for also this reason an approximation.
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Gérard TAILLE
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Re: Gote move vs sente move in yose
We did not handled the following position.
How do you prove that black "a" cannot be better than black "b"?
How do you prove that black "a" cannot be better than black "b"?
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Gérard TAILLE
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Re: Gote move vs sente move in yose
If a local double sente position is a position G without reversible plays, in which MGOTE > MB,SENTE, MW,SENTE, with only one option for each player and only one follow-up (the tree is only a depth-2 tree) then I can agree a local double sente does not exist.RobertJasiek wrote: "Presuppositions
We score due to a ruleset.
Let BB, BW, WB, WW ∈ ℤ,
G := {BB|BW||WB|WW},
B := (BB + BW) / 2, W := (WB + WW) / 2,
MGOTE := (B - W) / 2,
MB,SENTE := BW - W,
MW,SENTE := B - WB.
Suppose BB > BW, WB > WW, G is without reversible plays.
Suppose an environment without ko now or later.
Theorem 20 [non-existence of a local double sente]
G with MGOTE > MB,SENTE, MW,SENTE does not exist." [22]
Proof see [22]. Definition of reversible see [22] or the CGT literature.
https://www.lifein19x19.com/viewtopic.p ... 45#p143245
If however, knowing the ambiant temperature is T (not quite high) , a local double sente position is a position G in which white must answer to the initial black move and black must answer to the initial white move then a local double sente position do exist.
With your defintion a local double sente does not exist, but many go players use another defintion and local double sente do exist for them.
BTW do you think the majority of go players knows what reversible play means?
Robert, nobody is wrong. Your are right inside your theory and go players using another defintion are right inside their practice.
BTW, if in position G the players have several options you have not defined what "local double sente" means have you?
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Re: Gote move vs sente move in yose
What exists is a global double sente (a local endgame in a global position so that either starting player gets a local reply) - do not call this a local double sente and do not excuse all the traditionalists who only discussed local endgames when assessing the difference value as the alleged move value with the alleged justification of having a double sente!
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Re: Gote move vs sente move in yose
In my previous post I ask the following question:RobertJasiek wrote:What exists is a global double sente (a local endgame in a global position so that either starting player gets a local reply) - do not call this a local double sente and do not excuse all the traditionalists who only discussed local endgames when assessing the difference value as the alleged move value with the alleged justification of having a double sente!
"if in position G the players have several options you have not defined what "local double sente" means have you"
Could you at least answer the basic simplier following one:
"Assuming in position G both players have SEVERAL options, how do you define a black's local sente position G ?"