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 Post subject: Re: How evaluate double sente moves ?
Post #81 Posted: Tue Oct 20, 2020 2:23 pm 
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Bill Spight wrote:
Bill Spight wrote:
Bueno. :)

What about this combination?

{+22|-6},-3|-7} + {10|0}


Gérard TAILLE wrote:
well I would say:
black plays first => minimax = +3 = 10 + (-7)
white plays first => minimax = -3 = 0 + (-3)


Black can do better at temperature 0. :)


Oops yes Bill, I am a stupid boy!
(-6)in sente and then (+10) => +4


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 Post subject: Re: How evaluate double sente moves ?
Post #82 Posted: Tue Oct 20, 2020 2:46 pm 
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Gérard TAILLE wrote:
Bill Spight wrote:
Bill Spight wrote:
Bueno. :)

What about this combination?

{+22|-6},-3|-7} + {10|0}


Gérard TAILLE wrote:
well I would say:
black plays first => minimax = +3 = 10 + (-7)
white plays first => minimax = -3 = 0 + (-3)


Black can do better at temperature 0. :)


Oops yes Bill, I am a stupid boy!
(-6)in sente and then (+10) => +4


Now how about integer temperatures up to 5? :)

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 Post subject: Re: How evaluate double sente moves ?
Post #83 Posted: Tue Oct 20, 2020 3:07 pm 
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Bill Spight wrote:

What about this combination?

{+22|-6},-3|-7} + {10|0}

Now how about integer temperatures up to 5? :)


I can see that the game {+22|-6},-3|-7} becomes {+20|-6},-5|-5} at temperature 2 and the minimax -5 cannot change above that temperature.
For the game {10|0} it becomes {+5|+5} at temperature 5.
As a conclusion the minimax at temperature 5 is 0 whatever player is playing first and the minimax cannot change above temperature 5.


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 Post subject: Re: How evaluate double sente moves ?
Post #84 Posted: Tue Oct 20, 2020 3:13 pm 
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OK. Thermographs do two things. The thermograph of a game finds the mean value of the game, and it finds the result of minimax play in the game, starting with each player, at each temperature.

What else does your skeptic desire?

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 Post subject: Re: How evaluate double sente moves ?
Post #85 Posted: Tue Oct 20, 2020 10:31 pm 
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Gérard TAILLE wrote:
The definition [of a double sente] should be as near as possible as the common understanding of go players


Since not all players use values but players with a weak understanding of endgame only use an informal understanding, the common go players' understanding of double sente would be informal. However, some players have not reflected yet that local versus global considerations of double sente differ. Therefore, the common go players' understanding of double sente does not exist. Concerning global considerations, some players are aware that one should not always play a double sente immediately because it might be relatively small while other players (with a weak understanding of endgame) are not aware of that and instead believe overly simplistic traditional advice to play in double sente as early as possible. Only for local considerations, we can identify some common go players' understanding of double sente: that either player's local play is sente meaning an immediate reply by the opponent. In only informal terms, we cannot better characterise why an immediate local reply should be necessary.

In terms of values, we can characterise why an immediate local reply should be necessary: after either player's local play, the reply is more valuable. That is, the move value in the initial local endgame position is smaller than both replies' follow-up move values. Let us use these variables:

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.

Now, we can characterise a local double sente endgame be these value conditions:

M < Fb, Fw.

(This annotation abbreviates "M < Fb and M < Fw".)

However, simply speaking, the mathematically proven theorem says:

A local double sente endgame with M < Fb, Fw does not exist.

The common go players' understanding did not know this yet:)

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 Post subject: Re: How evaluate double sente moves ?
Post #86 Posted: Wed Oct 21, 2020 11:07 am 
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RobertJasiek wrote:
Gérard TAILLE wrote:
The definition [of a double sente] should be as near as possible as the common understanding of go players


Since not all players use values but players with a weak understanding of endgame only use an informal understanding, the common go players' understanding of double sente would be informal. However, some players have not reflected yet that local versus global considerations of double sente differ. Therefore, the common go players' understanding of double sente does not exist. Concerning global considerations, some players are aware that one should not always play a double sente immediately because it might be relatively small while other players (with a weak understanding of endgame) are not aware of that and instead believe overly simplistic traditional advice to play in double sente as early as possible. Only for local considerations, we can identify some common go players' understanding of double sente: that either player's local play is sente meaning an immediate reply by the opponent. In only informal terms, we cannot better characterise why an immediate local reply should be necessary.

In terms of values, we can characterise why an immediate local reply should be necessary: after either player's local play, the reply is more valuable. That is, the move value in the initial local endgame position is smaller than both replies' follow-up move values. Let us use these variables:

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.

Now, we can characterise a local double sente endgame be these value conditions:

M < Fb, Fw.

(This annotation abbreviates "M < Fb and M < Fw".)

However, simply speaking, the mathematically proven theorem says:

A local double sente endgame with M < Fb, Fw does not exist.

The common go players' understanding did not know this yet:)


Sorry Robert to be here a player with a weak understanding of endgame but let me try to treat myself.
Well, let's take the definition M < Fb, Fw.
As soon as you decide to define what is a double sente it exists doesn'it?

Click Here To Show Diagram Code
[go]$$W
$$ -----------------
$$ | . . . . . . . . |
$$ | . . . X O . . . |
$$ | . . . X O X . . |
$$ | X X X X 1 X . . |
$$ | . . . . O O O O |
$$ | . . . . . . . . |
$$ | . . . . . . . . |
$$ | . . . . . . . . |
$$ -------------------[/go]


In the diagram above you can see that the :w1: move is a quite big gote move and an answer by a black hane may be not big enough if it exists some other big gote moves on the board.
That means that :w1: creates a double sente area (OC in the sense of the definition you proposed above).
Can you explain with this exemple how mathematics can prove theorem: A local double sente endgame with M < Fb, Fw does not exist.

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 Post subject: Re: How evaluate double sente moves ?
Post #87 Posted: Wed Oct 21, 2020 11:43 am 
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Bill Spight wrote:
OK. Thermographs do two things. The thermograph of a game finds the mean value of the game, and it finds the result of minimax play in the game, starting with each player, at each temperature.

What else does your skeptic desire?


Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . b a X . . X |
$$ | X X X O O . O O |
$$ | . . X X O . O X |
$$ | . . . X X O O X |
$$ | . . . . X X X X |
$$ | . . . . . . . . |
$$ | . . . . . . . . |
$$ | . . . . . . . . |
$$ -----------------[/go]


The game above looks like G1 = {{+22|-6},-3|-7}
And my goal is to compare this game G1 with the game G2 = {-3|-7}

In order to do this comparaison I decide to build various environments Ei made of simple gote areas.
Formely you can write Ei = {gi,1|-gi,1} + {gi,2|-gi,2} + ...
In addition because I do not need high temperatures I may assume gi,j <= 5

Now to compare G1 and G2 I decide to compare the score of the games
{G1 + Ei} and {G2 + Ei}
Finaly, in order to get a good result I take a very large number of Ei, one million if you want but a finite number to be able to calculate a mean value.

The point is the following: unless I am wrong you have
∀i, score(G1 + Ei) >= score(G2 + Ei)
and ∃i, score(G1 + Ei) > score(G2 + Ei)
and this implies that
mean(score(G1 + Ei)) > mean(score(G2 + Ei))
and as a consequence I expected to see meanValue(G1) > meanValue(G2)
but we have meanValue(G1) = meanValue(G2) = 2

I know that with the ideal (monster?) environment Eideal we have
score(G1 + Eideal) = score(G2 + Eideal)
but when I take the average on a very large number of real environments G1 looks stricly better than G2.

I do not feel it is skepticism Bill. Maybe it is only that I expected more from the theory ?

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 Post subject: Re: How evaluate double sente moves ?
Post #88 Posted: Wed Oct 21, 2020 11:44 am 
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Unlike proofs by counter-example, the theorem cannot be proven by example because it applies to all such examples. Instead, the proof is by abstract verification. More later.

Can you please simplify your example so that there are not many follow-up moves and safely alive surrounding strings?

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 Post subject: Re: How evaluate double sente moves ?
Post #89 Posted: Wed Oct 21, 2020 11:46 am 
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Gérard TAILLE wrote:
As soon as you decide to define what is a double sente it exists doesn'it?


A double sente by definition is a finite combinatorial game whose thermograph has a left wall, L = u, and a Right wall, R = v, such that u > v.

Does such a double sente exist?

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 Post subject: Re: How evaluate double sente moves ?
Post #90 Posted: Wed Oct 21, 2020 12:03 pm 
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Gérard TAILLE wrote:
Bill Spight wrote:
OK. Thermographs do two things. The thermograph of a game finds the mean value of the game, and it finds the result of minimax play in the game, starting with each player, at each temperature.

What else does your skeptic desire?


Click Here To Show Diagram Code
[go]$$B
$$ -----------------
$$ | . . b a X . . X |
$$ | X X X O O . O O |
$$ | . . X X O . O X |
$$ | . . . X X O O X |
$$ | . . . . X X X X |
$$ | . . . . . . . . |
$$ | . . . . . . . . |
$$ | . . . . . . . . |
$$ -----------------[/go]


The game above looks like G1 = {{+22|-6},-3|-7}
And my goal is to compare this game G1 with the game G2 = {-3|-7}


To do so, you subtract G2 from G1. I. e., you consider the sum,

H = {{22|-6},-3|-7} + {7|3}

If White (Right) plays first, White cannot win. That is, if White plays to -7 in the game on the left, Black (Left) replies to 7 in the other game, for jigo (0). If White plays to 3 in the game on the right, Black replies to -3 in the other game, also for jigo.

If Black plays first she wins. She plays to {22|-6} + {7|3}. White's best play is to -6 on the left, after that Black plays to 7 in the other game, for a score of 7 - 6 = 1.

Therefore G1 > G2.

This question is answered with a difference game, not with thermography.

Quote:
I do not feel it is skepticism Bill. Maybe it is only that I expected more from the theory ?


As my shop teacher used to tell us, use the right tool for the job. :)

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 Post subject: Re: How evaluate double sente moves ?
Post #91 Posted: Wed Oct 21, 2020 1:24 pm 
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Bill Spight wrote:

To do so, you subtract G2 from G1. I. e., you consider the sum,

H = {{22|-6},-3|-7} + {7|3}

If White (Right) plays first, White cannot win. That is, if White plays to -7 in the game on the left, Black (Left) replies to 7 in the other game, for jigo (0). If White plays to 3 in the game on the right, Black replies to -3 in the other game, also for jigo.

If Black plays first she wins. She plays to {22|-6} + {7|3}. White's best play is to -6 on the left, after that Black plays to 7 in the other game, for a score of 7 - 6 = 1.

Therefore G1 > G2.

This question is answered with a difference game, not with thermography.



That is exactly what I tried to explained in my previous posts.
Though G1 > G2 the thermography claims meanValue(G1) = meanValue(G2).
When you look at the theory as a whole (CGT theorems, thermography, difference game etc) this result might appear as a contradiction. I just say it is a pity result that may logically cause some skepticism for the non mathematician go players who see in other cases a very acurate calculation of mean values and I fear it is difficult to convinced a non mathematician that it is not necessarily a contradiction (I know the assumptions behind thermography and difference game are quite different OC)

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 Post subject: Re: How evaluate double sente moves ?
Post #92 Posted: Wed Oct 21, 2020 2:31 pm 
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Gérard TAILLE wrote:
Bill Spight wrote:

To do so, you subtract G2 from G1. I. e., you consider the sum,

H = {{22|-6},-3|-7} + {7|3}

If White (Right) plays first, White cannot win. That is, if White plays to -7 in the game on the left, Black (Left) replies to 7 in the other game, for jigo (0). If White plays to 3 in the game on the right, Black replies to -3 in the other game, also for jigo.

If Black plays first she wins. She plays to {22|-6} + {7|3}. White's best play is to -6 on the left, after that Black plays to 7 in the other game, for a score of 7 - 6 = 1.

Therefore G1 > G2.

This question is answered with a difference game, not with thermography.



That is exactly what I tried to explained in my previous posts.
Though G1 > G2 the thermography claims meanValue(G1) = meanValue(G2).


As I tried to explain, the difference between G1 and G2 is not a number. It is a game. For people who are unfamiliar with combinatorial game theory, that doesn't make any sense. OTOH, a go player can fairly easily understand that it is better to have the position you constructed than one that corresponds to the game, {-3|-7}. Even if it is not obvious to them, you can show them or they can play around with it. :)

Quote:
When you look at the theory as a whole (CGT theorems, thermography, difference game etc) this result might appear as a contradiction.


I think it's the other way around. When you are unfamiliar with numbers and games is when it looks contradictory. Most people are only familiar with numbers, which are strictly ordered, and not with games, which are only partially ordered. Things that are partially ordered often appear illogical or contradictory until you get used to them.

Quote:
I just say it is a pity result that may logically cause some skepticism for the non mathematician go players who see in other cases a very acurate calculation of mean values and I fear it is difficult to convinced a non mathematician that it is not necessarily a contradiction (I know the assumptions behind thermography and difference game are quite different OC)


One reason I like to talk about difference games is that go players can play them out and see who wins or not. That can be very convincing. :)

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 Post subject: Re: How evaluate double sente moves ?
Post #93 Posted: Wed Oct 21, 2020 3:00 pm 
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RobertJasiek wrote:
Unlike proofs by counter-example, the theorem cannot be proven by example because it applies to all such examples. Instead, the proof is by abstract verification. More later.

Can you please simplify your example so that there are not many follow-up moves and safely alive surrounding strings?


Here under I tried to build such example:

Click Here To Show Diagram Code
[go]$$W White to play
$$ ------------------------
$$ | . . . . . . . . . . .|
$$ | . . . . . . X O . . .|
$$ | X X . . . . X O X . .|
$$ | . X X X X X X . X . .|
$$ | X X O O X X O O O O O|
$$ | X O O O X X . X X O .|
$$ | X O O O O . O O X O O|
$$ | X O X X X X X O O O O|
$$ | X X X X X X X X X O O|
$$ | X X X X X X X X X O O|
$$ | . X X X X X O O . O .|
$$ ------------------------[/go]


The idea is the following

Click Here To Show Diagram Code
[go]$$W White to play
$$ ------------------------
$$ | . . . . . . 3 . . . .|
$$ | . . . . . . X O . . .|
$$ | X X . . . . X O X . .|
$$ | . X X X X X X 1 X . .|
$$ | X X O O X X O O O O O|
$$ | X O O O X X . X X O .|
$$ | X O O O O 2 O O X O O|
$$ | X O X X X X X O O O O|
$$ | X X X X X X X X X O O|
$$ | X X X X X X X X X O O|
$$ | . X X X X X O O . O .|
$$ ------------------------[/go]


:w1: white is the biggest gote point and create the double sente (the two hane-tsugi)
The temperature is still too high (t=10) and unfortunetly black has to play first :b2:
Now the temperature has dropped so that the double sente move is of greatest importance and white is quite lucky to be able to play this double sente move of course before playing in the remaining gote!

If mathematics prove this double sente cannot exist I must be wrong somewhere but where Robert?

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 Post subject: Re: How evaluate double sente moves ?
Post #94 Posted: Wed Oct 21, 2020 3:19 pm 
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I attach my mathematical proof of non-existence of local double sente, which proceeds Bill's preliminary study.


Attachments:
DoubleSenteProofExtract.pdf [157.92 KiB]
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 Post subject: Re: How evaluate double sente moves ?
Post #95 Posted: Wed Oct 21, 2020 3:23 pm 
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Gérard TAILLE wrote:
I must be wrong somewhere but where Robert?


You do not calculate the move values. In your complex example, calculation is complex. Why not start with my simple, more extreme example? https://www.lifein19x19.com/viewtopic.p ... 33#p260633

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 Post subject: Re: How evaluate double sente moves ?
Post #96 Posted: Wed Oct 21, 2020 3:39 pm 
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RobertJasiek wrote:
I attach my mathematical proof of non-existence of local double sente, which proceeds Bill's preliminary study.

Do you mean precedes? Does it go back to the 1970s?

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 Post subject: Re: How evaluate double sente moves ?
Post #97 Posted: Wed Oct 21, 2020 3:46 pm 
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Gérard TAILLE wrote:
Now the temperature has dropped so that the double sente move is of greatest importance and white is quite lucky to be able to play this double sente move of course before playing in the remaining gote!

If mathematics prove this double sente cannot exist I must be wrong somewhere but where Robert?


To repeat myself, nobody says that double sente moves do not exist. The question is whether double sente positions exist. Do you claim that the top right corner after :w1: is a double sente position?

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 Post subject: Re: How evaluate double sente moves ?
Post #98 Posted: Wed Oct 21, 2020 3:50 pm 
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Gérard TAILLE wrote:
RobertJasiek wrote:
Unlike proofs by counter-example, the theorem cannot be proven by example because it applies to all such examples. Instead, the proof is by abstract verification. More later.

Can you please simplify your example so that there are not many follow-up moves and safely alive surrounding strings?


Here under I tried to build such example:

Click Here To Show Diagram Code
[go]$$W White to play
$$ ------------------------
$$ | . . . . . . . . . . .|
$$ | . . . . . . X O . . .|
$$ | X X . . . . X O X . .|
$$ | . X X X X X X . X . .|
$$ | X X O O X X O O O O O|
$$ | X O O O X X . X X O .|
$$ | X O O O O . O O X O O|
$$ | X O X X X X X O O O O|
$$ | X X X X X X X X X O O|
$$ | X X X X X X X X X O O|
$$ | . X X X X X O O . O .|
$$ ------------------------[/go]


The idea is the following

Click Here To Show Diagram Code
[go]$$W White to play
$$ ------------------------
$$ | . . . . . . 3 . . . .|
$$ | . . . . . . X O . . .|
$$ | X X . . . . X O X . .|
$$ | . X X X X X X 1 X . .|
$$ | X X O O X X O O O O O|
$$ | X O O O X X . X X O .|
$$ | X O O O O 2 O O X O O|
$$ | X O X X X X X O O O O|
$$ | X X X X X X X X X O O|
$$ | X X X X X X X X X O O|
$$ | . X X X X X O O . O .|
$$ ------------------------[/go]


:w1: white is the biggest gote point and create the double sente (the two hane-tsugi)
The temperature is still too high (t=10) and unfortunetly black has to play first :b2:
Now the temperature has dropped so that the double sente move is of greatest importance and white is quite lucky to be able to play this double sente move of course before playing in the remaining gote!

If mathematics prove this double sente cannot exist I must be wrong somewhere but where Robert?


Isn't this a counter-example? If the top right corner is really a double sente, why does Black play the gote, :b2:?

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 Post subject: Re: How evaluate double sente moves ?
Post #99 Posted: Wed Oct 21, 2020 4:04 pm 
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Bill Spight wrote:
RobertJasiek wrote:
which proceeds Bill's preliminary study.

Do you mean precedes?


Haha. I mean "continues". See the file for what I refer to.


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Post #100 Posted: Thu Oct 22, 2020 6:03 am 
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RobertJasiek wrote:

Since not all players use values but players with a weak understanding of endgame only use an informal understanding, the common go players' understanding of double sente would be informal. However, some players have not reflected yet that local versus global considerations of double sente differ. Therefore, the common go players' understanding of double sente does not exist. Concerning global considerations, some players are aware that one should not always play a double sente immediately because it might be relatively small while other players (with a weak understanding of endgame) are not aware of that and instead believe overly simplistic traditional advice to play in double sente as early as possible. Only for local considerations, we can identify some common go players' understanding of double sente: that either player's local play is sente meaning an immediate reply by the opponent. In only informal terms, we cannot better characterise why an immediate local reply should be necessary.

In terms of values, we can characterise why an immediate local reply should be necessary: after either player's local play, the reply is more valuable. That is, the move value in the initial local endgame position is smaller than both replies' follow-up move values. Let us use these variables:

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.

Now, we can characterise a local double sente endgame be these value conditions:

M < Fb, Fw.

(This annotation abbreviates "M < Fb and M < Fw".)

However, simply speaking, the mathematically proven theorem says:

A local double sente endgame with M < Fb, Fw does not exist.

The common go players' understanding did not know this yet:)


If we want to reach a common understanding on double sente moves we have to be a minimum rigourous. Knowing Robert made some proof about the existing of such "double sente" the only way the really progress is to take Robert definiion without any change.
If I understand correctly the proof made by Robert is based on the following defintion:

we can characterise a local double sente endgame be these value conditions: M < Fb, Fw

So let's take this simple defintion as it is and let's avoid any change, even a tiny one.

Robert ask for simplifying my following example
Click Here To Show Diagram Code
[go]$$W White to play
$$ ------------------------
$$ | . . . . . . . . . . .|
$$ | . . . . . . X O . . .|
$$ | X X . . . . X O X . .|
$$ | . X X X X X X . X . .|
$$ | X X O O X X O O O O O|
$$ | X O O O X X . X X O .|
$$ | X O O O O . O O X O O|
$$ | X O X X X X X O O O O|
$$ | X X X X X X X X X O O|
$$ | X X X X X X X X X O O|
$$ | . X X X X X O O . O .|
$$ ------------------------[/go]


OK the best I can do is to replace the complexe upper area by a simple formal game. Here it is
G = {21|{{18|4} | {0|-14}}

To begin with, could you please draw the thermograph of this game Robert (or Bill)?
The thermograph under t=7 seems easy but above above this temperature it looks a little more difficult. So let's see.

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