This 'n' that

Talk about improving your game, resources you like, games you played, etc.
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Gérard TAILLE
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Re: This 'n' that

Post by Gérard TAILLE »

Bill Spight wrote:Our discussion of Gérard's last post has revealed that the question of :w6: filling the ko threat is open with a larger ko ensemble, so let me revisit it when we add a simple gote, U = {u|-u}, u > 0.
Click Here To Show Diagram Code
[go]$$B Black first, var. 1
$$ ---------------------
$$ | 5 2 7 9 X X O O . |
$$ | 4 1 O O X X O O O |
$$ | 3 . O X X X O O O |
$$ | . O O X . X O O O |
$$ | . O X X . X O O O |
$$ | . X . . . X O 8 . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:w6: = -u

Result: +19 - u + t

There are a number of transpositions to get that result.
Click Here To Show Diagram Code
[go]$$B Black first, var. 1
$$ ---------------------
$$ | 5 2 7 9 X X O O . |
$$ | 4 1 O O X X O O O |
$$ | 3 . O X X X O O O |
$$ | . O O X . X O O O |
$$ | . O X X . X O O O |
$$ | . X . . . X O 8 . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:w6: = -u
Click Here To Show Diagram Code
[go]$$B Black first, var. 2
$$ ---------------------
$$ | 5 2 7 8 X X O O . |
$$ | 4 1 O O X X O O O |
$$ | 3 . O X X X O O O |
$$ | . O O X . X O O O |
$$ | . O X X . X O O O |
$$ | . X . . . X O 6 . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b9: = u
Click Here To Show Diagram Code
[go]$$Wm10 Black first, var. 2
$$ ---------------------
$$ | X 1 X O X X O O . |
$$ | 3 X O O X X O O O |
$$ | X 5 O X X X O O O |
$$ | . O O X . X O O O |
$$ | 2 O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b9: = u
your move :b9: = u and the following :w10: seem to me bad moves.
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------
$$ | X . X O X X O O . |
$$ | . X O O X X O O O |
$$ | X . O X X X O O O |
$$ | . O O X . X O O O |
$$ | a O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
The point is to compare the black hane at "a" immediatly or one move later as you suggest.
Let's take the environment g1, g2, g3, ...
Click Here To Show Diagram Code
[go]$$B Black begins by hane
$$ ---------------------
$$ | X 2 X O X X O O . |
$$ | 4 X O O X X O O O |
$$ | X 6 O X X X O O O |
$$ | . O O X . X O O O |
$$ | 1 O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b3: takes g1
:b5: takes g2
:b7: takes g3
scoreHaneImmediately = -7 + g1 + g2 + g3 - g4 + g5 - g6 ...
Click Here To Show Diagram Code
[go]$$B Black plays hane later
$$ ---------------------
$$ | X 4 X O X X O O . |
$$ | 6 X O O X X O O O |
$$ | X 8 O X X X O O O |
$$ | . O O X . X O O O |
$$ | 3 O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b1: takes g1
:w2: takes g2 (the point!)
:b5: takes g3
:b7: takes g4
:b9: takes g5

scoreHanelater = -7 + g1 - g2 + g3 + g4 + g5 - g6 ...

scoreHaneImmediately - scoreHanelater = -7 + g1 + g2 + g3 - g4 + g5 - g6 ... - -7 + g1 - g2 + g3 + g4 + g5 - g6 ... = 2(g2 -g4)

You see that by delaying black hane you lose 2(g2 -g4) points.
I perfectly know that you may have g2=g4 but for a technical point of view delaying the hane looks bad and it is dominated by the immediat hane.


Bill Spight wrote:So it looks like, even with the humungous threat, we want to add 3 simple gote to the ko ensemble, U = {u|-u}, V = {v|-v}, and W = {w|-w}, u ≥ v ≥ w > 1. :)
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | . X O X . . . . . |
$$ | X O O X . . . . . |
$$ | . O X X . . . . . |
$$ | . O X . . . . . . |
$$ | X X X . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
In this very simple ko, with the same arguement, why don't you want to add to the ko ensemble the simple gote U = {u|-u} ?

When your are facing a ko with a non ideal environment it is obviously a good idea to add some simple gote in order deal with such special environment. In our case why not considering simply an ideal environment? OC if you encounter a real difficulty you can always change your mind and add simple gote to the ko ensemble. Is it the case here or do you want really to study non ideal environment for this position?
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Bill Spight
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Re: This 'n' that

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote:Our discussion of Gérard's last post has revealed that the question of :w6: filling the ko threat is open with a larger ko ensemble, so let me revisit it when we add a simple gote, U = {u|-u}, u > 0.
Click Here To Show Diagram Code
[go]$$B Black first, var. 1
$$ ---------------------
$$ | 5 2 7 9 X X O O . |
$$ | 4 1 O O X X O O O |
$$ | 3 . O X X X O O O |
$$ | . O O X . X O O O |
$$ | . O X X . X O O O |
$$ | . X . . . X O 8 . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:w6: = -u

Result: +19 - u + t

There are a number of transpositions to get that result.
Click Here To Show Diagram Code
[go]$$B Black first, var. 1
$$ ---------------------
$$ | 5 2 7 9 X X O O . |
$$ | 4 1 O O X X O O O |
$$ | 3 . O X X X O O O |
$$ | . O O X . X O O O |
$$ | . O X X . X O O O |
$$ | . X . . . X O 8 . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:w6: = -u
Click Here To Show Diagram Code
[go]$$B Black first, var. 2
$$ ---------------------
$$ | 5 2 7 8 X X O O . |
$$ | 4 1 O O X X O O O |
$$ | 3 . O X X X O O O |
$$ | . O O X . X O O O |
$$ | . O X X . X O O O |
$$ | . X . . . X O 6 . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b9: = u
Click Here To Show Diagram Code
[go]$$Wm10 Black first, var. 2
$$ ---------------------
$$ | X 1 X O X X O O . |
$$ | 3 X O O X X O O O |
$$ | X 5 O X X X O O O |
$$ | . O O X . X O O O |
$$ | 2 O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b9: = u
your move :b9: = u and the following :w10: seem to me bad moves.
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------
$$ | X . X O X X O O . |
$$ | . X O O X X O O O |
$$ | X . O X X X O O O |
$$ | . O O X . X O O O |
$$ | a O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
The point is to compare the black hane at "a" immediatly or one move later as you suggest.
Let's take the environment g1, g2, g3, ...
Click Here To Show Diagram Code
[go]$$B Black begins by hane
$$ ---------------------
$$ | X 2 X O X X O O . |
$$ | 4 X O O X X O O O |
$$ | X 6 O X X X O O O |
$$ | . O O X . X O O O |
$$ | 1 O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b3: takes g1
:b5: takes g2
:b7: takes g3
scoreHaneImmediately = -7 + g1 + g2 + g3 - g4 + g5 - g6 ...
Click Here To Show Diagram Code
[go]$$B Black plays hane later
$$ ---------------------
$$ | X 4 X O X X O O . |
$$ | 6 X O O X X O O O |
$$ | X 8 O X X X O O O |
$$ | . O O X . X O O O |
$$ | 3 O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b1: takes g1
:w2: takes g2 (the point!)
:b5: takes g3
:b7: takes g4
:b9: takes g5

scoreHanelater = -7 + g1 - g2 + g3 + g4 + g5 - g6 ...

scoreHaneImmediately - scoreHanelater = -7 + g1 + g2 + g3 - g4 + g5 - g6 ... - -7 + g1 - g2 + g3 + g4 + g5 - g6 ... = 2(g2 -g4)

You see that by delaying black hane you lose 2(g2 -g4) points.
I perfectly know that you may have g2=g4 but for a technical point of view delaying the hane looks bad and it is dominated by the immediat hane.
You make some good points. :) But, as I said before, we have different objectives. I am looking to evaluate the ko ensemble. Without adding any simple gote to the one with just the ko corner and the humungous threat, I already did so, and maybe that's good enough. It's a 3 point Black sente. :) (Edit: That may not be so. I have not bothered to work out the thermograph the old fashioned way. I think I better just do that. It would have saved a lot of time, but not been as interesting. :lol: ) Adding U it is surprising how many sequences lead to no mast at a non-negative temperature. I have been playing around with adding two simple gote. It is an improvement, but still not simple. Maybe it's just not a great idea. {shrug}

I started off using von Neuman game theory and an environment of simple gote, but frankly, in trying to find a mast value for the ko ensemble, I did not work anything out from that perspective. I appreciate your pointing out what can be gleaned from that approach. :)
Bill Spight wrote:So it looks like, even with the humungous threat, we want to add 3 simple gote to the ko ensemble, U = {u|-u}, V = {v|-v}, and W = {w|-w}, u ≥ v ≥ w > 1. :)
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | . X O X . . . . . |
$$ | X O O X . . . . . |
$$ | . O X X . . . . . |
$$ | . O X . . . . . . |
$$ | X X X . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
In this very simple ko, with the same arguement, why don't you want to add to the ko ensemble the simple gote U = {u|-u} ?[/quote]

In the late 1980s I struggled with finding the best play for what Berlekamp called hyperactive ko positions, with an environment of simple gote and simple ko threats. They are deucedly difficult. I often resorted to finite environment, adding one gote or one ko threat at a time. Even so, they quickly became intractable. Since learning CGT and Berlekamp's komaster analysis, things which were difficult became easy. I have avoided complicating things.

So I find it very interesting how, with this particular ko position, it has seemed like a good idea to add a few gote to the ko ensemble. I appreciate your insights. :bow: But in general I try to avoid complications. :) KISS = keep it simple, sister. ;)

As for the admittedly simple ko above, it is easy to evaluate without reference to any gote.
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Gérard TAILLE
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Re: This 'n' that

Post by Gérard TAILLE »

Yes Bill, we have to make our maximum to keep things as simple as possible.

When I analyse a position in order to discover the best moves, the miai value and the mast value, the first phase consists of finding the best sequences. Here my view is that we must make our maximum to play the technically best moves. We must avoid technically bad moves as for example a bad order of the moves. In order to reach this goal I prefer to use a rich environment ε, 2ε, 3ε, 4ε ...
That way I can see a difference between the sequences
g1 + g2 + g3 - g4 + g5 - g6 ... and g1 - g2 + g3 + g4 + g5 - g6 ... = 2(g2 -g4) = 4ε
As soon as the best sequence has been discovered then I prefer to use the usual ideal environment to give a result as simple as possible.

OC if I want to show a small particularity of the position, depending of the environment, then I can build a complete environment.

What is your own approach Bill?
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Bill Spight
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Re: This 'n' that

Post by Bill Spight »

First, to all readers, let me apologize for any crankiness and resulting errors recently. I am not well, and have not been for some time. It's not too serious, but it has affected my motivation and concentration. :(
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Bill Spight
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Re: This 'n' that

Post by Bill Spight »

Gérard TAILLE wrote:Yes Bill, we have to make our maximum to keep things as simple as possible.

When I analyse a position in order to discover the best moves, the miai value and the mast value, the first phase consists of finding the best sequences. Here my view is that we must make our maximum to play the technically best moves. We must avoid technically bad moves as for example a bad order of the moves. In order to reach this goal I prefer to use a rich environment ε, 2ε, 3ε, 4ε ...
That way I can see a difference between the sequences
g1 + g2 + g3 - g4 + g5 - g6 ... and g1 - g2 + g3 + g4 + g5 - g6 ... = 2(g2 -g4) = 4ε
As soon as the best sequence has been discovered then I prefer to use the usual ideal environment to give a result as simple as possible.

OC if I want to show a small particularity of the position, depending of the environment, then I can build a complete environment.

What is your own approach Bill?
My main concern these days is spreading and promoting thermography in go. Thermography was invented by Conway in the 1970s and published in On Numbers and Games. A friend lent me a copy and thought that thermography might be of interest in go. Then thermography was defined in terms of applying a tax to plays. It seemed to produce the same evaluations of go positions and plays as methods that go players already used — I was unaware of the problems with complex ko positions at that time —, so I did not see any benefit from it.

That changed for me when I attended a lecture by Berlekamp in 1994 or 5 in which he presented his komaster theory. Despite the fact that it left open the question of whether the conditions for komaster were met in actual play, it provided a considerably more tractable theory for evaluating complex ko positions than the ko theory I had developed. My theory included all of the environment in the ko ensemble. The problem with doing that is that to evaluate a ko you have to read out the whole board. But, OC, if you can do that you don't need any theory. :lol:

I joined a small group consisting of Berlekamp, some of his students and former students, and visiting scholars, and myself, which mainly studied komaster theory. At first I solved problems by opining correct play and then drawing the thermograph from that. This irked Berlekamp, who was around 3 kyu, because he contended that thermography provided a way of finding correct play. He was right, OC. Thermographic lines generated by incorrect play do not appear in the final thermograph. :) At temperature 0, where the game is played out, thermography indicates correct play, but that is guaranteed only by exhaustive search, or by perhaps other means of proving correct play. (If there is an encore, thermography may apply below temperature 0, but in go this is highly dependent upon the rules.) What thermography does is to provide correct play at each temperature. A play or line of play may be incorrect at one temperature and correct at another. Any play, given otherwise correct play, that produces the best result at a given temperature for the player, will indicate a point on the thermograph at that temperature.

So, for instance,
Click Here To Show Diagram Code
[go]$$W White to play
$$ ---------------------
$$ | X 1 X O X X O O . |
$$ | 3 X O O X X O O O |
$$ | X 5 O X X X O O O |
$$ | 4 O O X . X O O O |
$$ | X O X X . X O O O |
$$ | 2 X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
This line of play gives the best result for Black at or below temperature 1 and will thus indicate the wall of the thermograph in that temperature range. :)
Click Here To Show Diagram Code
[go]$$W White to play
$$ ---------------------
$$ | X 1 X O X X O O . |
$$ | 3 X O O X X O O O |
$$ | X 5 O X X X O O O |
$$ | . O O X . X O O O |
$$ | X O X X . X O O O |
$$ | . X . . . X O O . |
$$ | . X . . . X X O O |
$$ | X X . . . . X X X |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b2:, :b4: elsewhere (in the environment)

This result is 2 points worse for Black on the board than the previous result, so it is preferable when t > 1.

Also,
Click Here To Show Diagram Code
[go]$$W White to play
$$ ---------------------
$$ | 1 X O X . . . . . |
$$ | X O O X . . . . . |
$$ | 3 O X X . . . . . |
$$ | 2 O X . . . . . . |
$$ | X X X . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
This is the best Black can do at temperature 0, and indicates the wall of the thermograph at that temperature.
Click Here To Show Diagram Code
[go]$$W White to play
$$ ---------------------
$$ | 1 X O X . . . . . |
$$ | X O O X . . . . . |
$$ | 3 O X X . . . . . |
$$ | C O X . . . . . . |
$$ | X X X . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:b2: elsewhere

OC, above temperature 0 Black will not play :b2:. :)

At temperature 0 one player or other will fill the dame. Doing so did not change the score, OC, before the Japanese 1989 rules, which scores the White group as 0 if the dame, :ec: , is unfilled. In fact, the Japanese used to be quite proud of not filling the dame. (The J89 rules included a loophole which allowed players to continue their practice of leaving dame unfilled before scoring. But that has led to problems since then.)
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Visualize whirled peas.

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Bill Spight
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Re: This 'n' that

Post by Bill Spight »

The meaning of the walls of the thermograph and why a simple gote of the form, {t|-t}, provides a good model for the environment at temperature, t.

Suppose, for instance, we have this position at territorial go.
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | a X O X . . . . . |
$$ | X O O X . . . . . |
$$ | O O X X . . . . . |
$$ | b O X . . . . . . |
$$ | X X X . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
White to play captures 2 stones for a result of -4 plus a dame. Black to play captures 6 stones for a result of +13.

The Black wall of the thermograph is the line, s = +13 - t up to t = 8½ and the White wall is the line, s = -4 + t up to t = 8½. The mast of the thermograph rises vertically from the point, (s,t) = (4½, 8½), where the two walls coincide.

What is the point on the Black wall when t = 5? The original thermography applied a tax of 5 to each play, so the point is (s,t) = (13 - 5,5) = (8,5). The point on the White wall is (1,5). s is the same as if Black played to 13 and then White played to -5, or if White played to -4 and then Black played to +5. :)

The rule, as shown above, is to play locally until the temperature drops below t. Earlier I said that rule applied to Berlekamp's komaster theory, which is true, but I didn't go far enough. it applies to all thermography. :)

----

What about the case mentioned above where we have the environment, g1 ≥ g2 ≥ g3 ≥ g4 ≥ g5 ≥ g6 ≥ ...? If we take t = g1, then to find the thermograph we must add as many {g1|-g1} games to the environment as necessary. If we take g2 = t, then we may have only one {g1|-g1}, where g1 > t, but it is not part of the environment, it is part of the game or ko ensemble. If we take g4 = t, the same reasoning applies, g1 ≥ g2 ≥ g3 > t and all of g1, g2, and g3 are not in the environment, but are in the game or ko ensemble. :)
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Gérard TAILLE
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Re: This 'n' that

Post by Gérard TAILLE »

Bill Spight wrote: My main concern these days is spreading and promoting thermography in go. Thermography was invented by Conway in the 1970s and published in On Numbers and Games. A friend lent me a copy and thought that thermography might be of interest in go. Then thermography was defined in terms of applying a tax to plays. It seemed to produce the same evaluations of go positions and plays as methods that go players already used — I was unaware of the problems with complex ko positions at that time —, so I did not see any benefit from it.

That changed for me when I attended a lecture by Berlekamp in 1994 or 5 in which he presented his komaster theory. Despite the fact that it left open the question of whether the conditions for komaster were met in actual play, it provided a considerably more tractable theory for evaluating complex ko positions than the ko theory I had developed. My theory included all of the environment in the ko ensemble. The problem with doing that is that to evaluate a ko you have to read out the whole board. But, OC, if you can do that you don't need any theory. :lol:

I joined a small group consisting of Berlekamp, some of his students and former students, and visiting scholars, and myself, which mainly studied komaster theory. At first I solved problems by opining correct play and then drawing the thermograph from that. This irked Berlekamp, who was around 3 kyu, because he contended that thermography provided a way of finding correct play. He was right, OC. Thermographic lines generated by incorrect play do not appear in the final thermograph. :) At temperature 0, where the game is played out, thermography indicates correct play, but that is guaranteed only by exhaustive search, or by perhaps other means of proving correct play. (If there is an encore, thermography may apply below temperature 0, but in go this is highly dependent upon the rules.) What thermography does is to provide correct play at each temperature. A play or line of play may be incorrect at one temperature and correct at another. Any play, given otherwise correct play, that produces the best result at a given temperature for the player, will indicate a point on the thermograph at that temperature.
Any theory allowing to help a player to find the best move is very valuable. Thermography (without ko) is a very strong tool. By just defining an ideal environment depending of only one parameter called temperature you are able to guess the local best move and this guess is correct for a very large panel of real (non ideal) environments.
The difficulty was to define the ideal environment which is not so obvious for a non mathematical guy.
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | . O b O O O a O . |
$$ | X X X X X X X O . |
$$ | . . . . . . O O . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Evaluating such corridor means OC to evaluate a move at "a" but you have first to analyse what happens with "b" after a white move at "a". To solve such problem you have to imagine a quite strange environment: in one hand the environment may have an arbitrary high number of gote points at temperature t but in the other hand you may also expect that the temperature may drop in order to be able to deal with the remaining move at "b".
As far as I am concerned I only visualise a rich environment ε, 2ε, 3ε, 4ε ... and I make the following assumption: it exists a sufficiently small value ε0 such that the best moves in the environment ε0, 2ε0, 3ε0, 4ε0 ... are the same as the best moves in the environment ε, 2ε, 3ε, 4ε ... providing ε ≤ ε0.

Taking into account ko is quite ambitious. This ambition have to be defined by various questions and in particular:
1) do we take into account only "simple" direct kos or do we want also to take into account more complex kos?
2) do we consider kos only in the local area, only in the environment or in both local area and environment?
3) do we want to take into account ko threats in the environment (remember the position we are studying with only one black ko threat)
4) do we want to take into account ko threats with various values?

As soon as you have clarified your ambitions then you can look for a new ideal enviroment to help you analyse the local area.

Just a small example to illustrate the case were you allow ko only in the enviroment
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O . . . |
$$ | . . . . O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O 1 . . |
$$ | . . . 2 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
The exchange :b1: :w2: is sente but generally not correct in a ko environment. First of all unless temperature is quite low black must prefer to play in the environment in order to keep :b1: as a ko threat.
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O . . . |
$$ | . . . 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Secondly, even if temperature is low it is generally better to play this cut in order to get at the end a local ko threat.
After this :b1: cut what is the best move for white?

First possibility:
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . 6 2 . O 5 . . |
$$ | . 4 3 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
with a black ko threat at :b1:

Second possibily
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . 4 3 6 O 5 . . |
$$ | . . 2 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
with still a black ko threat at :b1:

What is best for white? The second one is best because the ko threat is smaller as shown by the following diagram:
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . O 3 O O X . . |
$$ | . . O 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:w2: do not answer th ko threat
and white may later recapture two stones.
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O . . . |
$$ | . . 2 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
As you see a good go player can easily find the sequence :w1: :b2:.
The question now is the following: is it possible to build a theory and an ideal environment able find and show clearly this sequence?
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Bill Spight
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Re: This 'n' that

Post by Bill Spight »

Gérard TAILLE wrote:Any theory allowing to help a player to find the best move is very valuable. Thermography (without ko) is a very strong tool. By just defining an ideal environment depending of only one parameter called temperature you are able to guess the local best move and this guess is correct for a very large panel of real (non ideal) environments.
The difficulty was to define the ideal environment which is not so obvious for a non mathematical guy.
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | . O b O O O a O . |
$$ | X X X X X X X O . |
$$ | . . . . . . O O . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Evaluating such corridor means OC to evaluate a move at "a" but you have first to analyse what happens with "b" after a white move at "a". To solve such problem you have to imagine a quite strange environment: in one hand the environment may have an arbitrary high number of gote points at temperature t but in the other hand you may also expect that the temperature may drop in order to be able to deal with the remaining move at "b".
As far as I am concerned I only visualise a rich environment ε, 2ε, 3ε, 4ε ... and I make the following assumption: it exists a sufficiently small value ε0 such that the best moves in the environment ε0, 2ε0, 3ε0, 4ε0 ... are the same as the best moves in the environment ε, 2ε, 3ε, 4ε ... providing ε ≤ ε0.
As a practical matter, this is what Berlekamp did by making ε = 0.01. But to have enough simple gote to accommodate kos, he also had 99 or 101 multiples of each gote in the environment.

Such an environment will sometimes yield the wrong thermograph, but any error would very likely be tiny. For a simple ko, for instance, the difference between 0.33 and ⅓ is small.
Gérard TAILLE wrote:Taking into account ko is quite ambitious. This ambition have to be defined by various questions and in particular:
1) do we take into account only "simple" direct kos or do we want also to take into account more complex kos?
All ko and superko positions, although to resolve some questions you must rely upon the rules.
Gérard TAILLE wrote:2) do we consider kos only in the local area, only in the environment or in both local area and environment?
The environment consists of simple gote only.
Gérard TAILLE wrote:3) do we want to take into account ko threats in the environment (remember the position we are studying with only one black ko threat)
We may in some circumstances consider a pair of simple gote of the same size as a defensive ko threat, which prevents the komaster from becoming a komonster by gaining from the drop in temperature. But that is a feature, not a bug. :)
Gérard TAILLE wrote:Just a small example to illustrate the case were you allow ko only in the enviroment
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O . . . |
$$ | . . . . O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O 1 . . |
$$ | . . . 2 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
The exchange :b1: :w2: is sente but generally not correct in a ko environment. First of all unless temperature is quite low black must prefer to play in the environment in order to keep :b1: as a ko threat.
This is not a simple gote, and therefore not part of a thermographic environment. OC, it can be a game or part of a game, and ko threats in the game may well matter.
Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O . . . |
$$ | . . . 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Secondly, even if temperature is low it is generally better to play this cut in order to get at the end a local ko threat.
After this :b1: cut what is the best move for white?

First possibility:
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . 6 2 . O 5 . . |
$$ | . 4 3 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
with a black ko threat at :b1:

Second possibily
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . 4 3 6 O 5 . . |
$$ | . . 2 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
with still a black ko threat at :b1:

What is best for white? The second one is best because the ko threat is smaller as shown by the following diagram:
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . O 3 O O X . . |
$$ | . . O 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
:w2: do not answer th ko threat
and white may later recapture two stones.
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O . . . |
$$ | . . 2 1 O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
As you see a good go player can easily find the sequence :w1: :b2:.
The question now is the following: is it possible to build a theory and an ideal environment able find and show clearly this sequence?
If this is part of a larger game (ko ensemble) that includes a ko or potential ko, then sure. :)
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Gérard TAILLE
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Re: This 'n' that

Post by Gérard TAILLE »

Bill Spight wrote:
Gérard TAILLE wrote:Any theory allowing to help a player to find the best move is very valuable. Thermography (without ko) is a very strong tool. By just defining an ideal environment depending of only one parameter called temperature you are able to guess the local best move and this guess is correct for a very large panel of real (non ideal) environments.
The difficulty was to define the ideal environment which is not so obvious for a non mathematical guy.
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | . O b O O O a O . |
$$ | X X X X X X X O . |
$$ | . . . . . . O O . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Evaluating such corridor means OC to evaluate a move at "a" but you have first to analyse what happens with "b" after a white move at "a". To solve such problem you have to imagine a quite strange environment: in one hand the environment may have an arbitrary high number of gote points at temperature t but in the other hand you may also expect that the temperature may drop in order to be able to deal with the remaining move at "b".
As far as I am concerned I only visualise a rich environment ε, 2ε, 3ε, 4ε ... and I make the following assumption: it exists a sufficiently small value ε0 such that the best moves in the environment ε0, 2ε0, 3ε0, 4ε0 ... are the same as the best moves in the environment ε, 2ε, 3ε, 4ε ... providing ε ≤ ε0.
As a practical matter, this is what Berlekamp did by making ε = 0.01. But to have enough simple gote to accommodate kos, he also had 99 or 101 multiples of each gote in the environment.

Such an environment will sometimes yield the wrong thermograph, but any error would very likely be tiny. For a simple ko, for instance, the difference between 0.33 and ⅓ is small.
This problem seems easy to solve: as soon as you give a value result, you have to eliminate all terms which appear mathematically negligeable comparing to others.

Let's take a simple ko as an example:
Black takes the ko => scoreBlackTakesTheKo = N - g1 - g2 + g3 ...
Black takes g1 and White connects the ko => scoreWhiteConnectsTheKo = g1 + g2 - g3 + ...
scoreBlackTakesTheKo - scoreWhiteConnectsTheKo = (N - g1 - g2 + g3 ...) - (g1 + g2 - g3 + ...) = N - 2g1 - 2g2 + 2g3 - 2g4 ...
Assuming 2g2 - 2g3 + 2g4 ... = g2 then
scoreBlackTakesTheKo - scoreWhiteConnectsTheKo = N - 2g1 - g2 = N - 3g1 + ε
scoreBlackTakesTheKo ≥ scoreWhiteConnectsTheKo <=> N - 3g1 + ε ≥ 0 <=> g1 <= (N + ε) / 3
and here, from a mathematical point if view, we have ε negligeable comparing to N thus the result becomes
scoreBlackTakesTheKo ≥ scoreWhiteConnectsTheKo <=> g1 <= N / 3
Bill Spight wrote:
Gérard TAILLE wrote:2) do we consider kos only in the local area, only in the environment or in both local area and environment?
The environment consists of simple gote only.
with such answer you can forget my following example:
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O . . . |
$$ | . . . . O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Assuming there is no ko in the environment you cannot find the best sequence in this local area. OC it is a pity but if you claim you have not the ambitious to consider ko in the environment we cannot do anything with this local area.

BTW you cannot say that the environment consists of simple gote only if you accept to say that one player may be komaster. That means that you accept a number of ko threats in the environment but you do not accept a ko. Fine, it is your choice Bill, but we can also try other choices (not easy OC, is it?) to try and find really the best sequence in my example above.
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Bill Spight
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Re: This 'n' that

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote:Any theory allowing to help a player to find the best move is very valuable. Thermography (without ko) is a very strong tool. By just defining an ideal environment depending of only one parameter called temperature you are able to guess the local best move and this guess is correct for a very large panel of real (non ideal) environments.
The difficulty was to define the ideal environment which is not so obvious for a non mathematical guy.
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | . O b O O O a O . |
$$ | X X X X X X X O . |
$$ | . . . . . . O O . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Evaluating such corridor means OC to evaluate a move at "a" but you have first to analyse what happens with "b" after a white move at "a". To solve such problem you have to imagine a quite strange environment: in one hand the environment may have an arbitrary high number of gote points at temperature t but in the other hand you may also expect that the temperature may drop in order to be able to deal with the remaining move at "b".
As far as I am concerned I only visualise a rich environment ε, 2ε, 3ε, 4ε ... and I make the following assumption: it exists a sufficiently small value ε0 such that the best moves in the environment ε0, 2ε0, 3ε0, 4ε0 ... are the same as the best moves in the environment ε, 2ε, 3ε, 4ε ... providing ε ≤ ε0.
As a practical matter, this is what Berlekamp did by making ε = 0.01. But to have enough simple gote to accommodate kos, he also had 99 or 101 multiples of each gote in the environment.

Such an environment will sometimes yield the wrong thermograph, but any error would very likely be tiny. For a simple ko, for instance, the difference between 0.33 and ⅓ is small.
This problem seems easy to solve: as soon as you give a value result, you have to eliminate all terms which appear mathematically negligeable comparing to others.

Let's take a simple ko as an example:
Black takes the ko => scoreBlackTakesTheKo = N - g1 - g2 + g3 ...
Black takes g1 and White connects the ko => scoreWhiteConnectsTheKo = g1 + g2 - g3 + ...
scoreBlackTakesTheKo - scoreWhiteConnectsTheKo = (N - g1 - g2 + g3 ...) - (g1 + g2 - g3 + ...) = N - 2g1 - 2g2 + 2g3 - 2g4 ...
Assuming 2g2 - 2g3 + 2g4 ... = g2 then
scoreBlackTakesTheKo - scoreWhiteConnectsTheKo = N - 2g1 - g2 = N - 3g1 + ε
scoreBlackTakesTheKo ≥ scoreWhiteConnectsTheKo <=> N - 3g1 + ε ≥ 0 <=> g1 <= (N + ε) / 3
and here, from a mathematical point if view, we have ε negligeable comparing to N thus the result becomes
scoreBlackTakesTheKo ≥ scoreWhiteConnectsTheKo <=> g1 <= N / 3
I appreciate your efforts, but this is a solved problem. It is possible to eliminate any errors, given a particular position (game), but that takes some work. Berlekamp's idea was to have an environment that he could use for any position, with only negligible errors, without having to do the work to find all the relevant positions and temperatures before drawing the thermograph. Thermographs only promise approximations to perfect play, anyway. :) But suppose that we just want an ideal environment for both t = ½ and t = ⅓ (there is a ko or possible ko). An environment with a minimum positive temperature of 1/12 will do.

⅓ - ¼ + ⅙ - 1/12 = ⅙

½ - 5/12 + ⅙ = ¼

OC, to accommodate a ko fight we need a sufficiently large odd number of gote at the relevant temperatures. :) We could start out with 11 and increase the number if necessary.

N.B. If, because of conditions on the board, there turn out to be an even number of plays at the maximum temperature, the environment is still ideal. E.g.,

½ - ½ + 5/12 - ⅓ + ¼ - ⅙ + 1/12 = ¼ :)

OC, the environment is not ideal for t = 5/12, but that is a feature, not a bug. ;)
Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote:) do we consider kos only in the local area, only in the environment or in both local area and environment?
The environment consists of simple gote only.
with such answer you can forget my following example:
Click Here To Show Diagram Code
[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O . . . |
$$ | . . . . O O X X X |
$$ | O O O O X X X . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Assuming there is no ko in the environment you cannot find the best sequence in this local area.
I don't know where you get that idea.
Gérard TAILLE wrote:BTW you cannot say that the environment consists of simple gote only if you accept to say that one player may be komaster. That means that you accept a number of ko threats in the environment but you do not accept a ko.
If a thermographic environment consisting of simple gote cannot solve for komaster then Berlekamp's original komaster theory, based upon taxation, is wrong. That is not the case.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Gérard TAILLE
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Re: This 'n' that

Post by Gérard TAILLE »

Bill Spight wrote: I don't know where you get that idea.
Gérard TAILLE wrote:BTW you cannot say that the environment consists of simple gote only if you accept to say that one player may be komaster. That means that you accept a number of ko threats in the environment but you do not accept a ko.
If a thermographic environment consisting of simple gote cannot solve for komaster then Berlekamp's original komaster theory, based upon taxation, is wrong. That is not the case.
OK it seems I was not clear in my explanations. Let's take another example:
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | . . . b X . . . . |
$$ | . a O O X . . . . |
$$ | . . O X X . . . . |
$$ | . O O X . . . . . |
$$ | . O X X . . . . . |
$$ | . X . . . . . . . |
$$ | . X . . . . . . . |
$$ | X X . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Let me simplify the reasoning by considering for black only the three moves a, b and tenuki (I mean a play in the environment) and assume I am asking a good go player the basic following question : "which move is best in this position?"

OC Bill can skip here some of the following paragraphs which adress those who are not mastering thermography.

If she is a good player she will clearly see that the best move depends on the exact configuration of the environment and she will try to have some information about this environment.

Now begins the problem :
1)if you give a lof information about the environment the answer would be quite reliable but the analyse will be extremely complex because you will analyse a great number of various environments with more or less complex area, with more or less complex ko, with various kind of ko threat etc. etc.
2)Assume now you give no information about the environment. In that case she can only imagine what could be the environment of such position. I think she will assume that we are certainly not at the end of the yose phase. For the local area I guess she will choose to play at "a" to save various possible options but how deciding between a play at "a" and a tenuki (a move in the environment)?

Clearly we do need to give some information concerning the environment. What kind of information is the most relevant? Here I am sure everybody would appreciate what is called "temperature" which you can translate as the value of a move in the environment. OC the temperature does not give the exact configuration of the environment but it gives a very interesting information about it allowing to guess the best move with a high probability to be correct.

It remains a lot of incertainty concerning the exact configuration of the environment (which could be quite complex) but you cannot underestimate how good the guess of the best move could be correct with only this information. In addition you have to appreciate the simplicity of the result like:
above t = 9 you play tenuki; betwen t = 6 and t= 9 you play "a"; under t = 6 you play "a" or "b" (do not take any importance to the values here).

Now is my point Bill.

In order to analyse the position with only the temperature as information on the environment, the current theory imagine a set of pure gote points with various good properties. That sounds a good approach for simplifing the analyse but my feeling is that a good go player is able to analyse easily the position taking into account a far more complex environment.

As an exemple assume you know the temperature is t = 1. The simple analyse, with the ideal environment defined by the theory, will tell you to play "a" or "b" but the go player will imagine (without defining it precisely) a far more complex environment. She will say that a small (⅓ point or a little higher) ko may exist in the environment. In that case a move at "a" is a bad move because this move implies the loss of a local ko threat.
For a good go player it looks easy but, if I am right, this kind of analyse is not in the current theory because ko are not taken into account in the environment.

I do not know how we can improve the theory on this point. My feeing is that it is impossible to add in the environment various ko but because humans are able to take into account "potential ko" it must exist a way to define it and improve the analysis. BTW, in my previous post I mentioned that a go player is also able to choose a move that gives the best ko threat.

IOW I think that by keeping only temperature of the environment we can imporve the analysis by taking into account the "potential" kos that may exist in the environment. Sure we will find some good ideas in the near future, simply because humans manage to do that without major difficulties. OC,we certainly have to limit our ambition to simple (and small?) "potential" kos. We will see.
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Bill Spight
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Re: This 'n' that

Post by Bill Spight »

I know I did some work on this position some years ago, because I commented on it on SL, at https://senseis.xmp.net/?L2GroupWithDescent#toc4 . But it doesn't ring a bell. There are a number of kos in the game tree, but I am not well, and I am not interested in doing a full analysis, at least not now.
Click Here To Show Diagram Code
[go]$$ Corner ko
$$ --------------
$$ | . . . . X . .
$$ | . . O O X . .
$$ | . . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]
However, a few days ago I found some interesting things with the following first 4 plays.
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]
At this point White threatens to win the ko in 1 move. We assume that t > 1.
Click Here To Show Diagram Code
[go]$$ Corner ko
$$ --------------
$$ | . 2 . . X . .
$$ | 4 1 O O X . .
$$ | 3 6 O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]
:b5: = t

Since Black played first we can leave it at that.

Result: -5½ + t

Or Black can kill the corner in 3 net moves.
Click Here To Show Diagram Code
[go]$$ Corner ko
$$ --------------
$$ | 5 2 7 9 X . .
$$ | 4 1 O O X . .
$$ | 3 . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]

:w6:, :w8:, :w10: = t

Result: 21 - 3t

The temperature of indifference occurs when

-5½ + t = 21 -3t, or when

t = 6⅝

We anticipate each play in the ko gaining 6½ points on average, not 6⅝. Verrry interesting. ;)

More later. :)
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At some point, doesn't thinking have to go on?
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Bill Spight
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Re: This 'n' that

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote: I don't know where you get that idea.
Gérard TAILLE wrote:BTW you cannot say that the environment consists of simple gote only if you accept to say that one player may be komaster. That means that you accept a number of ko threats in the environment but you do not accept a ko.
If a thermographic environment consisting of simple gote cannot solve for komaster then Berlekamp's original komaster theory, based upon taxation, is wrong. That is not the case.
OK it seems I was not clear in my explanations. Let's take another example:
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------
$$ | . . . b X . . . . |
$$ | . a O O X . . . . |
$$ | . . O X X . . . . |
$$ | . O O X . . . . . |
$$ | . O X X . . . . . |
$$ | . X . . . . . . . |
$$ | . X . . . . . . . |
$$ | X X . . . . . . . |
$$ | . . . . . . . . . |
$$ ---------------------[/go]
Let me simplify the reasoning by considering for black only the three moves a, b and tenuki (I mean a play in the environment) and assume I am asking a good go player the basic following question : "which move is best in this position?"

OC Bill can skip here some of the following paragraphs which adress those who are not mastering thermography.

If she is a good player she will clearly see that the best move depends on the exact configuration of the environment and she will try to have some information about this environment.

Now begins the problem :
1)if you give a lof information about the environment the answer would be quite reliable but the analyse will be extremely complex because you will analyse a great number of various environments with more or less complex area, with more or less complex ko, with various kind of ko threat etc. etc.
2)Assume now you give no information about the environment. In that case she can only imagine what could be the environment of such position. I think she will assume that we are certainly not at the end of the yose phase. For the local area I guess she will choose to play at "a" to save various possible options but how deciding between a play at "a" and a tenuki (a move in the environment)?

Clearly we do need to give some information concerning the environment. What kind of information is the most relevant? Here I am sure everybody would appreciate what is called "temperature" which you can translate as the value of a move in the environment. OC the temperature does not give the exact configuration of the environment but it gives a very interesting information about it allowing to guess the best move with a high probability to be correct.

It remains a lot of incertainty concerning the exact configuration of the environment (which could be quite complex) but you cannot underestimate how good the guess of the best move could be correct with only this information. In addition you have to appreciate the simplicity of the result like:
above t = 9 you play tenuki; betwen t = 6 and t= 9 you play "a"; under t = 6 you play "a" or "b" (do not take any importance to the values here).

Now is my point Bill.

In order to analyse the position with only the temperature as information on the environment, the current theory imagine a set of pure gote points with various good properties. That sounds a good approach for simplifing the analyse but my feeling is that a good go player is able to analyse easily the position taking into account a far more complex environment.

As an exemple assume you know the temperature is t = 1. The simple analyse, with the ideal environment defined by the theory, will tell you to play "a" or "b" but the go player will imagine (without defining it precisely) a far more complex environment. She will say that a small (⅓ point or a little higher) ko may exist in the environment. In that case a move at "a" is a bad move because this move implies the loss of a local ko threat.
For a good go player it looks easy but, if I am right, this kind of analyse is not in the current theory because ko are not taken into account in the environment.

I do not know how we can improve the theory on this point. My feeing is that it is impossible to add in the environment various ko but because humans are able to take into account "potential ko" it must exist a way to define it and improve the analysis. BTW, in my previous post I mentioned that a go player is also able to choose a move that gives the best ko threat.

IOW I think that by keeping only temperature of the environment we can imporve the analysis by taking into account the "potential" kos that may exist in the environment. Sure we will find some good ideas in the near future, simply because humans manage to do that without major difficulties. OC,we certainly have to limit our ambition to simple (and small?) "potential" kos. We will see.
It seems to me that you are using the term, environment, here to mean the rest of the board asid from the local position. You then seem to be complaining that knowing only the temperature of the environment is not enough to say what is best play. But that is a claim that nobody is making. {shrug}
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Gérard TAILLE
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Re: This 'n' that

Post by Gérard TAILLE »

Bill Spight wrote:I know I did some work on this position some years ago, because I commented on it on SL, at https://senseis.xmp.net/?L2GroupWithDescent#toc4 . But it doesn't ring a bell. There are a number of kos in the game tree, but I am not well, and I am not interested in doing a full analysis, at least not now.
Click Here To Show Diagram Code
[go]$$ Corner ko
$$ --------------
$$ | . . . . X . .
$$ | . . O O X . .
$$ | . . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]
However, a few days ago I found some interesting things with the following first 4 plays.
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]
At this point White threatens to win the ko in 1 move. We assume that t > 1.
Click Here To Show Diagram Code
[go]$$ Corner ko
$$ --------------
$$ | . 2 . . X . .
$$ | 4 1 O O X . .
$$ | 3 6 O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]
:b5: = t

Since Black played first we can leave it at that.

Result: -5½ + t

Or Black can kill the corner in 3 net moves.
Click Here To Show Diagram Code
[go]$$ Corner ko
$$ --------------
$$ | 5 2 7 9 X . .
$$ | 4 1 O O X . .
$$ | 3 . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]

:w6:, :w8:, :w10: = t

Result: 21 - 3t

The temperature of indifference occurs when

-5½ + t = 21 -3t, or when

t = 6⅝

We anticipate each play in the ko gaining 6½ points on average, not 6⅝. Verrry interesting. ;)

More later. :)
OK Bill my understanding is the following
Click Here To Show Diagram Code
[go]$$ Corner ko
$$ --------------
$$ | . O . . X . .
$$ | O X O O X . .
$$ | X . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]
if t > 6⅝ both players play in the environment
if 6½ < t < 6⅝ white will not play in the environment; black will play in the corner and white will not defend the corner:
Click Here To Show Diagram Code
[go]$$B Corner ko
$$ --------------
$$ | 1 O 3 5 X . .
$$ | O X O O X . .
$$ | X . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]
:w2: tenuki
:w4: tenuki
:w6: tenuki
Finally if t < 6½ both player will play in the corner. If the case black plays in the corner then white will defend with
Click Here To Show Diagram Code
[go]$$B Corner ko
$$ --------------
$$ | 1 O 3 4 X . .
$$ | O X O O X . .
$$ | X . O X X . .
$$ | . O O X . . .
$$ | . O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]
:w2: tenuki
Click Here To Show Diagram Code
[go]$$B Corner ko
$$ --------------
$$ | X 6 X O X . .
$$ | 8 X O O X . .
$$ | X 0 O X X . .
$$ | . O O X . . .
$$ | 5 O X X . . .
$$ | . X . . . . .
$$ | . X . . . . .
$$ | X X . . . . .
$$ | . . . . . . .
$$ | . . . , . . .[/go]
:b7: tenuki
:b9: tenuki
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Gérard TAILLE
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Re: This 'n' that

Post by Gérard TAILLE »

Bill Spight wrote: It seems to me that you are using the term, environment, here to mean the rest of the board asid from the local position. You then seem to be complaining that knowing only the temperature of the environment is not enough to say what is best play. But that is a claim that nobody is making. {shrug}
Yes I use the term environment to mean the rest of the board asid from the local position.
But I am not complaining that knowing only the temperature of the environment is not enough to say what is best play. On contrary I appreciate to try and find the best move with only this information. What I am saying is that, only with this temperature, we can go further in the analyse of the local position in order to try and find best move, taking into account the building of ko threats. The point being that you do not know if a ko appears in the environment but it could be and the probability is certainly high in practice.
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