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| Thermography http://www.lifein19x19.com/viewtopic.php?f=12&t=17788 |
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| Author: | Gérard TAILLE [ Sun Feb 07, 2021 9:28 am ] |
| Post subject: | Re: Thermography |
Here is an example where all possibilties have to be carefully analysed It seems white can get a draw in two ways: and white wins the ko or and again white wins the ko (one ko threat for black and one ko threat white) but the second sequence is not correct. Black must play and now black wins by one point by or and now black wins the the ko because black has two ko threats against only one for white. Not so easy is it? |
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| Author: | Gérard TAILLE [ Sun Feb 07, 2021 10:11 am ] |
| Post subject: | Re: Thermography |
Gérard TAILLE wrote: Bill Spight wrote: Because in the position proposed the key point is the number of ko threats I think you obviously answered here a little too quickly. The move  in the above diagram is not correct. You have to play:or and in any case black gets a good ko threat OC the best sequence for white is because the black threat is smaller |
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| Author: | Gérard TAILLE [ Mon Feb 15, 2021 5:00 am ] |
| Post subject: | Re: Thermography |
Let me propose the following small yose problem: As we all know you usely cannot get the best yose move without knowing the exact environment. Here I assume area counting, I assume black is komaster and I assume temperature equal to zero. Note : I hope the white sequence is unique against the best black defense! |
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| Author: | Bill Spight [ Mon Feb 15, 2021 1:44 pm ] |
| Post subject: | Re: Thermography |
Gérard TAILLE wrote: Let me propose the following small yose problem: As we all know you usely cannot get the best yose move without knowing the exact environment. Here I assume area counting, I assume black is komaster and I assume temperature equal to zero. Note : I hope the white sequence is unique against the best black defense! A couple of thoughts. No guarantees.   takes back at  Seki. Black gets the last play.  takes back at Seki. White gets the last play. Better for White. |
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| Author: | Gérard TAILLE [ Mon Feb 15, 2021 3:23 pm ] |
| Post subject: | Re: Thermography |
Very good Bill. If I am not wrong the result (area counting) for each move are the following: move at "a" point : score -7 move at "b" points : score -5 move at "c" points : score -3 move at "d" points : score -1 tenuki : score +1 For me, the correct move at "a" looked quite difficult to find. Let me mentionned another tricky variation: Because black is komaster  is possible and white cannot reach the score -7 with this variation.
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| Author: | Bill Spight [ Tue Feb 16, 2021 11:14 am ] |
| Post subject: | Re: Thermography |
Gérard TAILLE wrote: Very good Bill. If I am not wrong the result (area counting) for each move are the following: move at "a" point : score -7 move at "b" points : score -5 move at "c" points : score -3 move at "d" points : score -1 tenuki : score +1 BTW, to adjust area score results for comparison with territory scoring, I add to them the number of White stones minus the number of Black stones in the original position. In this position there are 13 White stones and 6 Black stones, so we add 7. The adjusted scores are then 0 for move a, 2 for move b, etc. |
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| Author: | Gérard TAILLE [ Tue Feb 16, 2021 1:20 pm ] |
| Post subject: | Re: Thermography |
Bill Spight wrote: BTW, to adjust area score results for comparison with territory scoring, I add to them the number of White stones minus the number of Black stones in the original position. In this position there are 13 White stones and 6 Black stones, so we add 7. The adjusted scores are then 0 for move a, 2 for move b, etc. Oops I do not understand Bill. You are very aware that lots of sequences lead to a seki (your own two proposals are good example). In such case only the number of stones captured during the sequence are relevant and that does not look to fit your formula, does it? |
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| Author: | Bill Spight [ Tue Feb 16, 2021 1:59 pm ] |
| Post subject: | Re: Thermography |
Gérard TAILLE wrote: Bill Spight wrote: BTW, to adjust area score results for comparison with territory scoring, I add to them the number of White stones minus the number of Black stones in the original position. In this position there are 13 White stones and 6 Black stones, so we add 7. The adjusted scores are then 0 for move a, 2 for move b, etc. Oops I do not understand Bill. You are very aware that lots of sequences lead to a seki (your own two proposals are good example). In such case only the number of stones captured during the sequence are relevant and that does not look to fit your formula, does it? It's not a conversion, it is for making comparisons. Of the two sequences I gave, the one starting with D-09 gets a territory result of +1, not 0, while one starting with E-09 gets a territory score of +2, which agrees with the adjusted score. Typically the adjusted score will be within 1 point of the territory score, depending on the specific rules. |
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| Author: | Gérard TAILLE [ Tue Feb 16, 2021 2:27 pm ] |
| Post subject: | Re: Thermography |
Bill Spight wrote: Gérard TAILLE wrote: Bill Spight wrote: BTW, to adjust area score results for comparison with territory scoring, I add to them the number of White stones minus the number of Black stones in the original position. In this position there are 13 White stones and 6 Black stones, so we add 7. The adjusted scores are then 0 for move a, 2 for move b, etc. Oops I do not understand Bill. You are very aware that lots of sequences lead to a seki (your own two proposals are good example). In such case only the number of stones captured during the sequence are relevant and that does not look to fit your formula, does it? It's not a conversion, it is for making comparisons. Of the two sequences I gave, the one starting with D-09 gets a territory result of +1, not 0, while one starting with E-09 gets a territory score of +2, which agrees with the adjusted score. Typically the adjusted score will be within 1 point of the territory score, depending on the specific rules. Yes Bill. Precisely because the adjusted score will be within 1 point, unfortunatly, comparing two sequences in area or territory scoring may give different results: The sequences beginning with "a" or "b" in the above diagram leads to the same score (+1) in territory scoring. In area scoring the sequence beginning with "a" is two points better than the sequence beginning with "b". That the reason I chose area counting for this problem. |
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| Author: | Bill Spight [ Tue Feb 16, 2021 4:27 pm ] |
| Post subject: | Re: Thermography |
Gérard TAILLE wrote: The sequences beginning with "a" or "b" in the above diagram leads to the same score (+1) in territory scoring. In area scoring the sequence beginning with "a" is two points better than the sequence beginning with "b". That the reason I chose area counting for this problem. Sure. No problem. |
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| Author: | dhu163 [ Sun Jun 13, 2021 5:16 am ] |
| Post subject: | Re: Thermography |
I am gradually reading through this thread and several others to see what I can learn. I found GT's question in post 33 interesting. I think that it should be possible to say a bit more about which environments correspond to situations, but I don't know how (yet). Thermography deals with this question restricting to ideal environments. Is it true that in all environments, in that diagram, kosumi is dominated by max(keima, monkey jump)? Taking the question literally, my answer is: However, based on the above, I have now realised that What went wrong? Can this be fixed? (this was written before I realised the above) post 207 Is there a nonzero solution to G+G+G=0? (edit: removed lots of nonsense) I'm guessing an infinite game is required. For example, as a Go player who knows CGT only to a shallow level, a ko should work. G = {-a|H}, H={G|2a}. |
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| Author: | Gérard TAILLE [ Sun Jun 13, 2021 10:48 am ] |
| Post subject: | Re: Thermography |
dhu163 wrote: I am gradually reading through this thread and several others to see what I can learn. I found GT's question in post 33 interesting. I think that it should be possible to say a bit more about which environments correspond to situations, but I don't know how (yet). Thermography deals with this question restricting to ideal environments. Is it true that in all environments, in that diagram, kosumi is dominated by max(keima, monkey jump)? Taking the question literally, my answer is: I like your answer which is very interesting. My question was the following : does it exist a non-ko environment for which kosumi is strictly better than both keima and monkey jump? I am not sure your example is really valid because: and white cannot win this game without winning the ko at  which is in the environment ... though I was asking for a non-ko environment.I am not convinced to have played the best white moves. Maybe you will find another sequence in which white will not be forced to win a ko in the environment. That is the point. dhu163 wrote: NB: if Black could play on the right to draw, then the kosumi would be a reverse. Hmm, if black attaches, and white blocks on the right, then black blocks on the right and draws. If black attaches, white connects, black keima on left does seem to draw though. If black attaches, white ataris instead, then black plays a monkey jump on the left and draws. In most other variations, if W gets sente to block on the left, normally black will not be able to draw. If we replace kosumi with keima on the right instead, (edit: changed my mind, that seems to reverse too, but not by playing the attachment. Black has to play the crude push on the right at N6 instead. If white responds, then black plays keima on the left) I do not understand this NB. Could you please explain with diagrams? |
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| Author: | Bill Spight [ Sun Jun 13, 2021 11:53 am ] |
| Post subject: | Re: Thermography |
dhu163 wrote: Using convention LEFT wants to minimise, RIGHT wants to maximise. G={T|A,B,C} What convention is that? The usual Cartesian convention? Conway, for whatever reason, reversed the order of the Cartesian lateral axis for CGT, so that values increase as you move left. In CGT Black corresponds to the Left player and White corresponds to the Right player, and Black tries to maximize her scores. Now that Conway, Berlekamp, and Guy have all passed away, perhaps, in time the lateral axis in CGT will revert to the usual Cartesian order, but I don't think that time has yet arrived. |
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| Author: | dhu163 [ Sun Jun 13, 2021 11:59 am ] |
| Post subject: | Re: Thermography |
I'm not sure how helpful it is to argue that you ban ko takes for a "non-ko" environment, because that changes the rules of the game. So your would be the first invalid move. But I guess your logic is consistent if you ban the opponent from taking kos. I'm not too clear what "non-ko" environment means myself.My point was that on the left diagram, (call the right one the environment) the kosumi move is strictly better than the keima as well as the monkey jump (this is implied if kosumi and keima are incomparable and kosumi and monkey jump are incomparable). Hence, this is a NO answer to the question (if only on positions) Proof: However, in my second hide, I realise that all 3 moves are reverses, so in practice, I prove that it is impossible for the kosumi to be the only best move globally (i.e. locally and environment), which is like a YES answer to the question. (assuming all the difference games are correct) So I guess kosumi <= max(keima, monkey jump, environment best move) is the correct statement. (NB In your diagram, I think  is strange but ok,  is a mistake unless B has enough ko threats,  can draw by playing at . But I agree that with  , the best score is a draw. see below)The reason is that your actually does draw (if I read it right). This means that kosumi can always be answered with the attachment at M7 without black losing anything.Proof: Keima reverses Proof Monkey jump reverses Proof NB: this does not hold for the general 1st line problem, because normally the keima doesn't reverse and only gains. It only reverses here because the J7 is so close by, allowing the crude push to be a viable move. |
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| Author: | Bill Spight [ Sun Jun 13, 2021 2:11 pm ] |
| Post subject: | Re: Thermography |
dhu163 wrote: I'm not sure how helpful it is to argue that you ban ko takes for a "non-ko" environment, because that changes the rules of the game. So your would be the first invalid move. But I guess your logic is consistent if you ban the opponent from taking kos. I'm not too clear what "non-ko" environment means myself.I think think that we can have kos if there is no ko fight. For instance, in this sequence, If does not fill the ko and takes it, White is not allowed to take the ko back. Somewhat artificial, but there you go.Another possibility is that whoever takes a ko is komaster, which means that on their next turn they have to prevent the ko from being retaken. So if takes the ko,  must win it.AFAIK, the implications of difference games have only been proven for non-ko positions. |
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| Author: | Gérard TAILLE [ Sun Jun 13, 2021 2:37 pm ] |
| Post subject: | Re: Thermography |
dhu163 wrote: I'm not sure how helpful it is to argue that you ban ko takes for a "non-ko" environment, because that changes the rules of the game. So your would be the first invalid move. But I guess your logic is consistent if you ban the opponent from taking kos. I'm not too clear what "non-ko" environment means myself.It seems the misunderstanding is here. Look the link giving what a difference game is : https://senseis.xmp.net/?DifferenceGame. You will find the following article: Ko caveat Go is not strictly a combinatorial game because of kos. So difference games involving kos may not behave according to theory. Also, it may be right to make the play that the difference game says is wrong because it produces more or bigger ko threats for you or fewer or smaller threats for your opponent. My view is the following : playing a difference game, even with ko, may be helpful for understanding a position and the various moves but, if you find a ko then you cannot claim for a reliable conclusion. As a consequence you cannot say kosumi, keima, monkey jump are imcomparable according to difference games. Let me reformulate my question in order to avoid any ambiguity. I showed you a position in which black keima is the best move in a non-ko environment and I showed you another position in which black monkey jump is the best move in another non-ko environment. What about black kosumi? Here is my reformulated question : Take as constraint that your are not allowed to use the kosumi move. Can you build in a non-ko environment in order to build a position for which you cannot reach the best score due to this constraint? |
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| Author: | Gérard TAILLE [ Sun Jun 13, 2021 2:57 pm ] |
| Post subject: | Re: Thermography |
Bill Spight wrote: I think think that we can have kos if there is no ko fight. For instance, in this sequence, Bill Spight wrote: If does not fill the ko and takes it, White is not allowed to take the ko back. Somewhat artificial, but there you go.Another possibility is that whoever takes a ko is komaster, which means that on their next turn they have to prevent the ko from being retaken. So if takes the ko, must win it.AFAIK, the implications of difference games have only been proven for non-ko positions. I have another suggestion. When playing a difference game consider always that the one who is playing first is komaster. That way, if you do not manage to win though you are komaster this result seems reliable. |
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| Author: | Gérard TAILLE [ Mon Jun 14, 2021 2:33 am ] |
| Post subject: | Re: Thermography |
dhu163 wrote: I'm not sure how helpful it is to argue that you ban ko takes for a "non-ko" environment, because that changes the rules of the game. So your would be the first invalid move. But I guess your logic is consistent if you ban the opponent from taking kos. I'm not too clear what "non-ko" environment means myself.My point was that on the left diagram, (call the right one the environment) the kosumi move is strictly better than the keima as well as the monkey jump (this is implied if kosumi and keima are incomparable and kosumi and monkey jump are incomparable). Hence, this is a NO answer to the question (if only on positions) Proof: However, in my second hide, I realise that all 3 moves are reverses, so in practice, I prove that it is impossible for the kosumi to be the only best move globally (i.e. locally and environment), which is like a YES answer to the question. (assuming all the difference games are correct) So I guess kosumi <= max(keima, monkey jump, environment best move) is the correct statement. (NB In your diagram, I think is strange but ok, is a mistake unless B has enough ko threats, can draw by playing at . But I agree that with , the best score is a draw. see below)The reason is that your actually does draw (if I read it right). This means that kosumi can always be answered with the attachment at M7 without black losing anything.Proof: Keima reverses Proof Monkey jump reverses Proof NB: this does not hold for the general 1st line problem, because normally the keima doesn't reverse and only gains. It only reverses here because the J7 is so close by, allowing the crude push to be a viable move. The basic question is the following : can black play and draw in the diagram above. I think we agree that the three moves above are the beginning of the best sequence. But here our sequences differ: you play at "a" and you conclude to the draw. Fine but that means that you must find another white move to try to win doesn't you? For that purpose I suggested the "strange" move white at "bAfter at "b" I played and you react by saying : ":b5: is a mistake unless B has enough ko threats". Your are right but here is really the point: if instead you play another move then black will simply lose without ko! The is the only move avoiding the loss without condition. In that sense is the best move.What conclusion? In the initial position the best result black can reach is a disadvantageous ko for a draw. IOW if black is komaster on the environment then black manages to draw otherwise black will lose. |
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| Author: | Gérard TAILLE [ Mon Jun 14, 2021 3:38 am ] |
| Post subject: | Re: Thermography |
dhu163 wrote: I'm not sure how helpful it is to argue that you ban ko takes for a "non-ko" environment, because that changes the rules of the game. So your would be the first invalid move. But I guess your logic is consistent if you ban the opponent from taking kos. I'm not too clear what "non-ko" environment means myself.My point was that on the left diagram, (call the right one the environment) the kosumi move is strictly better than the keima as well as the monkey jump (this is implied if kosumi and keima are incomparable and kosumi and monkey jump are incomparable). Hence, this is a NO answer to the question (if only on positions) Proof: However, in my second hide, I realise that all 3 moves are reverses, so in practice, I prove that it is impossible for the kosumi to be the only best move globally (i.e. locally and environment), which is like a YES answer to the question. (assuming all the difference games are correct) So I guess kosumi <= max(keima, monkey jump, environment best move) is the correct statement. (NB In your diagram, I think is strange but ok, is a mistake unless B has enough ko threats, can draw by playing at . But I agree that with , the best score is a draw. see below)The reason is that your actually does draw (if I read it right). This means that kosumi can always be answered with the attachment at M7 without black losing anything.Proof: Keima reverses Proof Monkey jump reverses Proof NB: this does not hold for the general 1st line problem, because normally the keima doesn't reverse and only gains. It only reverses here because the J7 is so close by, allowing the crude push to be a viable move. You use a lot of time the wording "reverse". What does it means exactly to you ? It looks not the definition you can find here: https://senseis.xmp.net/?Reversible and, as a consequence, I am not sure to understand what you are really saying. |
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| Author: | dhu163 [ Thu Jun 17, 2021 12:51 pm ] |
| Post subject: | Re: Thermography |
Thanks for your explanations. They all make sense, especially the variation with on the monkey jump. That ko does seem to be critical, so my "proof" is flawed for missing it out.I meant for "reverse" to be the same as the SL definition. Instead of "if not" can black with the move win [the difference game], I tried to prove "can white on the previous move draw with a local response" which is equivalent IIUC. Though the colors in my diagram are switched relative to SL. |
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at 
is not ko due to shortage of liberties, atari, connect and die.
at 