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Thermography http://www.lifein19x19.com/viewtopic.php?f=12&t=17788 |
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Author: | Bill Spight [ Sat Oct 03, 2020 1:12 pm ] |
Post subject: | Re: Thermography |
Gérard TAILLE wrote: Taking the three moves kosumi, keima and monkey jump is it possible to build a good (non ko) environment for which kosumi is the only correct move? This is true for the keima and the monkey jump but what about the kosumi? {snip}BTW, do you have the feeling that such environment exist or do you have some doubts? In general I am leery of saying that thus and such situation on the go board cannot exist. To review the current position and plays: In an ideal environment Black plays the large monkey jump with sente and White replies with the sequence through . The result has a count of -3 in the marked region at or above temperature 2. (Berlekamp coined the term, orthodox, to refer to correct play in an ideal environment.) Below temperature 2 Black continues with - for a net local score of -1. We can transpose to the orthodox line, starting with the kosumi. This transposition avoids the following reply to the large monkey jump. This line is played by White below temperature 1 to prevent the Black continuation above. The reason is that the result is a local score of -2, 1 point better than the result after sacrificing a stone. The transposition is worse for Black than the orthodox line. However, the sagari, , is the orthodox reply to the (unorthodox) kosumi. The result is a count of -4 at or above temperature 1. This is 1 point worse for Black, on average, than the orthodox result at temperature 2 or above. But it is 1 point better than the local score if White gets to play locally instead of Black. That fact suggests that this play might be better in some non-ideal environment with a temperature of 2 or above. The keima is another unorthodox play where orthodox play after results in a local count of -4. It also suggests an environment with temperature 2 or above. The fact that the keima and the kosumi are incomparable with similar preconditions to playing one of them instead of the large monkey jump makes me think that there is probably a non-ko environment in which the kosumi dominates the other two. I really had not thought about that question much before now. |
Author: | Bill Spight [ Sat Oct 03, 2020 1:23 pm ] |
Post subject: | Re: Thermography |
Gérard TAILLE wrote: Oops the notation I used is not correct because it is not clear when I am reasonning one two boards and when I switch to one board. As a a consequence I see that what I wrote is quite unclear. Let me take some time to rephrase all my analysis before rediscussing. Using a second board is not necessary. It is only a convenience to indicate that the two positions are independent. In the past, discussions about difference games on a single board have run into difficulties because truly independent positions were not constructed. Using two boards makes the construction easy. In the board I used as illustration, for instance, I did not take the time to construct independently living groups, as I technically should have. I intended the positions to be understood as independent, given the prior discussion between us. Fortunately you understood my intent. Please do not get sidetracked by the question of two boards or one. Independence and the lack of a ko fight are the criteria. |
Author: | Gérard TAILLE [ Sat Oct 03, 2020 1:29 pm ] |
Post subject: | Re: Thermography |
Bill Spight wrote: Gérard TAILLE wrote: Oops the notation I used is not correct because it is not clear when I am reasonning one two boards and when I switch to one board. As a a consequence I see that what I wrote is quite unclear. Let me take some time to rephrase all my analysis before rediscussing. Using a second board is not necessary. It is only a convenience to indicate that the two positions are independent. In the past, discussions about difference games on a single board have run into difficulties because truly independent positions were not constructed. Using two boards makes the construction easy. In the board I used as illustration, for instance, I did not take the time to construct independently living groups, as I technically should have. I intended the positions to be understood as independent, given the prior discussion between us. Fortunately you understood my intent. Please do not get sidetracked by the question of two boards or one. Independence and the lack of a ko fight are the criteria. OK Bill I will try to review my analysis using only one board and I will come back for your precious comments! Thank you very much indeed! |
Author: | Gérard TAILLE [ Sat Oct 03, 2020 2:20 pm ] |
Post subject: | Re: Thermography |
Bill Spight wrote: Gérard TAILLE wrote: Oops the notation I used is not correct because it is not clear when I am reasonning one two boards and when I switch to one board. As a a consequence I see that what I wrote is quite unclear. Let me take some time to rephrase all my analysis before rediscussing. Using a second board is not necessary. It is only a convenience to indicate that the two positions are independent. In the past, discussions about difference games on a single board have run into difficulties because truly independent positions were not constructed. Using two boards makes the construction easy. In the board I used as illustration, for instance, I did not take the time to construct independently living groups, as I technically should have. I intended the positions to be understood as independent, given the prior discussion between us. Fortunately you understood my intent. Please do not get sidetracked by the question of two boards or one. Independence and the lack of a ko fight are the criteria. Here is my updated analysis using only one board: Let's consider two positions A et B surrounded by an environment E with "good" carateristics (independancy? non-ko? ...) Assume for example that, black to play, the optimum result of a game beginning from A+E is a win for black by say 10 points Assume also that, black to play, the optimum result of a game beginning from B+E is a win for black by say 7 points Let's call B' the mirror position of position B The amazing result of theory is the following: black to play will wins the game A+B' by at least 3 points !!! Let's us try to prove this "theorem": Let's call E' the mirror position of position E and put on the board the four areas A, B', E, E' Add on this board a very small area D made of one dame point. Because that cannot penalise white, you can always impose to white to avoid using the D region except maybe at the very last move of the game. First of all it is easy for black to win this new game by exactly 3 points by means of the following strategy: Black begins by playing in A or E exactly as if she where playing a game with only the area A and E. From this point till the end of the game the strategy of black is the following: if white plays a move in A or E, black answers also in A or E exactly as if black were playing a game with only the area A and E on the board if white plays a move in B' or E', black answers also in B' or E' exactly as if black were playing a game with only the area B' and E' on the board in case white plays the last move in region A+E or in region B'+E', black answers with a move in D. With this strategy is is clear that black will win the game by exactly 3 points. Of course it may happen that this winning strategy for black is not the best result for black. That means that, by following the real best strategy, black may win by more than 3 points, say for example 5 points. At that point comes the assumption that all areas (A, B', E, E', D) have good caracteristics allowing the following simplification: The above game is made of the five areas A, B', E, E' and D. When you look at these five areas you see in particular the areas E and E' which look like perfect miai areas. Here, we discover the basic assumption of all the theory: Because E and E' are perfect miai areas, if black can win the game A+B'+E+E'+D by 5 points then, providing good independance between the five areas, we can completly ignore the presence of the two areas E and E' => black wins the game A+B'+D by again 5 points. In addition you can now ignore also the dame in D => black wins the game A+B' by again 5 points. As a conclusion we have the equation minMax(A-B) >= minMax(A+E) - minMax(B+E) Is it now understandable and correct Bill? |
Author: | Bill Spight [ Sat Oct 03, 2020 3:15 pm ] |
Post subject: | Re: Thermography |
Gérard TAILLE wrote: Bill Spight wrote: Gérard TAILLE wrote: Oops the notation I used is not correct because it is not clear when I am reasonning one two boards and when I switch to one board. As a a consequence I see that what I wrote is quite unclear. Let me take some time to rephrase all my analysis before rediscussing. Using a second board is not necessary. It is only a convenience to indicate that the two positions are independent. In the past, discussions about difference games on a single board have run into difficulties because truly independent positions were not constructed. Using two boards makes the construction easy. In the board I used as illustration, for instance, I did not take the time to construct independently living groups, as I technically should have. I intended the positions to be understood as independent, given the prior discussion between us. Fortunately you understood my intent. Please do not get sidetracked by the question of two boards or one. Independence and the lack of a ko fight are the criteria. Here is my updated analysis using only one board: Let's consider two positions A et B surrounded by an environment E with "good" carateristics (independancy? non-ko? ...) Assume for example that, black to play, the optimum result of a game beginning from A+E is a win for black by say 10 points Assume also that, black to play, the optimum result of a game beginning from B+E is a win for black by say 7 points Let's call B' the mirror position of position B The amazing result of theory is the following: black to play will wins the game A+B' by at least 3 points !!! Let's us try to prove this "theorem": Let's call E' the mirror position of position E and put on the board the four areas A, B', E, E' Add on this board a very small area D made of one dame point. Because that cannot penalise white, you can always impose to white to avoid using the D region except maybe at the very last move of the game. Given the condition that E is a combinatorial game, you can exclude E + E' from the play without affecting the von Neumann game. And the dame will not affect the final score, either. So you can ignore it, as well. (Dame actually matter in CGT, but that's a nicety we can ignore when considering the von Neumann game. ) You can ignore E, E', and D in the von Neumann game, and doing so will simplify your task and your argument. Edit: I mean the von Neumann game A - B. OC, E may well affect the games A + E and B + E. |
Author: | Bill Spight [ Tue Oct 06, 2020 12:41 am ] |
Post subject: | Re: Thermography |
To return to the main theme For the region of play, here is the thermograph. Attachment: gerardTG.png [ 2.74 KiB | Viewed 18063 times ] Edit: The thermograph is in error. See corrected thermograph in #70. My apologies. I have to stop posting late at night. In an actual game, it is not too hard to find the count, -3, and the gain of the reverse sente, 4, as well as the bottom part of the right wall. The bottom part of the left wall, which reflects different strategies, is no so obvious, and might well be skipped in actual play. |
Author: | Bill Spight [ Tue Oct 06, 2020 4:51 am ] |
Post subject: | Re: Thermography |
A brief explanation of the thermograph The mast Above temperature 4 the mast rises vertically at count -3. Up to temperature 17½ it is colored blue, which indicates that Black can play the monkey jump with sente, threatening to kill the White group. Above that the mast is black, indicating that neither player will play locally. (Not that in actual play a go board will have anything like an ideal environment with a temperature that high. ) The right wall The right wall is red, indicating that White plays first. Between temperature 4 and 1 White to play plays the reverse sente. At or below temperature 1 Black continues with the hanetsugi, for a local score of -6. The left wall Above temperature 2 Black plays the sente in the diagram above. Between temperature 2 and temperature 1⅓ (Correction: temperature 1) Black continues and saves her two stones, for a local score of -1. Edit: Correction. This is orthodox play at or below temperature 1. The discussion below is incorrect, the basis for the incorrect thermograph. Between temperature 1⅓ and ⅚ White replies differently to the monkey jump. The local count is -2⅓, ⅔ point worse, on average, than the sacrifice above, but below temperature 1⅓ it is better than letting Black save her two stones, as above. After Black plays elsewhere White has the following sente. After the local temperature has dropped to ⅔. Between temperature ⅚ and ½ Black continues and saves her single stone. The count is -1½. At or below temperature ½ White continues, holding Black to 1 point in the corner. The local score is -2. |
Author: | Bill Spight [ Tue Oct 06, 2020 6:45 am ] |
Post subject: | Re: Thermography |
Now let's look at the thermograph for this position Attachment: gerardTG01.png [ 2.71 KiB | Viewed 18029 times ] Explanation of the thermograph The mast With the addition of the position at the bottom the count has shifted 2½ points to the left, to -½. The right wall Between temperature 4 and temperature 2½ White plays the reverse sente to a count of -4½. Between temperature 2½ and temperature 1 Black continues and captures the two White stones one the bottom side, for a count of -2. At or below temperature 1 White gains one point with the hane, . The local count is -3. The left wall Above temperature 2½ Black plays the monkey jump with sente. Between temperature 2½ and temperature 2 Black continues and takes the two White stones on the bottom side, for a local count of +2. Between temperature 2 and temperature 1 White will continue and capture two Black stones on the top side, for a count of 0. We expect and to be played later. At or below temperature 1 Black starts with the keima to keep sente and capture the two White stones on the bottom side. White then takes his sente with . The local score is +1. |
Author: | Gérard TAILLE [ Tue Oct 06, 2020 10:04 am ] |
Post subject: | Re: Thermography |
Bill Spight wrote: Between temperature 1⅓ and ⅚ White replies differently to the monkey jump. The local count is -2⅓, ⅔ point worse, on average, than the sacrifice above, but below temperature 1⅓ it is better than letting Black save her two stones, as above. After Black plays elsewhere White has the following sente. After the local temperature has dropped to ⅔. After some time understanding your analysis I have now some doubts about your left wall at the temperature: 5/6 <= temperature <= 1 At such temperature, instead of your sequence above, isn't better to choose the following one ? |
Author: | Bill Spight [ Tue Oct 06, 2020 11:31 am ] | ||
Post subject: | Re: Thermography | ||
Gérard TAILLE wrote: Bill Spight wrote: Between temperature 1⅓ and ⅚ White replies differently to the monkey jump. The local count is -2⅓, ⅔ point worse, on average, than the sacrifice above, but below temperature 1⅓ it is better than letting Black save her two stones, as above. After Black plays elsewhere White has the following sente. After the local temperature has dropped to ⅔. After some time understanding your analysis I have now some doubts about your left wall at the temperature: 5/6 <= temperature <= 1 At such temperature, instead of your sequence above, isn't better to choose the following one ? You are right. That was my original impression, which is why I suggested this sequence way back when. But when I went to draw the thermograph last night, I miscounted the next position as -2 instead of -1. So the thermograph is simpler.
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Author: | Gérard TAILLE [ Tue Oct 06, 2020 12:50 pm ] |
Post subject: | Re: Thermography |
I am not sure the thermograph is simplier Bill, My view is the following: if 1⅓ <= temperature <= 1 then black plays: but if 1 >= temperature >= ⅚ then black plays: In your new thermograph I believe you didn't take into account the first diagram above. |
Author: | Bill Spight [ Tue Oct 06, 2020 1:38 pm ] |
Post subject: | Re: Thermography |
Gérard TAILLE wrote: I am not sure the thermograph is simplier Bill, My view is the following: if 1⅓ <= temperature <= 1 then black plays: but if 1 >= temperature >= ⅚ then black plays: In your new thermograph I believe you didn't take into account the first diagram above. Since both sequences started from the same position and each sequence has an even number of alternating plays, we can compare them with a difference game. Black first wins by 1 pt. connects the ko for jigo. If is at 2, at 1 makes a mirror position and jigo. |
Author: | Gérard TAILLE [ Tue Oct 06, 2020 1:50 pm ] |
Post subject: | Re: Thermography |
Bill Spight wrote: Gérard TAILLE wrote: I am not sure the thermograph is simplier Bill, My view is the following: if 1⅓ <= temperature <= 1 then black plays: but if 1 >= temperature >= ⅚ then black plays: In your new thermograph I believe you didn't take into account the first diagram above. Since both sequences started from the same position and each sequence has an even number of alternating plays, we can compare them with a difference game. Black first wins by 1 pt. Jigo. If is at 2, at 1 makes a mirror position and jigo. It seems you don't see my point: if 1⅓ <= temperature <= 1 then black plays: and not |
Author: | Bill Spight [ Tue Oct 06, 2020 2:42 pm ] |
Post subject: | Re: Thermography |
Gérard TAILLE wrote: Bill Spight wrote: Gérard TAILLE wrote: I am not sure the thermograph is simplier Bill, My view is the following: if 1⅓ <= temperature <= 1 then black plays: but if 1 >= temperature >= ⅚ then black plays: In your new thermograph I believe you didn't take into account the first diagram above. Since both sequences started from the same position and each sequence has an even number of alternating plays, we can compare them with a difference game. Black first wins by 1 pt. Jigo. If is at 2, at 1 makes a mirror position and jigo. It seems you don't see my point: if 1⅓ <= temperature <= 1 then black plays: and not raises the local temperature to 2, as I recall, and gets a local score of -1 in sente (gote for Black). In this diagram gets a local score of -2 in gote (sente for Black). In this diagram White gets a count of -2⅓ in gote, which is worse for Black than either other diagram. What is the scaffold for as the extension? White decides how to reply, so it is this: min(-2, -1-t). Thus it is a vertical line below temperature 1, and a line inclined upwards to the right at 45° above temperature 1. These are the lines of the left wall of the corrected thermograph. What is the scaffold for as the jump? Between temperature 1⅓ and temperature ⅚ it is a vertical line at -2⅓, which is worse for Black than both -2 and -1-t, except at temperature 1⅓, where the two scaffolds touch. |
Author: | Bill Spight [ Tue Oct 06, 2020 9:12 pm ] |
Post subject: | Re: Thermography |
Now how about the thermograph for this position? Attachment: gerardTG04.png [ 3.13 KiB | Viewed 17770 times ] Edit: Corrected thermograph. |
Author: | Bill Spight [ Wed Oct 07, 2020 9:28 am ] |
Post subject: | Re: Thermography |
How about this one? Attachment: gerardTG00.png [ 2.69 KiB | Viewed 17924 times ] At this point, the top and bottom are strictly miai, simple gote that gain 2 points. Each player gains 2 points for net 0 gain. Thus the straight vertical line at a count of -1 down to temperature 1. At or below temperature 1, however, Black plays the keima to keep sente at the cost of 1 point on the top, but then is able to gain 2 points on the bottom, for a net gain of 1 point. |
Author: | Gérard TAILLE [ Wed Oct 07, 2020 2:30 pm ] |
Post subject: | Re: Thermography |
It is not that easy but at least I believe I undertood your thermographs in your last posts. BTW I continue to fail finding an environment in which kosumi is better than both keima and monkey jump. It seems that if this environment exists then after if black should play in the environment and depending on white answer, black chooses "a" or "b" accordingly (but I am not completly sure of that fact!) |
Author: | Gérard TAILLE [ Wed Oct 07, 2020 2:39 pm ] |
Post subject: | Re: Thermography |
Concerning the building of the left wall in the position above, is it true that beginning with is correct (but not the only solution) at all temperatures? |
Author: | Bill Spight [ Wed Oct 07, 2020 3:31 pm ] |
Post subject: | Re: Thermography |
Gérard TAILLE wrote: It is not that easy but at least I believe I undertood your thermographs in your last posts. BTW I continue to fail finding an environment in which kosumi is better than both keima and monkey jump. Yeah, me too. Not that I have tried hard. It appears that for the keima and the kosumi to be in the running, the best follow-up to the monkey jump needs to be in the environment. Then it seems like keima and the kosumi come into play only below temperature 1. We can prove stuff about play at that level, so maybe there is a proof that the kosumi cannot be dominant in non-ko environments. |
Author: | Bill Spight [ Wed Oct 07, 2020 5:42 pm ] |
Post subject: | Re: Thermography |
Gérard TAILLE wrote: Concerning the building of the left wall in the position above, is it true that beginning with is correct (but not the only solution) at all temperatures? You surely need to work out the scaffold for it. Edit: Anyway, above temperature 1 the play goes like this. This leaves a gote at temperature 2. The local count is -3. Between temperature 2 and temperature 1 Black continues, saving her stones. The local score is -1. |
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