Re: This 'n' that
Posted: Thu Apr 18, 2019 9:05 am
Pente, anyone?jlt wrote:Tic-Tac-Toe is very hard for a go player, because you always try to capture opponent's stones.
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This 'n' that
Page 38 of 71
Re: This 'n' that
Posted: Tue Apr 30, 2019 1:15 am
In his new book, Rational Endgame ( viewtopic.php?f=17&t=16567 ), Antti Tormanen does without the terms, sente and gote. (Edit: Correction. Tormanen uses sente but not gote or reverse sente.) Those hoary terms are hoary because they are useful, but, like most words, they also have accrued different meanings, and that can cause confusion. Can we really do without them?
Well, we can. I am reminded of when I first began exploring the endgame. I realized that a theory of the endgame could be built using only final scores. OC, the bots do that, but their theory is based upon errors. Can we do that assuming correct play? Sure. Here is a simple example.
Play takes place only inside the corridors. All outside stones are alive. Should Black play at "a", or at "b"?
OC, this is easy enough to read out.
If Black plays at "a" White plays at "b". White wins by 1 pt.
If Black plays at "b" White plays at "a", and then Black connects to get the last play. Black wins by 1 pt.
So where is the theory? Using CGT notation we can write position "a" as {7 | -3} (ignoring dame). And we can write position "b" as { 4 | -3 || -8}. The theory for a position with these two types of plays is to compare particular score differences for each position. For "a" it is the difference between 7 (after one Black play) and -3 (after one White play), which is 10. For "b" it is the difference between 4 (after two Black plays) and -8 (after one White play), which is 12. 12 > 10, so Black should play at "b". We do not have to worry about whether "b" is sente or not. That does not matter. Suppose that "b" was {8 | -3 || -4}. It would obviously be sente, and since {8 | -3} is hotter than {7 | -3} we should play "b". But that comparison is superfluous, since the rule tells us to play "b", anyway. To read the position out we would have to take {8 | -3} into account, but the rule tells us what to play without having to read the position out. That's what the theory gets us.
Obviously, the theory so far is about comparing these specific types of plays. We can avoid reading the position out, but there will be many rules to memorize. However, these rules will tell us what correct play is.
What about the standard theory? "a" is obviously gote, with a count of 2; each play gains 5 pts. "b" is less obviously gote. It has a count of -3¾; each play gains 4¼ pts. The position after Black plays has a count of +½, and each play gains 3½ pts. Standard theory tells us that we should normally play the move that gains the most. In this case that would be wrong. Standard theory also tells us that getting the last play before a drop in temperature could provide an exception to playing the hottest move. The drop of 3½ pts. is a big clue. But standard theory does not guarantee making the correct play.
Well, we can. I am reminded of when I first began exploring the endgame. I realized that a theory of the endgame could be built using only final scores. OC, the bots do that, but their theory is based upon errors. Can we do that assuming correct play? Sure. Here is a simple example.
Play takes place only inside the corridors. All outside stones are alive. Should Black play at "a", or at "b"?
OC, this is easy enough to read out.
If Black plays at "a" White plays at "b". White wins by 1 pt.
If Black plays at "b" White plays at "a", and then Black connects to get the last play. Black wins by 1 pt.
So where is the theory? Using CGT notation we can write position "a" as {7 | -3} (ignoring dame). And we can write position "b" as { 4 | -3 || -8}. The theory for a position with these two types of plays is to compare particular score differences for each position. For "a" it is the difference between 7 (after one Black play) and -3 (after one White play), which is 10. For "b" it is the difference between 4 (after two Black plays) and -8 (after one White play), which is 12. 12 > 10, so Black should play at "b". We do not have to worry about whether "b" is sente or not. That does not matter. Suppose that "b" was {8 | -3 || -4}. It would obviously be sente, and since {8 | -3} is hotter than {7 | -3} we should play "b". But that comparison is superfluous, since the rule tells us to play "b", anyway. To read the position out we would have to take {8 | -3} into account, but the rule tells us what to play without having to read the position out. That's what the theory gets us.
Obviously, the theory so far is about comparing these specific types of plays. We can avoid reading the position out, but there will be many rules to memorize. However, these rules will tell us what correct play is.
What about the standard theory? "a" is obviously gote, with a count of 2; each play gains 5 pts. "b" is less obviously gote. It has a count of -3¾; each play gains 4¼ pts. The position after Black plays has a count of +½, and each play gains 3½ pts. Standard theory tells us that we should normally play the move that gains the most. In this case that would be wrong. Standard theory also tells us that getting the last play before a drop in temperature could provide an exception to playing the hottest move. The drop of 3½ pts. is a big clue. But standard theory does not guarantee making the correct play.
Re: This 'n' that
Posted: Tue Apr 30, 2019 2:18 am
Bill, would you mind explaining a few CGT basics underneath this post of yours?
1) And we can write position "b" as { 4 | -3 || -8}.
-- where does the "-3" come from?
2)
The theory for a position with these two types of plays is to compare particular score differences for each position. For "a" it is the difference between 7 (after one Black play) and -3 (after one White play), which is 10. For "b" it is the difference between 4 (after two Black plays) and -8 (after one White play), which is 12. 12 > 10, so Black should play at "b".
-- Why does it not matter here that the "4" is reached after two Black plays?
3)
We do not have to worry about whether "b" is sente or not. That does not matter. Suppose that "b" was {8 | -3 || -4}. It would obviously be sente,
-- Why does it make sense to suppose that "b" was {8 | -3 || -4}?
-- And why is that then obviously sente?
1) And we can write position "b" as { 4 | -3 || -8}.
-- where does the "-3" come from?
2)
The theory for a position with these two types of plays is to compare particular score differences for each position. For "a" it is the difference between 7 (after one Black play) and -3 (after one White play), which is 10. For "b" it is the difference between 4 (after two Black plays) and -8 (after one White play), which is 12. 12 > 10, so Black should play at "b".
-- Why does it not matter here that the "4" is reached after two Black plays?
3)
We do not have to worry about whether "b" is sente or not. That does not matter. Suppose that "b" was {8 | -3 || -4}. It would obviously be sente,
-- Why does it make sense to suppose that "b" was {8 | -3 || -4}?
-- And why is that then obviously sente?
Re: This 'n' that
Posted: Tue Apr 30, 2019 2:40 am
After Black plays and White replies, the local score is 4 pts. for Black minus 7 pts. for White, or -3. In { 4 | -3 || -8} 4 is the result after two Black plays, -3 is the result after one Black play and one White reply, and -8 is the result after one White play.Knotwilg wrote:Bill, would you mind explaining a few CGT basics underneath this post of yours?
1) And we can write position "b" as { 4 | -3 || -8}.
-- where does the "-3" come from?
Oh, it does matter. The theory assumes that if Black plays first in "b" White will reply in "a", and then Black will make a second play in "b". If we rely upon the theory instead of reading the play out, we do not have to check whether White will reply in "b" instead of "a".2)
The theory for a position with these two types of plays is to compare particular score differences for each position. For "a" it is the difference between 7 (after one Black play) and -3 (after one White play), which is 10. For "b" it is the difference between 4 (after two Black plays) and -8 (after one White play), which is 12. 12 > 10, so Black should play at "b".
-- Why does it not matter here that the "4" is reached after two Black plays?
To show that the theory gives the same answer in that case.3)
We do not have to worry about whether "b" is sente or not. That does not matter. Suppose that "b" was {8 | -3 || -4}. It would obviously be sente,
-- Why does it make sense to suppose that "b" was {8 | -3 || -4}?
Because a play in {8 | -3} is bigger than a play in {7 | -3}.-- And why is that then obviously sente?
Re: This 'n' that
Posted: Tue Apr 30, 2019 3:04 am
Now let's switch sides.
If White plays in "b" Black replies in "a" and wins by 1 pt.
If White plays in "b" Black replies in "b", then White gets the last play in "b" and wins by 1 pt.
We may write "a" as {8 | -3} and "b" as {4 | 2 || -7}. Since White plays first the relevant score difference in "b" is 2 - ( -7) = 9. That is 2 pts. less than the score difference in "a", so White plays in "a".
Edit: I think it best to continue this on this page.
In this example "a" is a gote with a count of 2½ and each move gains 5½. "b" is also gote with a count of -2 and each play gains 5. The standard theory helps White to make the right choice. However, the comparison is not with 3 - (-7) = 10, where 3 is the count after Black plays, but with 2 - (-7) = 9, where 2 is the score after Black plays and White replies. This theory treats {{ A | B} | C}, where A > B > C, as sente when White is to play and as gote when Black is to play (when the only other play is a single gote). Obviously, with this theory we cannot call that position sente or gote.
If White plays in "b" Black replies in "a" and wins by 1 pt.
If White plays in "b" Black replies in "b", then White gets the last play in "b" and wins by 1 pt.
We may write "a" as {8 | -3} and "b" as {4 | 2 || -7}. Since White plays first the relevant score difference in "b" is 2 - ( -7) = 9. That is 2 pts. less than the score difference in "a", so White plays in "a".
Edit: I think it best to continue this on this page.
In this example "a" is a gote with a count of 2½ and each move gains 5½. "b" is also gote with a count of -2 and each play gains 5. The standard theory helps White to make the right choice. However, the comparison is not with 3 - (-7) = 10, where 3 is the count after Black plays, but with 2 - (-7) = 9, where 2 is the score after Black plays and White replies. This theory treats {{ A | B} | C}, where A > B > C, as sente when White is to play and as gote when Black is to play (when the only other play is a single gote). Obviously, with this theory we cannot call that position sente or gote.
Re: This 'n' that
Posted: Tue Apr 30, 2019 3:50 am
I understand everything you write, except the "suppose that "b" was {8 | -3 || -4}"
The CGT means Black plays two moves and gets 8, Black plays White replies -3, White plays -4. Where in the diagram are these moves?
Or is {8 | -3 || -4} some kind of reversal of { 4 | -3 || -8}, from White's perspective? Then shouldn't -3 be 3?
The CGT means Black plays two moves and gets 8, Black plays White replies -3, White plays -4. Where in the diagram are these moves?
Or is {8 | -3 || -4} some kind of reversal of { 4 | -3 || -8}, from White's perspective? Then shouldn't -3 be 3?
Re: This 'n' that
Posted: Tue Apr 30, 2019 6:44 am
For better or worse, he does not do without the term sente; according to my PDF search the word is found on 40 of the book's 126 pages. I do not see gote, though.Bill Spight wrote:In his new book, Rational Endgame ( viewtopic.php?f=17&t=16567 ), Antti Tormanen does without the terms, sente and gote.
Re: This 'n' that
Posted: Tue Apr 30, 2019 7:13 am
Thanks for the correction. Sorry, I misremembered his and my email exchange. It is reverse sente that he leaves out. If he uses sente, then he can simply regard non-sente plays and sequences as gain making without labeling them further. And if he labels some positions as sente, then the others are simply unlabeled non-sente positions.dfan wrote:For better or worse, he does not do without the term sente; according to my PDF search the word is found on 40 of the book's 126 pages. I do not see gote, though.Bill Spight wrote:In his new book, Rational Endgame ( viewtopic.php?f=17&t=16567 ), Antti Tormanen does without the terms, sente and gote.
Edit: I wonder how he defines sente, however. Even CGT, which uses (or used to use) the terms, equitable and excitable, regards equitable positions as more basic. Without gote positions and plays you do not have sente positions and plays.
Re: This 'n' that
Posted: Tue Apr 30, 2019 7:29 am
Sorry for not being clear.Knotwilg wrote:I understand everything you write, except the "suppose that "b" was {8 | -3 || -4}"
The CGT means Black plays two moves and gets 8, Black plays White replies -3, White plays -4. Where in the diagram are these moves?
Or is {8 | -3 || -4} some kind of reversal of { 4 | -3 || -8}, from White's perspective? Then shouldn't -3 be 3?
{8 | -3 || -4} is the same as {{8 | -3} | -4}. White to play moves to -4; Black to play moves to {8 | -3}, which, I trust, makes sense.
If you reverse the colors of the stones, {4 | -3 || -8} becomes { 8 || 3 | -4}. The ||s indicate non-scored positions with followers to the left for Black options and to the right for White options. { | -3} represents a position where White can move to a positions worth -3, while Black has no move. We don't really need to represent such positions. One possibility would be a completely surrounded White group with 4 one point eyes. White to play can fill one of the eyes and Black has no play.
Re: This 'n' that
Posted: Tue Apr 30, 2019 8:01 am
That I understandBill Spight wrote: {8 | -3 || -4} is the same as {{8 | -3} | -4}.
It's that bit, which, unfortunately, doesn't. Let me show the diagram for "b" again.Bill Spight wrote: White to play moves to -4; Black to play moves to {8 | -3}, which, I trust, makes sense.
A White play here gives White 8 points, so it "moves" to -8. A Black play moves to 4 | (4-7)=-3
But we had that already.
I just don't get what "suppose b is {8 | -3 || -4}" means in relation to diagram "b". I see no White move leading to 4 points, nor a Black move leading to a {8|-3} postion. I must be blind
Re: This 'n' that
Posted: Tue Apr 30, 2019 8:16 am
Sorry. I meant, suppose that b were a different position with those values, not the one in the diagram. The comparison would still be 12 pts. vs. 10 pts.Knotwilg wrote:That I understandBill Spight wrote: {8 | -3 || -4} is the same as {{8 | -3} | -4}.
It's that bit, which, unfortunately, doesn't. Let me show the diagram for "b" again.Bill Spight wrote: White to play moves to -4; Black to play moves to {8 | -3}, which, I trust, makes sense.
A White play here gives White 8 points, so it "moves" to -8. A Black play moves to 4 | (4-7)=-3
But we had that already.
I just don't get what "suppose b is {8 | -3 || -4}" means in relation to diagram "b". I see no White move leading to 4 points, nor a Black move leading to a {8|-3} postion. I must be blind
Re: This 'n' that
Posted: Thu May 02, 2019 2:09 am
Here is another small problem with a position we do not call reverse sente.
No komi. All play and scoring is only in corridors. The framing stones are alive.
Enjoy.
No komi. All play and scoring is only in corridors. The framing stones are alive.
Enjoy.
Re: This 'n' that
Posted: Thu May 02, 2019 4:27 am
I know how to play and win, but not based on CGT
Re: This 'n' that
Posted: Thu May 02, 2019 8:50 am
The little theory I am illustrating could be considered part of CGT. These corridors are combinatorial games, and it is a theory.Knotwilg wrote:I know how to play and win, but not based on CGT
I suppose that your final figures are the result of reading out the board with alternating play.Re: This 'n' that
Posted: Thu May 02, 2019 10:58 am
New to this, but trying out the formula you gave: