This 'n' that

moha · Post by **moha** » Fri Sep 29, 2017 4:27 pm

I think what confused me is that you were talking about the whole position complex, while I'm only about the E15 area... But now I think that even if that area is double sente, that still not necessarily means that the best line always starts there (in other, different positions).

Bill Spight · Post by **Bill Spight** » Fri Sep 29, 2017 4:55 pm

Well, if we are only talking about the E-15 region, things are even more complex. Each player has both a sente option and a gote option.

What do we call it? An ambiguous double sente/gote?

Click Here To Show Diagram Code: [go]$$Wc White 1 pt. sente $$ ---------------------- $$ | . . . . . . . X O . . $$ | . . . . . . X X O . . $$ | . X . X . . X O . O . $$ | O X O X 2 X X O . , . $$ | X X X X 1 O X O . . . $$ | O X O 6 X O X O . . . $$ | O X 4 5 X O X O . . . $$ | O O O O O 3 O . . . . $$ | . . . . . . . . . . . $$ | . . . , . . . . . , .[/go]

Click Here To Show Diagram Code: [go]$$Wc White 1 pt. gote $$ ---------------------- $$ | . . . . . . . X O . . $$ | . . . . . . X X O . . $$ | . X . X . . X O . O . $$ | O X O X . X X O . , . $$ | X X X X 2 O X O . . . $$ | O X O . X O X O . . . $$ | O X 1 . X O X O . . . $$ | O O O O O 3 O . . . . $$ | . . . . . . . . . . . $$ | . . . , . . . . . , .[/go]

Click Here To Show Diagram Code: [go]$$Bc Black 1 pt. sente $$ ---------------------- $$ | . . . . . . . X O . . $$ | . . . . . . X X O . . $$ | . X . X . . X O . O . $$ | O X O X . X X O . , . $$ | X X X X 1 O X O . . . $$ | O X O . X O X O . . . $$ | O X . . X O X O . . . $$ | O O O O O 2 O . . . . $$ | . . . . . . . . . . . $$ | . . . , . . . . . , .[/go]

Click Here To Show Diagram Code: [go]$$Bc Black 1 pt. gote $$ ---------------------- $$ | . . . . . . . X O . . $$ | . . . . . . X X O . . $$ | . X . X . . X O . O . $$ | O X O X . X X O . , . $$ | X X X X 1 O X O . . . $$ | O X O 5 X O X O . . . $$ | O X 3 4 X O X O . . . $$ | O O O O O 2 O . . . . $$ | . . . . . . . . . . . $$ | . . . , . . . . . , .[/go]

moha · Post by **moha** » Sat Sep 30, 2017 6:20 am

moha wrote:I think what confused me is that you were talking about the whole position complex, while I'm only about the E15 area... But now I think that even if that area is double sente, that still not necessarily means that the best line always starts there (in other, different positions).

Actually this may also be shown right here. Suppose B to play, and he takes top gote first. Then W's best line seems to also ignore the double sente at E15 area, and take the gote there instead.

So taking double sente CAN be a mistake (even at roughly correct temperatures, when the opponent actually responds, though this seems a special case here since W's sente forces B to take a valuable gote as well - BTW is white's sente in E15 area really a +1? Not a 0?)

Bill Spight · Post by **Bill Spight** » Sat Sep 30, 2017 8:09 am

moha wrote:
moha wrote:I think what confused me is that you were talking about the whole position complex, while I'm only about the E15 area... But now I think that even if that area is double sente, that still not necessarily means that the best line always starts there (in other, different positions).
Actually this may also be shown right here. Suppose B to play, and he takes top gote first. Then W's best line seems to also ignore the double sente at E15 area, and take the gote there instead.

You mean this sequence, right?

Click Here To Show Diagram Code: [go]$$Bc Black takes gote first $$ ---------------------- $$ | . . . . . . . 3 1 2 . $$ | . . . . . . X X O . . $$ | . X . X . . X O . O . $$ | O X O X . X X O . , . $$ | X X X X . O X O . . . $$ | O X O . X O X O . . . $$ | O X 4 . X O X O . . . $$ | O O O O O . O . . . . $$ | . . . . . . . . . . . $$ | . . . , . . . . . , .[/go]

OC, now both locally and globally Black needs to take her sente, nothing ambiguous about it.

Click Here To Show Diagram Code: [go]$$Bc Black 5 takes double sente $$ ---------------------- $$ | . . . . . . . 3 1 2 . $$ | . . . . . . X X O . . $$ | . X . X . . X O . O . $$ | O X O X . X X O . , . $$ | X X X X 5 O X O . . . $$ | O X O . X O X O . . . $$ | O X 4 . X O X O . . . $$ | O O O O O 6 O . . . . $$ | . . . . . . . . . . . $$ | . . . , . . . . . , .[/go]

So taking double sente CAN be a mistake

Absolutely.

(even at roughly correct temperatures, when the opponent actually responds, though this seems a special case here since W's sente forces B to take a valuable gote as well)

Well, once Black has taken the hane-and-connect, what is left is doubly ambiguous between sente and gote, so it's a very special case.

BTW is white's sente in E15 area really a +1? Not a 0?)

The size of the sente is determined by how much the reverse sente gains, and the reverse sente gains 1 pt.

If Black took her sente option instead, it would gain 0 pts. but that's normal. Sente gains nothing.

moha · Post by **moha** » Sat Sep 30, 2017 9:06 am

Bill Spight wrote:
moha wrote:BTW is white's sente in E15 area really a +1? Not a 0?)
The size of the sente is determined by how much the reverse sente gains, and the reverse sente gains 1 pt. If Black took her sente option instead, it would gain 0 pts.

Hm. I guess you mean B's reverse sente sequence that gains 1pt in E15 area is C13 D13 D14 (since starting with atari would not really seem reverse sente, but a sente followed by an optional gote)?

Bill Spight · Post by **Bill Spight** » Sat Sep 30, 2017 4:06 pm

moha wrote:
Bill Spight wrote:
moha wrote:BTW is white's sente in E15 area really a +1? Not a 0?)
The size of the sente is determined by how much the reverse sente gains, and the reverse sente gains 1 pt. If Black took her sente option instead, it would gain 0 pts.
Hm. I guess you mean B's reverse sente sequence that gains 1pt in E15 area is C13 D13 D14 (since starting with atari would not really seem reverse sente, but a sente followed by an optional gote)?

These complicated positions strain the standard classifications. Indeed, sente followed by an optional gote is a kind of reverse sente in this position. Each player has the choice of playing sente or gote, and that is how Black makes the choice: sente and stop, or sente and continue.

I have more to say about this position, but let me make this observation. I have to use a game tree, because I don't know of any such actual position on the go board, but one probably exists.

In the tree / represents a move by Black and \ represents a move by White. Numbers are scores from Black's point of view. BIG stands for some big number or other.

Code: Select all

                             A
                            / \ \     (Black has one possible move, White has two)                                 /   \ \_____ -1
                          /     \
                         B       C
                        / \     / \
                      BIG  0   0  -BIG

This may look like a kind of ambiguous double sente, but, unless there is a ko fight, the White move from A to C is not good. How come? Because the result for White is a local score of 0. A is better for White than that because White has the option of playing from A to a local score of -1, while the best that Black can do is to play to B with sente, for a local score of 0. A can be classified as a Black sente.

Code: Select all

                             A
                            / \ \     
                           /   \ \_____ -1
                          /     \
                         B       C
                        / \     / \
                      BIG  D   0  -BIG
                          / \
                         1  -1

A is now like the position around E-15. The count of D is 0, but now the White move from A to C is a possibility. Why? Because Black has the move from D to a score of 1, to act as a reverse sente for C. Without that Black move, the White move from A to C has no value, outside of a ko fight.

Bill Spight · Post by **Bill Spight** » Sat Sep 30, 2017 7:08 pm

Easy tsumego by yours truly

All my problems are easy, eh?

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

Grin Weepa · Post by **Grin Weepa** » Sun Oct 01, 2017 10:15 am

Not sure if I'm right about this,
just thought I'd give it a go.

Bill Spight · Post by **Bill Spight** » Sun Oct 01, 2017 10:31 am

Grin Weepa wrote:Not sure if I'm right about this,
just thought I'd give it a go.
A18 then after capture, B19 then D19 makes seki if black does not like the ko?

Close.

Grin Weepa · Post by **Grin Weepa** » Sun Oct 01, 2017 11:15 am

Close but no cigar. It was a fun problem

moha · Post by **moha** » Sun Oct 01, 2017 11:53 am

Bill Spight wrote:unless there is a ko fight, the White move from A to C is not good. ... A can be classified as a Black sente.

This seems to imply one follows the other. But even if C is not better than A in points (as far as EV is comparable to a collapsed result), W may still be interested (even outside ko fights), if it leaves better parity on board (parity of last big gote moves etc.). Or are these dynamics out of scope here?

Bill Spight · Post by **Bill Spight** » Sun Oct 01, 2017 12:03 pm

Endgame problem

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

As I said, endgame and tsumego go together well.

Post by **Joaz Banbeck** » Sun Oct 01, 2017 12:43 pm

Bill Spight · Post by **Bill Spight** » Sun Oct 01, 2017 12:50 pm

Back to the game tree for E-15

Code: Select all

                             A
                            / \ \     
                           /   \ \_____ -1
                          /     \
                         B       C
                        / \     / \
                      BIG  D   0  -BIG
                          / \
                         1  -1

Let's simplify it by removing White's sente option.

Code: Select all

What is this? Another ambiguous sente/gote?

Not really, even though Black could play A'-> B -> D as a ko threat. Kos aside, A' = D. Maybe that is obvious to you, but let me show that.

Now, with no ko fight, games add and subtract. So A' = D means A' - D = 0. How do you subtract D? You form the negative of D and add it. So how do you form the negative of D? In go it's easy, you just reverse the color of the stones. For a game you flip the tree and reverse the signs of the scores.

Let's do that for D.

First, flip the tree:

Code: Select all

                           D'   
                          / \
                        -1   1

Second, reverse the signs:

Code: Select all

                           D''   
                          / \
                         1  -1

So the negative of D is D! How about that?

Now to find out if A' - D = 0. That is so if the result with best play, after each player has made the same number of moves, is 0, no matter who plays first. It is also the case with a seki, or standoff, where neither player wants to play or is able to play. For instance, D' above = 0. Black prefers a score of 0 to -1, and White prefers 0 to 1 (for Black), so neither play wants to play.

Let's look at A' - D = A' + D.

Code: Select all

                           A'   +     D
                          / \        / \
                         B  -1      1  -1
                        / \     
                      BIG  D   
                          / \
                         1  -1

First, suppose that Black plays first.
1) Let Black play from A' to B; then White will reply from B to D. As we now know, D + D = 0.
2) Let Black play from D to 1. Then White will play from A' to -1. 1 - 1 = 0.

Next, suppose that White plays first.
1) Let White play from A' to -1. Then Black will play from D to 1. 1 - 1 = 0.
2) Let White play from D to -1. Then Black will play A' -> B -> D -> 1. 1 - 1 = 0.

So A' = D. It's just a gote, except in ko fights.

In summary, in A, D is necessary to retain the option, C, by providing a possible reverse sente for it; and C is necessary to keep A from reducing to D.

Bill Spight · Post by **Bill Spight** » Sun Oct 01, 2017 12:55 pm

moha wrote:
Bill Spight wrote:unless there is a ko fight, the White move from A to C is not good. ... A can be classified as a Black sente.
This seems to imply one follows the other. But even if C is not better than A in points (as far as EV is comparable to a collapsed result), W may still be interested (even outside ko fights), if it leaves better parity on board (parity of last big gote moves etc.). Or are these dynamics out of scope here?

Why would White want to remove his option to play reverse sente? Maybe Black will play the sente and it will come to the same thing, but for White to play sente (except possibly in case of a ko fight) simply does Black's job for her. It is never better than doing nothing.

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