Life In 19x19

I'd like to combine a few hobby horses here, applying modern endgame theory to a game of Shuei and evaluate it with AI. Myself I've been raised with deiri counting so please bear with me.

The following diagram comes from a no komi game of Shuei (W) against Tamura Yasuhisa, whom I found to be no other than the later Honinbo Shusai, when looking up in SL.

Click Here To Show Diagram Code

[go]$$ Position at move 162
$$ ---------------------------------------
$$ | . . . . . . X X . X . . . . . . . . . |
$$ | . . . . O O O X X . X O . . f X . . . |
$$ | . . . O . O X . X X O O . . O X . . . |
$$ | . . . , O . b . . O . . O . O , X . . |
$$ | . . X . . . . O . O O O O . . X . . . |
$$ | . . . O . . . . O X X X . . . . X X X |
$$ | . . . . . . c . X . . . . . . O O O X |
$$ | . . O . O . . . . . . X O O . . . . O |
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | . X O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |
$$ | . X . . X O X X O . . O . X O O O X g |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

The marked move is the last move played. Locally E is a natural answer but is it also the largest move? I'll try and evaluate moves A through F, plus the obviously small G for a particular reason, and invite you to join in and improve, especially if you can provide the miai values of the moves, but in general where your evaluation differs or just for the fun of exercising. Here we go.

I'll start with G Next A
B and C are related with each other, which likely makes them smaller individually in terms of follow-up and sort of miai.
Then the ko at D
Then the local answer at E Finally F, which is pretty straightforward.

Summary:

Knotwilg wrote:Then the ko at D

$$ Ko
$$ | . . O . O . . . . . . X O O . . . . O |
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X 3 O 1 O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | . X O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |

Click Here To Show Diagram Code

[go]$$ Ko
$$ | . . O . O . . . . . . X O O . . . . O |
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X 3 O 1 O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | . X O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |[/go]

Black's 5 points have a local tally of 3, so the gote value is 10/3

BTW, Elf's recommendation:

Click Here To Show Diagram Code

[go]$$W
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | . X O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |
$$ | . X . . X O X X O . . O . X O O O X 1 |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

You have set modern endgame theory.

Black 1 results in the local count B = R = 2.


Suppose a local gote:

Usually, White has the privilege ko capture, Black connects. The result is 0 local points of territory plus -1 point for the black prisoner stone plus the count 1/3 for the remaining white ko stone, in total, White 1 results in the local count W = 0 + (-1) + 1/3 = -2/3.

The initial tentative gote move value is Mg = (B - W) / 2 = (2 - (-2/3)) / 2 = (2 2/3) / 2 = 1 1/3.


Local position after White 1:

If Black continues, the local count is 1. If White continues, he executes his privilege (sente sequence) ko capture and Black connects, the local count is -2/3. The follow-up has the sente follow-up move value F = 1 - (-2/3) = 1 2/3. The increasing move values Mg < F <=> 1 1/3 < 1 2/3 indicate that the hypothesis of the initial local endgame being a local gote was wrong.


Hence the initial local endgame is a local sente:

White 1 is answered by Black 2 connecting for the resulting local count S = 1. The correct initial sente move value is Ms = R - S = 2 - 1 = 1.


2 EDITs.

RobertJasiek wrote:

$$W
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | . X O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |
$$ | . X . . X O X X O . . O . X O O O X 1 |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | . X O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |
$$ | . X . . X O X X O . . O . X O O O X 1 |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

You have set modern endgame theory.

Black 1 results in the local count B = 2.

White 1 is played in gote and, usually, has White's privilege ko capture, Black connects. The result is 0 local points of territory plus -1 point for the black prisoner stone plus the count 1/3 for the remaining white ko stone, in total, White 1 results in the the local count W = 0 + (-1) + 1/3 = -2/3.

The initial gote move value is (B - W) / 2 = (2 - (-2/3)) / 2 = (2 2/3) / 2 = 1 1/3.

EDIT

WAIT. Why is White 1 played in gote? Is it? Need to verify!

is a 1 point sente.

Bill Spight wrote::w1: is a 1 point sente.

Yes, could not edit as fast as you have replied. See my 2nd edit above:)

Be aware that there is a major back story to this game, part of which is that the result was probably fixed and Shuei deliberately made boundary play errors deliberately to achieve a certain result. See "Games of Shuei".

I'll try modern endgame theory on move A, applying the procedure I learnt from Robert's application on move G (appreciated!)

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | C C . O X . X O O X X . e . . , O . . |
$$ | C C . O X . O d O O . . . O . . . . . |
$$ | C O . O X X X O X O O . O . . . X . . |
$$ | 1 X O O X . O X X O X . X O O . . . . |
$$ | S O X X X X O O X X X . X X O . . O O |
$$ | S X . . X O X X O . . O . X O O O X g |
$$ | S X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

We'll start from this as reference move. The circled points are White's, the captured stone counts as 1 point. The squared points are neutral.
W = R = 6. The follow-up moves cancel out:

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O C O O X . O X X O X . X O O . . . . |
$$ | 3 O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X g |
$$ | 2 X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

White's follow-up gains another point.

Click Here To Show Diagram Code

[go]$$B
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O . O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X g |
$$ | C X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Black's follow-up gains a point for Black. (Black A is sente, as we know)

So we can assess the position as W = R = 6

Click Here To Show Diagram Code

[go]$$B
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | 6 8 . O X . X O O X X . e . . , O . . |
$$ | 5 4 . O X . O d O O . . . O . . . . . |
$$ | 3 O . O X X X O X O O . O . . . X . . |
$$ | 7 X O O X . O X X O X . X O O . . . . |
$$ | 1 O X X X X O O X X X . X X O . . O O |
$$ | . X . . X O X X O . . O . X O O O X g |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Assume local gote. Next Black executes this sente sequence. B = -4
Mg = (6-(-4)/2 = 5

Now look at the position after

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | 1 O . O X X X O X O O . O . . . X . . |
$$ | a X O O X . O X X O X . X O O . . . . |
$$ | X W X X X X O O X X X . X X O . . O O |
$$ | . X . . X O X X O . . O . X O O O X g |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

We now know that A is White's 1 point sente.
B = -4 in sente (captured stone plus two first line points)
W = 4 - 2 = 2 in gote (White saves 4 points of the original count, while Black captures a stone and makes 1 first line point)
F = (2 - (-4))/1 = 6

Since F=6 > Mg=5, the assumption that the original move is gote, is wrong and A is a 5 point Black sente. (Shuei seems to agree: he answered)

Thanks for verifying this exercise!

Click Here To Show Diagram Code

[go]$$B
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O . O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X g |
$$ | C X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

For now, just a random thought: you also need to assess if Black 1 is gote or sente.

And on F

Click Here To Show Diagram Code

[go]$$W
$$ ---------------------------------------
$$ | . . . . . . X X . X B W C C 5 3 4 . . |
$$ | . . . . O O O X X . X O C C 1 X 6 . . |
$$ | . . . O . O X . X X O O C C O X . . . |
$$ | . . . , O . b . . O . . O . O , X . . |
$$ | . . X . . . . O . O O O O . . X . . . |
$$ | . . . O . . . . O X X X . . . . X X X |[/go]

We assume the marked sente exchange. We take as the reference, assuming is sente. W = R = 6

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------------------
$$ | . . . . . . X X . X B W . . S C C . . |
$$ | . . . . O O O X X . X O T a 1 X C . . |
$$ | . . . O . O X . X X O O T T O X . . . |
$$ | . . . , O . b . . O . . O . O , X . . |
$$ | . . X . . . . O . O O O O . . X . . . |
$$ | . . . O . . . . O X X X . . . . X X X |[/go]

We asume local gote, making the 3 circled points. The follow-up at A is gote.
If Black gets it he makes an additional squared point with 50% probability.
f White gets it, she recovers the 3 triangled points, plus makes an extra point and destroys a Black one with 50% probability.

B = -3 + (-1/2+4)/2 = -5/4

Mg = (W-B)/2 = (6+5/4)/2 = 29/8 ~ 4-

We have already calculated F = (-1+3)/2 = 1; Mg > F so the assumption of local gote was correct.

Endgame move is thus a 4 point gote.

RobertJasiek wrote:

$$B
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O . O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X g |
$$ | C X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$B
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O . O O X . O X X O X . X O O . . . . |
$$ | a O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X g |
$$ | C X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

For now, just a random thought: you also need to assess if Black 1 is gote or sente.

Well, I can reuse the assessment of G for that purpose, no? You did that for me

John Fairbairn wrote:Be aware that there is a major back story to this game, part of which is that the result was probably fixed and Shuei deliberately made boundary play errors deliberately to achieve a certain result. See "Games of Shuei".

Having reviewed a number of pro games with the Elf annotation files, one thing that struck me about this game was the relative lack of definite errors by either player. Shuei may have played safe, and generated small errors that way, but it is not clear that we can call such plays errors.

OC, in an 8 dan vs. 3 dan game, simply playing Black is a woefully inadequate handicap. Elf identifies as an error which brought the game pretty close to par. Then was a definite error, and Black let the game slip away. The last definite error before the current position was , but Black may have been lost at that point, anyway. OC, Katago can adjust for the lack of komi.

Knotwilg, you can also reuse G to answer whether Black 1, which is one move esrlier(!!!), is gote or sente. The major effort is still to be done.

RobertJasiek wrote:Knotwilg, you can also reuse G to answer whether Black 1, which is one move esrlier(!!!), is gote or sente. The major effort is still to be done.

Sorry I don't understand. How is analyzing whether A in this diagram (not my original label A) is sente, any different from analyzing if G is sente, which you did, concluding that it is? The positions are equivalent.

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | C C . O X . X O O X X . e . . , O . . |
$$ | C C . O X . O d O O . . . O . . . . . |
$$ | C O . O X X X O X O O . O . . . X . . |
$$ | 1 B O O X . O X X O X . X O O . . . . |
$$ | 5 O X X X X O O X X X . X X O . . O O |
$$ | 4 X . . X O X X O . . O . X O O O X g |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

After , is ambiguous. It gains 1 point but then so does , to stay even. So we may assess the result as 7 points for White.

Click Here To Show Diagram Code

[go]$$B
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | C C . O X . X O O X X . e . . , O . . |
$$ | C C . O X . O d O O . . . O . . . . . |
$$ | 2 O . O X X X O X O O . O . . . X . . |
$$ | 4 X O O X . O X X O X . X O O . . . . |
$$ | 1 W X X X X O O X X X . X X O . . O O |
$$ | C X . . X O X X O . . O . X O O O X g |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

After , if White replies with , then later - connects is a sente sequence. So we can regard this result as net 2 points for White. Assuming is locally correct, we may regard as a 5 point sente.

Click Here To Show Diagram Code

[go]$$B :w2: elsewhere
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | 6 8 . O X . X O O X X . e . . , O . . |
$$ | 5 4 . O X . O d O O . . . O . . . . . |
$$ | 3 O . O X X X O X O O . O . . . X . . |
$$ | 7 X O O X . O X X O X . X O O . . . . |
$$ | 1 W X X X X O O X X X . X X O . . O O |
$$ | C X . . X O X X O . . O . X O O O X g |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

The standard assumption is that White cannot afford to make a ko with so this is the standard sente sequence. The result is 3 points for Black.

If the original position is gote, then the swing is between 3 points for Black and 7 points for White. The miai value of the gote is then 5 points. This is exactly the same as the result if the position is a Black sente. So this position is ambiguous between sente and gote, with a miai value of 5 points and a territorial estimate of 2 points for White.