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 Post subject: Carpenter's Square Endgame Evaluation
Post #1 Posted: Mon Oct 21, 2019 10:52 pm 
Tengen

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I evaluate the following carpenter's square as a local endgame on the marked locale. I apply the modern endgame theory explained in [14].

Click Here To Show Diagram Code
[go]$$B Carpenter's Square
$$------------------
$$. . . C C C C C C|
$$. . X . X W C C C|
$$. . . . X W C C C|
$$. . . . X W W W C|
$$. . . . X X X X C|
$$. . . . . . . . .|
$$. . . . . . . X .|
$$. . . . . . . . .|[/go]


For Black's start, I presume this sequence:

Click Here To Show Diagram Code
[go]$$B Black's Sequence
$$------------------
$$. . . . . 4 9 a b|
$$. . X . X O 3 1 2|
$$. . . . X O . 8 6|
$$. . . . X O O O 5|
$$. . . . X X X X 7|
$$. . . . . . . . .|
$$. . . . . . . X .|
$$. . . . . . . . .|[/go]


Furthermore, I assume this sequence and the studied variations to be dominating. Further study should verify this. If a different ko variation should be dominating, the values might have to be corrected slightly. White starts on the 2-2, of course.


The most important conclusions are as follows:


Initial position:

Count = 4 2/3

Move value = 11 2/3

Type = gote

Length of sequence worth playing successively = 1


In practice, it can often be correct to play the first five moves successively because their gains are at least 10 2/3 and therefore similar to the initial move value. The gains of the 6th and especially 7th moves are much smaller though: 5 2/3 and 1 2/3.


Moves with move value 9 2/3 (as in the created ko):

Moves 8 to 11.

In particular, it would be a mistake to derive the wrong initial values from the sente follower after move 10 as the count 2 2/3 and move value 9 2/3, as done in the book Yose Size List.



Black's alternating sequence

Code:
after move   count     move   gain      move value  type    length of successive sequence(s)

0            4 2/3     1      11 2/3    11 2/3      gote    1
1            16 1/3    2      10 2/3    5 2/3       gote    5
2            5 2/3     3      10 2/3    10 2/3      gote    3
3            16 1/3    4      11 11/12  5 2/3       gote    3
4            4 5/12    5      11 11/12  7 11/12     gote    1
5            16 1/3    6      5 2/3     5 2/3       gote    1
6            10 2/3    7      1 2/3     1 2/3       sente   Black's 5 White's 4
7            12 1/3    8      9 2/3     9 2/3       sente   4
8            2 2/3     9      9 2/3     9 2/3       gote    3
9            12 1/3    10     9 2/3     9 2/3       sente   2
10           2 2/3     11     9 2/3     9 2/3       ko      Black's 2 White's 1
11           12 1/3                     9 2/3       ko      Black's 1 White's 2




Copy and save the following SGF file, best viewed with GoWrite:




(;SZ[19]CA[UTF-8]GM[1]FF[4]ST[2]AP[GOWrite:3.0.10]AB[mb][oe][ob][pe][qe][re][oc][od][rg]PM[2]FG[259:]C[Each just stated value is a count.

The locale is marked.

M is the move value of the currently studied hypothesis and position.

Gb1, Gb2,... are the gains of move 1, 2,... of Black's alternating sequence of the currently studied hypothesis and position.

Gw1, Gw2,... are the gains of move 1, 2,... of White's alternating sequence of the currently studied hypothesis and position.

So far, we assume, but do not verify, that Black's alternating sequence and its variations shown are dominating.

Refuted Hypotheses

Black's 7/9/11-move sequence

gote move value M = (12 1/3 - (-7)) / 2 = (19 1/3) / 2 = 9 2/3

M > Gb6
9 2/3 > 1 2/3

Refuted Hypotheses

Black's 8/10-move sequence

sente move value M = 2 2/3 - (-7) = 9 2/3

M > Gb6
9 2/3 > 1 2/3

Refuted Hypothesis

Black's 6-move sequence

sente move value M = 10 2/3 - (-7) = 17 2/3

M > Gb6
17 2/3 > 1 2/3

Refuted Hypotheses

Black's 3/5-move sequence

gote move value M = (16 1/3 - (-7)) / 2 = (23 1/3) / 2 = 11 2/3

M > Gb2
11 2/3 > 10 2/3

Refuted Hypothesis

Black's 4-move sequence

sente move value M = 4 5/12 - (-7) = 11 5/12

M > Gb2
11 5/12 > 10 2/3

Refuted Hypothesis

Black's 2-move sequence

sente move value M = 5 2/3 - (-7) = 12 2/3

M > Gb2
12 2/3 > 10 2/3

Confirmed Hypothesis

gote count = (16 1/3 + (-7)) / 2 = (9 1/3) / 2 = 4 2/3

gote move value M = (16 1/3 - (-7)) / 2 = (23 1/3) / 2 = 11 2/3

Gb1 = 11 2/3

Gw1 = 11 2/3

M <= Gb1
11 2/3 <= 11 2/3

M <= Gw1
11 2/3 <= 11 2/3
]PW[ ]SQ[rd][sd][se][na][oa][pa][qa][ra][sa][pb][qb][rb][sb][pc][qc][rc][sc][pd][qd]AW[rd][pc][pb][pd][qd]PB[ ]GN[ ]
(
;B[rb]
;FG[259:]C[16 1/3

position after move 1

refuted hypotheses

White's 6/8/10-move sequence

sente move value M = 9 2/3

M > Gw6
9 2/3 > 1 2/3

refuted hypotheses

White's 7/9-move sequence

gote move value M = (22 - 2 2/3) / 2 = 9 2/3

M > Gw6
9 2/3 > 1 2/3

confirmed hypothesis

White's 5-move sequence

gote count = (22 + 10 2/3) / 2 = (32 2/3) / 2 = 16 1/3

gote move value M = (22 - 10 2/3) / 2 = (11 1/3) / 2 = 5 2/3

Gb1 = 5 2/3

Gw1 = 10 2/3

M <= Gb1
5 2/3 <= 5 2/3

M <= Gw1, Gw2, Gw3, Gw4, Gw5
5 2/3 <= 10 2/3, 10 2/3, 11 11/12, 11 11/12, 5 2/3]PM[2]
(
;W[sb]
;FG[259:]C[5 2/3

position after move 2

refuted hypotheses

Black's 5/7/9-move sequence and White's 1/3-move sequence

gote move value M = (12 1/3 - (-5)) / 2 = (17 1/3) / 2 = 8 2/3

M > Gb5
8 2/3 > 1 2/3

refuted hypotheses

Black's 5/7/9-move sequence and White's 2-move sequence

sente move value M = 12 1/3 - 0 = 12 1/3

M > Gb5
12 1/3 > 1 2/3

refuted hypotheses

Black's 6/8-move sequence and White's 1/3-move sequence

sente move value M = 2 2/3 - (-5) = 7 2/3

M > Gb5
7 2/3 > 1 2/3

refuted hypotheses

Black's 4-move sequence and White's 1/3-move sequence

sente move value M = 10 2/3 - (-5) = 15 2/3

M > Gb4
15 2/3 > 5 2/3

refuted hypothesis

Black's 1/3-move sequence and White's 3-move sequence

gote move value M = (16 1/3 - (-5)) / 2 = (21 1/3) / 2 = 10 2/3

M > Gw3
10 2/3 > 5

refuted hypothesis

Black's 3-move sequence and White's 2-move sequence

sente move value M = 16 1/3 - 0 = 16 1/3

M > Gw2
16 1/3 > 5

confirmed hypothesis

Black's 3-move sequence and White's 1-move sequence

gote count = (16 1/3 + (-5)) / 2 = (11 1/3) / 2 = 5 2/3

gote move value M = (16 1/3 - (-5)) / 2 = (21 1/3) / 2 = 10 2/3

Gb1 = 10 2/3

Gw1 = 10 2/3

M <= Gb1, Gb2, Gb3
10 2/3 <= 10 2/3, 11 11/12, 11 11/12

M <= Gw1
10 2/3 <= 10 2/3]PM[2]
(
;B[qb]
;FG[259:]C[16 1/3

position after move 3

refuted hypotheses

White's 4/6/8-move sequence

sente move value M = 22 - 12 1/3 = 9 2/3

M > Gw4
9 2/3 > 1 2/3

refuted hypotheses

White's 5/7-move sequence

gote move value M = (22 - 2 2/3) / 2 = (19 1/3) / 2 = 9 2/3

M > Gw4
9 2/3 > 1 2/3

confirmed hypothesis

White's 3-move sequence

gote count = (22 + 10 2/3) / 2 = (32 2/3) / 2 = 16 1/3

gote move value M = (22 - 10 2/3) / 2 = (11 1/3) / 2 = 5 2/3

Gb1 = 5 2/3

Gw1 = 16 1/3 - 4 5/12 = 11 11/12

M <= Gb1
5 2/3 <= 5 2/3

M <= Gw1, Gw2, Gw3
5 2/3 <= 11 11/12, 11 11/12, 5 2/3]PM[2]
(
;C[ ]W[pa]
;FG[259:]C[4 5/12

position after move 4

refuted hypotheses

Black's 3/5/7-move sequence and White's 4/2-move sequence

sente move value M = 12 1/3 - 0 = 12 1/3

M > Gb2
12 1/3 > 1 2/3

refuted hypotheses

Black's 3/5/7-move sequence and White's 3-move sequence

gote move value M = (12 1/3 - (-5)) / 2 = (17 1/3) / 2 = 8 2/3

M > Gb2
8 2/3 > 1 2/3

refuted hypotheses

Black's 3/5/7-move sequence and White's 1-move sequence

gote move value M = (12 1/3 - (-3 1/2)) / 2 = (15 5/6) / 2 = 7 11/12

M > Gb2
7 11/12 > 1 2/3

refuted hypotheses

Black's 6/4-move sequence and White's 3-move sequence

sente move value M = 2 2/3 - (-5) = 7 2/3

M > Gb2
7 2/3 > 1 2/3

refuted hypotheses

Black's 6/4-move sequence and White's 1-move sequence

sente move value M = 2 2/3 - (-3 1/2) = 6 1/6

M > Gb2
6 1/6 > 1 2/3

refuted hypothesis

Black's 2-move sequence and White's 3-move sequence

sente move value M = 10 1/2 - (-5) = 15 1/2

M > Gb2
15 1/2 > 1 2/3

refuted hypothesis

Black's 2-move sequence and White's 1-move sequence

gote move value M = 10 1/2 - (-3 1/2) = 14

M > Gb2
14 > 1 2/3

refuted hypotheses

Black's 1-move sequence and White's 4/2-move sequence

sente move value M = 12 1/3 - 0 = 12 1/3

M > Gw2
12 1/3 > 3 1/2

refuted hypothesis

Black's 1-move sequence and White's 3-move sequence

gote move value M = (12 1/3 - (-5)) / 2 = (17 1/3) / 2 = 8 2/3

M > Gw2
8 2/3 > 3 1/2

confirmed hypothesis

Black's 1-move sequence and White's 1-move sequence

gote count = (12 1/3 + (-3 1/2)) / 2 = (8 5/6) / 2 = 4 5/12

gote move value M = (12 1/3 - (-3 1/2)) / 2 = (15 5/6) / 2 = 7 11/12

Gb1 = 7 11/12

Gw1 = 7 11/12

M <= Gb1
7 11/12 <= 7 11/12

M <= Gw1
7 11/12 <= 7 11/12
]PM[2]
(
;B[sd]
;FG[259:]C[16 1/3

position after move 5

Hypothesis 1

White's long sente with White's 6-move sequence

sente count = 12 1/3

sente move value M = 22 - 12 1/3 = 9 2/3

Gb1 = 9 2/3

Gw1 = 1 2/3

refuting Hypothesis 1\:

M > Gw1
9 2/3 > 1 2/3

Hypothesis 2

White's long gote with White's 5-move sequence

gote count = (22 + 2 2/3) / 2 = (24 2/3) / 2 = 12 1/3

gote move value M = (22 - 2 2/3) / 2 = (19 1/3) / 2 = 9 2/3

Gb1 = 9 2/3

Gw1 = 1 2/3

refuting Hypothesis 2\:

M > Gw1
9 2/3 > 1 2/3

Hypothesis 3

White's long sente with White's 4-move sequence

sente count = 12 1/3

sente move value M = 22 - 12 1/3 = 9 2/3

Gb1 = 9 2/3

Gw1 = 1 2/3

refuting Hypothesis 3\:

M > Gw1
9 2/3 > 1 2/3

Hypothesis 4

White's long gote with White's 3-move sequence

gote count = (22 + 2 2/3) / 2 = (24 2/3) / 2 = 12 1/3

gote move value M = (22 - 2 2/3) / 2 = (19 1/3) / 2 = 9 2/3

Gb1 = 9 2/3

Gw1 = 1 2/3

refuting Hypothesis 4\:

M > Gw1
9 2/3 > 1 2/3

Hypothesis 5

White's local sente with White's 2-move sequence

sente count = 12 1/3

sente move value M = 22 - 12 1/3 = 9 2/3

Gb1 = 9 2/3

Gw1 = 1 2/3

refuting Hypothesis 5\:

M > Gw1
9 2/3 > 1 2/3

Hypothesis 6

White's local gote with White's 1-move sequence

gote count = (22 + 10 2/3) / 2 = (32 2/3) / 2 = 16 1/3

gote move value M = (22 - 10 2/3) / 2 = (11 1/3) / 2 = 5 2/3

Gb1 = 5 2/3

Gw1 = 5 2/3

confirming Hypothesis 6\:

M <= Gb1
5 2/3 <= 5 2/3

M <= Gw1
5 2/3 <= 5 2/3]PM[2]
(
;W[sc]
;FG[259:]C[position after move 6

Hypothesis 1

White's long sente with Black's 5-move sequence and White's 4-move sequence

sente count = 10 2/3

sente move value M = 12 1/3 - 10 2/3 = 1 2/3

Gb1 = 1 2/3

Gw1 = 9 2/3

confirming Hypothesis 1\:

M <= Gb1, Gb2, Gb3, Gb4, Gb5
1 2/3 <= 1 2/3, 9 2/3, 9 2/3, 9 2/3, 9 2/3

M <= Gw1, Gw2, Gw3, Gw4
9 2/3 <= 9 2/3, 9 2/3, 9 2/3, 9 2/3]PM[2]
(
;B[se]
;FG[259:]C[position after move 7

Hypothesis 1

White's long sente

sente count = 12 1/3

sente move value M = 22 - 12 1/3 = 9 2/3

Gb1 = 9 2/3

Gw1 = 9 2/3

confirming Hypothesis 1\:

M <= Gb1
9 2/3 <= 9 2/3

M <= Gw1, Gw2, Gw3, Gw4
9 2/3 <= 9 2/3, 9 2/3, 9 2/3, 9 2/3]PM[2]
(
;W[rc]
;FG[259:]C[position after move 8

Hypothesis 1

Black's long gote

gote count = (12 1/3 + (-7)) / 2 = (5 1/3) / 2 = 2 2/3

gote move value M = (12 1/3 - (-7)) / 2 = (19 1/3) / 2 = 9 2/3

Gb1 = 9 2/3

Gw1 = 9 2/3

confirming Hypothesis 1\:

M <= Gb1, Gb2, Gb3
9 2/3 <= 9 2/3, 9 2/3, 9 2/3

M <= Gw1
9 2/3 <= 9 2/3]PM[2]
(
;B[qa]
;FG[259:]C[position after move 9

Hypothesis 1

White's local sente

sente count = 12 1/3

sente move value M = 22 - 12 1/3 = 9 2/3

Gb1 = 9 2/3

Gw1 = 9 2/3

confirming Hypothesis 1\:

M <= Gb1
9 2/3 <= 9 2/3

M <= Gw1, Gw2
9 2/3 <= 9 2/3, 9 2/3]PM[2]
(
;W[ra]
;FG[259:]C[position after move 10

ordinary ko

move value
(22 - (-7)) / 3 = 29/3 = 9 2/3

count
-7 + 1 * 9 2/3 = 2 2/3]PM[2]
(
;B[sa]
;FG[259:]PM[2]MN[1]C[position after move 11

ordinary ko

move value
(22 - (-7)) / 3 = 29/3 = 9 2/3

count
22 - 1 * 9 2/3 = 12 1/3]
(
;W[ra];B[tt];C[-7]W[qc]
)
(
;FG[259:]PM[2];B[ra]C[22]
)

)
(
;FG[259:]MN[1]PM[2]
(
;B[sa];W[tt];B[ra]C[22]
)
(
;FG[259:]PM[2];C[-7]W[qc]
)

)

)
(
;FG[259:]MN[1]PM[2]
(
;B[ra]C[22]
)
(
;FG[259:]PM[2];C[2 2/3]W[ra]
;B[sa]C[12 1/3

Gw2 = 9 2/3]
)

)

)
(
;FG[259:]MN[1]PM[2]
(
;B[qa]C[12 1/3]
;C[2 2/3

Gb2 = 9 2/3]W[ra]
;B[sa]C[12 1/3

Gb3 = 9 2/3]
)
(
;FG[259:]PM[2];C[-7]W[ra]
)

)

)
(
;FG[259:]MN[1]PM[2]
(
;B[rc]C[22]
)
(
;FG[259:]PM[2];C[2 2/3]W[rc]
;B[qa]C[12 1/3

Gw2 = 9 2/3]
;C[2 2/3

Gw3 = 9 2/3]W[ra]
;B[sa]C[12 1/3

Gw4 = 9 2/3]
)

)

)
(
;FG[259:]MN[1]PM[2]
(
;B[se]C[12 1/3]
;C[2 2/3

Gb2 = 9 2/3]W[rc]
;B[qa]C[12 1/3

Gb3 = 9 2/3]
;C[2 2/3

Gb4 = 9 2/3]W[ra]
;B[sa]C[12 1/3

Gb5 = 9 2/3]
)
(
;FG[259:]PM[2]
;C[Hypothesis 1

Black's long gote

gote count = (10 2/3 + (-8 2/3)) / 2 = 2/2 = 1

gote move value M = (10 2/3 - (-8 2/3)) / 2 = (19 1/3) / 2 = 9 2/3

Gb2 = 11 1/3

Gw2 = 9 2/3

confirming Hypothesis 1\:

M <= Gb2, Gb3, Gb4
9 2/3 <= 9 2/3, 9 2/3, 9 2/3

M <= Gw2
9 2/3 <= 9 2/3]W[ra]
(
;B[qa]C[10 2/3

Gw2 = 9 2/3]
;C[best because W avoids approach ko

2 2/3 + (-1 2/3) = 1

Gw3 = 9 2/3]W[rc]
;B[sa]C[10 2/3

Gw4 = 9 2/3

After dissolution of the ko, the count of the remaining endgame with W's privilege on the right side, with a locale temporarily expanded by one intersection, is\: -2/3

Shrinking the expanded locale means modifying the count by -1.

Accounted for the initial locale, the the remaining endgame has the adjusted count -1 2/3.

In the initial locale, the count is 12 1/3.

In the initial locale, the total count including the remaining local endgame is 12 1/3 + (-1 2/3) = 10 2/3.]
)
(
;FG[259:]MN[2]PM[2]
;C[simply speaking, this is the best move

-7 + (-1 2/3) = -8 2/3]W[rc]
)

)

)

)
(
;FG[259:]MN[1]PM[2]
(
;B[sc]C[22]
)
(
;FG[259:]C[2 2/3

Gw3 = 9 2/3]PM[2]
;C[10 2/3]W[sc]
;B[se]C[12 1/3

Gw2 = 1 2/3]
;C[2 2/3

Gw3 = 9 2/3]W[rc]
;B[qa]C[12 1/3

Gw4 = 9 2/3]
;C[2 2/3

Gw5 = 9 2/3]W[ra]
;B[sa]C[12 1/3

Gw6 = 9 2/3]
)

)

)
(
;FG[259:]MN[1]PM[2]
(
;B[sd]C[12 1/3]
;C[10 2/3

Gb2 = 1 2/3]W[sc]
;B[se]C[12 1/3

Gb3 = 1 2/3]
;C[2 2/3

Gb4 = 9 2/3]W[rc]
;B[qa]C[12 1/3

Gb5 = 9 2/3]
;C[2 2/3

Gb6 = 9 2/3]W[ra]
;B[sa]C[12 1/3

Gb7 = 9 2/3]
)
(
;FG[259:]PM[2]
;C[-3 1/2

best choice because possible seki is better than the kos

In locale, white follower's count -8.

In expanded locale, white follower's count -7.

In locale with accounting remaining endgame of expanded locale to the locale, white follower's count -7.

Hypothesis 1

Black's long gote

gote count = -3 1/2

gote move value M = 3 1/2

Gb2 = 3 1/2
Gb3 = 12
Gb4 = 5

Gw2 = 3 1/2

confirming Hypothesis 1\:

M <= Gb2, Gb3, Gb4
3 1/2 <= 3 1/2, 12, 5

M <= Gw2
3 1/2 <= 3 1/2]W[rc]
;B[ra]C[best

sente count 0

Gw2 = 3 1/2]
;C[sente seki is best

with expanded locale\:

gote count -5

Gw3 = 12]W[qa]
;B[sd]C[0

Gw4 = 5]
)

)

)
(
;FG[259:]MN[1]PM[2]
(
;B[pa]C[22]
)
(
;FG[259:]PM[2];C[4 5/12]W[pa]
;B[sd]C[16 1/3

Gw2 = 11 11/12]
;C[10 2/3

Gw3 = 5 2/3]W[sc]
;B[se]C[12 1/3

Gw4 = 1 2/3]
;C[2 2/3

Gw5 = 9 2/3]W[rc]
;B[qa]C[12 1/3

Gw6 = 9 2/3]
;C[2 2/3

Gw7 = 9 2/3]W[ra]
;B[sa]C[12 1/3

Gw8 = 9 2/3]
)

)

)
(
;FG[259:]MN[1]PM[2]
;B[qb]C[16 1/3]
;C[4 5/12

Gb2 = 11 11/12]W[pa]
;B[sd]C[16 1/3

Gb3 = 11 11/12]
;C[10 2/3

Gb4 = 5 2/3]W[sc]
;B[se]C[12 1/3

Gb5 = 1 2/3]
;C[2 2/3

Gb6 = 9 2/3]W[rc]
;B[qa]C[12 1/3

Gb7 = 9 2/3]
;C[2 2/3

Gb8 = 9 2/3]W[ra]
;B[sa]C[12 1/3

Gb9 = 9 2/3]
)

(
;FG[259:]MN[1]PM[2]
;C[-5

because

Black next sente result -5

White next result -6]W[rc]
;B[sd]C[0

because Black next sente result 0

Gw2 = 5]
;C[-5

Gw3 = 5]W[ra]
)

)
(
;FG[259:]MN[1]PM[2]
;B[sd]C[22]
)

(
;FG[259:]MN[1]PM[2]
;C[5 2/3]W[sb]
;B[qb]C[16 1/3

Gw2 = 10 2/3]
;C[4 5/12

Gw3 = 11 11/12]W[pa]
;B[sd]C[16 1/3

Gw4 = 11 11/12]
;C[10 2/3

Gw5 = 5 2/3]W[sc]
;B[se]C[12 1/3

Gw6 = 1 2/3]
;C[2 2/3

Gw7 = 9 2/3]W[rc]
;B[qa]C[12 1/3

Gw8 = 9 2/3]
;C[2 2/3

Gw9 = 9 2/3]W[ra]
;B[sa]C[12 1/3

Gw10 = 9 2/3]
)

)
(
;FG[259:]PM[2];C[-7]W[rb]
)

)


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 Post subject: Re: Carpenter's Square Endgame Evaluation
Post #2 Posted: Mon Oct 21, 2019 11:57 pm 
Honinbo

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Many thanks, Robert! :D

You may need some SGF tags in that post. :)

I did a fairly thorough analysis of the Carpenter's Square in the early 2000s. If I didn't trust you I might try to dig it up now. (Java problems on my machine make that difficult at the moment.) Sometime this year I may have something to add to the discussion.

Adelante!

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 Post subject: Re: Carpenter's Square Endgame Evaluation
Post #3 Posted: Tue Oct 22, 2019 12:16 am 
Tengen

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SGF tags do not help because my file is more complicated on its SGF-level than supported here.

Your later additions are welcome, also because it is so easy to make accidental mistakes, such as overlooking another but relevant variation.

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 Post subject: Re: Carpenter's Square Endgame Evaluation
Post #4 Posted: Tue Oct 22, 2019 3:55 am 
Honinbo

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Here is an SGF with some Carpenter's Square variations. For evaluation you need to add more, OC. :)


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At some point, doesn't thinking have to go on?

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This post by Bill Spight was liked by: Gomoto
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 Post subject: Re: Carpenter's Square Endgame Evaluation
Post #5 Posted: Tue Oct 22, 2019 5:26 am 
Lives in sente

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Gomoto, how do you evaluate the Carpenter"s Square?

I try to avoid it, I lost once a tournament game because misevaluating it.


I have only found one pro game with carpenter square in my database of recent games (It is a game of Yeonwoo by the way! Perhaps something for her channel.):


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