Life In 19x19

Players are set for 20th Nongshim Cup.

Korea:Park Junghwan, Lee Sedol, Choi Cheolhan, Shin Minjoon, Ahn Kukhyun
China:Ke Jie, Shi Yue, Gu Zhihao, Fan Tingyu, Dang Yifei
Japan:Iyama Yuuta, Kyo Kagan, Ichiriki Ryo, Katsuya Motoki, Toramaru Shibano

Schedule,

!st round - 10/16, 17, 18, 19
2nd round - 11/18
3rd round - 2/19

10/16 1st game: Ahn Kukhyun vs Toramaru Shibano

Two years ago, I wrote a program to calculate winning probabilities. I resurrected it this year:

Since I don't know how the teams will order their players, I assume they put stronger players last, excepting Shibano, who has been announced as the first for Japan. Assuming my program works (verifying it's correct for large teams is a pain), the odds are:

Japan wins: 6.8%
Korea wins: 29.8%
China wins: 63.4%
China has a noticably stronger team, but also the advantage of starting last, which is big. Japan's team members are all among their best players, and it makes sense to give up a little bit to give younger players international competition. While China's team is not its absolute best, they have four top ten players. The Korean team differs a lot from the strongest team you could hand-pick, but it is fun to see Choi's name up there.

Game 1 so far. Elf says Ahn (white) did well to move 50, getting up to 90% but the ko trade was great for black who was at 90% himself by move 80 and not much change to now. Let's see what happens to that big white dragon.

10/16 1st game: Toramaru Shibano defeated Ahn Kukhyun by resign.
10/17 2nd game: Toramaru Shibano vs Fan Tingyu

Korea:Park Junghwan, Lee Sedol, Choi Cheolhan, Shin Minjoon, Ahn Kukhyun
China:Ke Jie, Shi Yue, Gu Zhihao, Fan Tingyu, Dang Yifei
Japan:Iyama Yuuta, Kyo Kagan, Ichiriki Ryo, Katsuya Motoki, Toramaru Shibano

Bold case - remaining players

Hyperpape, you should rerun after each game. It would be interesting to see.

What happens to those rates if one team put its strongest player first?

oren: I'll try to do so.

macelee: I'm not sure. I was thinking about that earlier today, and I'll try it out.

Updated numbers. Note that the "previous" figures don't match my earlier post because I moved Fan Tingyu to first position.

Japan: 9.5% (previously 6.6%)
Korea: 24.8% (29.7)
China: 65.6% (63.7)

Rotating Ke Jie to be first gives:

Japan 6.8%
Korea: 30.2%
China: 63.0%

Rotating Park Junghwan to first gives:

Japan 6.6%
Korea: 26.4%
China: 67%

Rotating Iyama to first gives:

Japan 6.3%,
Korea: 28.8%
China: 64.8%

If Shibano had lost:

Japan 4.3%
China: 62.1%
Korea: 33.7%

Note that moving the number 1 players to first gives them more chances to be 'randomly' knocked out by a weaker opponent.

I think that's it, but I think it's only true if there's more than two teams. With two teams, it appears to me that you'll get the same results regardless.

I started to write a long explanation of why this was intuitive, but halfway through I decided I didn't understand or believe it. My intuition for probability sucks. =\

I think you get the same result only if the team are equals. See this simple exemple :

Team AB against A'B'

A win 55% of the time against A', and 65% against B'
B win 40% of the time against A', and 50% against B'

That means that A is the strongest player, followed by A', and B and B' are equals


Case 1 : Suppose B' play first, then A'


If A play first :

A win both matchs : 0.65*0.55 = 35.75%
A win first match, lose second against A', and B win the last game : 0.65*0.45*0.4 = 11.7%
A lose first match, and B win both matches : 0.35*0.4*0.5 = 7%

Team AB win against B'A' with probability 54.45%


If B play first :

B win both games : 0.5*0.4 = 20%
B win first match, lose second, A win last : 0.5*0.6*0.55 = 16.5%
B lose first, A win both : 0.5*0.65*0.55 = 17.875%

Team BA win against B'A' with probability 54.375%


Case 2 : if A' play first :

If A play first :

A win both matchs : 0.55*0.65 = 35.75%
A win first match, lose second against B', and B win the last game : 0.55*0.35*0.5 = 9.625%
A lose first match, and B win both matches : 0.45*0.4*0.5 = 9%

Team AB win against A'B' with probability 54.375%


If B play first :

B win both games : 0.4*0.5 = 20%
B win first match, lose second, A win last : 0.4*0.5*0.65 = 13%
B lose first, A win both : 0.5*0.65*0.55 = 21.45%

Team BA win against A'B' with probability 54.45%



So, in this situation, the ' team wants to have A' in the same position as A, while the no' team want to have A in the same position as B'

Shibano resigned in middlegame (153 not played), he played an unusual move (p2) in the lower right joseki which lead to him feeling the need to invade and extricate his group from the lower side; Elf preferred to just d7 turn and d3 in sente (they threaten to invade the lower side with attitude because you can counterattack white's lower left if white ignores) and give it to white. Elf wanted c8 and d9 because then when the game trade happens (Elf sometimes struggles to see white's f5 tesuji but recognises it as very good when played) black can e10 hane to grow the left white's taking white's liberties. Shibano was down to 5% when he started the centre fight at m7.



I thought this was a particularly interesting shape lesson that both Elf and LZ agreed Shibano got wrong: when white haned at 1 black played the classic good shape net of 2.

Click Here To Show Diagram Code

[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . 2 . X X . . |
$$ | . . X . . . . . . . . . . . O X O X . |
$$ | . . X O . . . . . . . 1 X X X O O . . |
$$ | . X O O . . . . . . . . O O X O . X . |
$$ | . X X O . . . . . , . . O X O X X . . |
$$ | . X O . . O . . . . . . O X O O O O . |
$$ | . . . . . . . . . . . . X . X . . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ ---------------------------------------[/go]

Instead he should have empty triangled. White 3 is sente now (just as it is with the good shape net, but that also gives white choice of n8 sente as Fan used well in the game), which we normally think of as painful in this shape but a lot of that's because usually the next push at a is also sente (it's not with the net, so net only gives them one forcing move) but here it's not sente yet (if white pushes black connects at b and is attacking the corner) so white has to capture and then black invades the lower side. During that fight it white pushes at a black can consider ignoring and allowing the painful hane because he can capture the 4 white stones in reply (and white's hane still has a cut, and white lost a little endgame in the corner). Also black could make the thick turn at a (a bit slack) and because 2 filled a white liberty moves like black c are more powerful in the future.

Click Here To Show Diagram Code

[go]$$Wc Bots say better
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . a 4 . . X X . . |
$$ | . . X . . . . . . . . 3 2 . O X O X . |
$$ | . . X O . . . . . c . 1 X X X O O . . |
$$ | . X O O . . . . . . . . O O X O . X . |
$$ | . X X O . . . . . , . . O X O X X . . |
$$ | . X O . . O . . . . . . O X O O O O . |
$$ | . . . . . . . . . . . . X b X . . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ ---------------------------------------[/go]

Compare with the net if white takes the m7 sente (aji keshi, n8 might be better) and black plays a gote (less need for black to play a gote here as less reverse sente to it, white's push doesn't have the sente hane follow-up):

Click Here To Show Diagram Code

[go]$$Wc Liberty at n7
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . 6 4 2 . X X . . |
$$ | . . X . . . . . . . . 3 . . O X O X . |
$$ | . . X O . . . . . . . 1 X X X O O . . |
$$ | . X O O . . . . . . . . O O X O . X . |
$$ | . X X O . . . . . , . . O . O X X . . |
$$ | . X O . . O . . . . . . O . O O O O . |
$$ | . . . . . . . . . . . . X 5 X . . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ ---------------------------------------[/go]

Click Here To Show Diagram Code

[go]$$Wc No liberty at n7
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . 6 4 . . X X . . |
$$ | . . X . . . . . . . . 3 2 . O X O X . |
$$ | . . X O . . . . . . . 1 X X X O O . . |
$$ | . X O O . . . . . . . . O O X O . X . |
$$ | . X X O . . . . . , . . O . O X X . . |
$$ | . X O . . O . . . . . . O . O O O O . |
$$ | . . . . . . . . . . . . X 5 X . . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ ---------------------------------------[/go]

10/17 2nd game: Fan Tingyu defeated Toramaru Shibano by resugb,
10/18 3rd game: Fan Tingyu vs Shin Minjoon

Korea:Park Junghwan, Lee Sedol, Choi Cheolhan, Shin Minjoon, Ahn Kukhyun
China:Ke Jie, Shi Yue, Gu Zhihao, Fan Tingyu, Dang Yifei
Japan:Iyama Yuuta, Kyo Kagan, Ichiriki Ryo, Katsuya Motoki, Toramaru Shibano

Bold case - remaining players

I don't see how the tesuji at F5 works after Black plays atari on the outside, can anyone explain?