Some technical details of the Mlily Cup final

macelee · #1

Several days have passed since the Mlily Cup final. There are still lots of confusions around the area-scoring-specific technique Ke Jie used to beat Lee Sedol. I read a lot of analysis and a number of quite interesting variations. I will post a few variations in this thread.

To summarise first. Ke Jie used a technique to play dame moves first before connecting the last half-point ko. Because dame moves matter in area scoring, he managed to gain extra points needed to secure his victory. A numbers of sources, including commentaries made by several professional players, suggest that Lee Sedol's W250 was a final mistake and Lee could win by playing elsewhere. This series of post is to validate that argument.

macelee · #2

Click Here To Show Diagram Code: [go]$$W $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | . O X X O O X . X . . . . X X X . . . | $$ | 7 O O O . O X X X , X X X O O X . X . | $$ | 5 X O O . O O X . . O X . X O O X X O | $$ | 6 X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | 1 O X X . . X X X O . . . . . . . O O | $$ | . O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O . X X X O O . . . . . 3 | $$ | . . . O . X . X O . O O O O . . O O 2 | $$ | . . X O X X X O . O O X O X O O O X 4 | $$ | . . O O X O O . O . X X O X X O X X . | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | . O . X . . O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

This is the real game. :w1:

(W250) is normally a sensible move. It is based on a popular end-game strategy based on the concept of miai points - because :b2:

and

are of exactly the same value (2 points in gote), white can play :w1:

first (1 point in reverse sente) - even if :w1:

is significantly smaller white won't lost anything. However, as can be seen, :b2:

created many ko threats there and eventually white lost the game because he did not have enough ko threats. That's probably why in many commentaries :w1:

was considered to be the losing move.

macelee · #3

Click Here To Show Diagram Code: [go]$$W $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | 7 O X X O O X . X . . . . X X X . . . | $$ | 6 O O O . O X X X , X X X O O X . X . | $$ | 8 X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | 4 O X X . . X X X O . . . . . . . O O | $$ | 5 O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O . X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O . . O O 3 | $$ | . . X O X X X O . O O X O X O O O X 1 | $$ | . . O O X O O . O . X X O X X O X X 2 | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | . O . X . . O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Several pro players suggested that white can win this game by playing :w1:

instead. If :w1:

,

and

are the only remaining endgame moves, one can see black has one more point than in the real game. But as seen in real game, the special area-scoring-technique is worth more than 1 point.

The question now is: can white really win by playing this way? I will post more tomorrow.

RobertJasiek · #4

Thank you for throwing more light on the endgame. Here is more related discussion:
viewtopic.php?p=197285#p197285
viewtopic.php?f=13&t=12012&start=80

Bill Spight · #5

macelee wrote:

Click Here To Show Diagram Code: [go]$$W $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | 7 O X X O O X . X . . . . X X X . . . | $$ | 6 O O O . O X X X , X X X O O X . X . | $$ | 8 X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | 4 O X X . . X X X O . . . . . . . O O | $$ | 5 O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O . X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O . . O O 3 | $$ | . . X O X X X O . O O X O X O O O X 1 | $$ | . . O O X O O . O . X X O X X O X X 2 | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | . O . X . . O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Several pro players suggested that white can win this game by playing :w1:

instead. If :w1:

,

and

are the only remaining endgame moves, one can see black has one more point than in the real game. But as seen in real game, the special area-scoring-technique is worth more than 1 point.

The question now is: can white really win by playing this way? I will post more tomorrow.

Except that now Black does not have to win the ko after eliminating the dame, winning the ko will do. To win the game, White will have to win the ko.

Edit: Comment unhidden after macelee's later posts.

macelee · #6

Because the game involves ko fights, it is better to first examine the ko threat situations. This happens to be quite complex. I tried my best but my analysis may contain errors.

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X b . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O a . . . . . . . | $$ | . . . O O X O . X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O . . O O O | $$ | . . X O X X X O . O O X O X O O O X O | $$ | . . O O X O O . O . X X O X X O X X X | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | . O . X . . O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Some ko threats are clearly seen, such as 'a' for black and 'b' for white (assuming the nearby ko is filled). Others in the game are very hard to spot.

How many ko threats are there in the upper-left area inside black territory?

How many ko threats are there in the left side inside white territory?

So it appears that the two sets of ko threats hidden in the above diagrams counteract each other. So for future analysis we can ignore both sets.

Finally, assuming the game involves in such as way that 'c' isn't an eye, then black has an hidden ko threat. Can you see that? Every ko threat matters!

Click Here To Show Diagram Code: [go]$$B $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X . . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X 2 . . . . , O . . | $$ | . X . . O O X X O O O 1 . . . . . . . | $$ | . . . O O X O X X X X O O . . . . . . | $$ | . . . O . X . X O X O O O O 3 . O O O | $$ | . . X O X X X O O O O X O X O O O X O | $$ | . . O O X O O O O O X X O X X O X X X | $$ | . O O X X X O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | . O . X X O O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Assuming that all the dame moves are filled and black played the ko threat at :b1:

,

is actually an additional threat for black. Can you see why?

Click Here To Show Diagram Code: [go]$$Bm5 $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X . . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X O . . . . , O . . | $$ | . X . . O O X X O O O X 1 7 3 . . . . | $$ | . . . O O X O X X X X O O 2 4 5 9 . . | $$ | . . . O . X . X O X O O O O X 6 O O O | $$ | . . X O X X X O O O O X O X O O O X O | $$ | . . O O X O O O O O X X O X X O X X X | $$ | . O O X X X O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | . O . X X O O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

If

plays elsewhere, black can capture everything using a squeeze tesuji.

macelee · #7

Now we have enough background knowledge. Let's pick up the diagram in post #3 which I reproduce here:

Click Here To Show Diagram Code: [go]$$W $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | 7 O X X O O X . X . . . . X X X . . . | $$ | 6 O O O . O X X X , X X X O O X . X . | $$ | 8 X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | 4 O X X . . X X X O . . . . . . . O O | $$ | 5 O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O . X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O . . O O 3 | $$ | . . X O X X X O . O O X O X O O O X 1 | $$ | . . O O X O O . O . X X O X X O X X 2 | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | . O . X . . O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Click Here To Show Diagram Code: [go]$$Wm9 $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X . . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O . X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O . . O O O | $$ | . . X O X X X O . O O X O X O O O X O | $$ | . . O O X O O . O . X X O X X O X X X | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X b X X X O X . . X X X . X . X . | $$ | . O . X a 1 O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

is the largest move now. It destroys one point. Then should white get 'a' it can further destroy one point at 'b'. So :w9:

's value on paper is 1 and 1/2 points (assuming that each side has 50% chance to get 'a').

I have some comments unrelated to this game so I hide them here:

Next, black has three options as far as I can see. Please think hard. I need to remind everyone here that when the special technique of filling dame before connecting ko applies, a seemingly larger yose move can become the wrong move, as shown in this much simpler example (externally at Go4Go: http://www.go4go.net/go/games/sgfview/46079)

macelee · #8

Click Here To Show Diagram Code: [go]$$Bm10 $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X . . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O c X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O . . O O O | $$ | . . X O X X X O a O O X O X O O O X O | $$ | . . O O X O O . O 1 X X O X X O X X X | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | . O . X b O O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Following the discussion in the previous post, :b10:

is one way of playing. :b10:

is actually a smart move - it destroys one point at 'a' at the same time prevents white from playing 'b'. But as I already mentioned, one extra point here or there doesn't matter in this game. The important thing is to win the last ko! By playing :b10:

black would leave three additional ko threats - white can throw in 'c' twice. So black would eventually lose the ko fight and lose the game!

macelee · #9

Click Here To Show Diagram Code: [go]$$Bm10 $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X a X c . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X b X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O d . . . . . . . | $$ | . . . O O X O 3 X X X O O . . . . . . | $$ | . . . O 9 X . X O 4 O O O O . . O O O | $$ | . . X O X X X O . O O X O X O O O X O | $$ | . . O O X O O 8 O 2 X X O X X O X X X | $$ | . O O X X 7 O O X X . X O O X O X . . | $$ | 6 O X O . X O O X . O X O X X O X . . | $$ | O X X . X X X O X . . X X X . X . X . | $$ | 0 O 5 X 1 O O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Alternatively black plays :b10:

here, leaving white :w11:

with one point. If white wants that point, :b12:

becomes sente so all the ko threats there are destroyed.

In the end, only two kos left at 'a' and 'b'. Black connect either one and white takes the other. Now recall the ko threat analysis earlier: white has 4 threats inside black territory plus 'c'; black has 4 threats inside white territory plus 'd'. So each side has 5 ko threats and white takes ko first. So black would lose the ko fight and lose the game!

macelee · **#10**

Ok, I stop here for the final analysis. There are still works to do on my board. As you can see no matter what the result, this is already a very interesting game.

macelee · **#11**

Wow, I just found a mistake in my analysis so I have to change my final conclusion. It looks like Lee Sedol indeed can win this game!

Just when I about to give up, I find another way for black:

Click Here To Show Diagram Code: [go]$$Bm10 $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X . . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O 1 X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O . . O O O | $$ | . . X O X X X O a O O X O X O O O X O | $$ | . . O O X O O . O . X X O X X O X X X | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X b X X X O X . . X X X . X . X . | $$ | . O . X 2 O O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Is

here a better move? Its purpose is to remove all local ko threats at the same time destroy the point at 'a'. The price black has to pay is that after :w11:

the point at 'b' is gone. So in terms of point, this variation is exactly the same as the one in the previous post. So how about the ko threat situation. Let's play out.

Click Here To Show Diagram Code: [go]$$Bm10 $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X a . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O b . . . . . . . | $$ | . . . O O X O 1 X X X O O . . . . . . | $$ | . . . O c X . X O 7 O O O O e . O O O | $$ | . . X O X X X O 8 O O X O X O O O X O | $$ | . . O O X O O 0 O d X X O X X O X X X | $$ | . O O X X 9 O O X X . X O O X O X . . | $$ | 4 O X O . X O O X . O X O X X O X . . | $$ | O X X 3 X X X O X . . X X X . X . X . | $$ | 6 O 5 X 2 O O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Ok, we can stop here for the final analysis:

It is now white's turn to take a ko. Remember white has 4 threats inside black territory plus 'a'. So white has 5 ko threats in total.

Black also has 4 threats inside white territory plus 'b'.

So black is still short of ONE ko threat. White would win by the smallest margin.

Remember that for black to win he needs to both win the ko fight and play the last dame point. So you might want to argue with me that white can use the dame at 'c' or 'd' as a ko threat, so white has two more ko threats than black. That is INCORRECT - still remember the squeeze I show earlier? When all the liberties are gone, black 'e' becomes a ko threat. So white indeed only has one more threat.

Bill Spight · **#12**

macelee wrote:

Click Here To Show Diagram Code: [go]$$Wm9 $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X . . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O . X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O . . O O O | $$ | . . X O X X X O c O O X O X O O O X O | $$ | . . O O X O O . O 2 X X O X X O X X X | $$ | . O O X X . O O X X . X O O X O X . . | $$ | . O X O . X O O X . O X O X X O X . . | $$ | O X X b X X X O X . . X X X . X . X . | $$ | . O . X a 1 O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

is the largest move now. It destroys one point. Then should white get 'a' it can further destroy one point at 'b'. So :w9:

's value on paper is 1 and 1/2 points (assuming that each side has 50% chance to get 'a').

For a while, that's what I thought, too. But, as macelee has pointed out, Black responds at 10 (which I have marked in the diagram), preventing White "a" and taking away the potential point at "b". :w9:

and

are in fact, miai.

Click Here To Show Diagram Code: [go]$$Wm9 $$ +---------------------------------------+ $$ | . . . . . . O O O O O X . . . . . . . | $$ | . . O . . O O X O X X X . . . . . . . | $$ | O O X X O O X . X . . . . X X X . . . | $$ | X O O O . O X X X , X X X O O X . X . | $$ | X X O O . O O X . . O X . X O O X X O | $$ | . X X X O O X O O . . X X O . O O X . | $$ | . . . . X O X X O X X X O O O . O X X | $$ | X X . . . X . X X O O O O . . O X O X | $$ | X O X X . . X X X O . . . . . . . O O | $$ | O O O O X X . X O X . . . . . , O . . | $$ | . X . . O O X X O O O . . . . . . . . | $$ | . . . O O X O . X X X O O . . . . . . | $$ | . . . O . X . X O . O O O O b . O O O | $$ | . . X O X X X O a O O X O X O O O X O | $$ | . . O O X O O e O 1 X X O X X O X X X | $$ | 3 O O X X d O O X X . X O O X O X . . | $$ | 2 O X O . X O O X . O X O X X O X . . | $$ | O X X c X X X O X . . X X X . X . X . | $$ | . O . X . 4 O O X . . . . . X . X . . | $$ +---------------------------------------+[/go]

Since they are miai, IMO White should play :w9:

in this diagram. That makes an eye at "a" and forestalls the potential ko threat at "b". It also leaves White an eventual ko threat at "c".

Remember also that, having given up a point at move 250, White cannot use dame as tertiary ko threats, so Black has a ko threat at "d". Unlike in the actual game, White cannot fill at "e" to force Black to play "d". Black will simply win the ko.

I think that White can win the ko, but I may have overlooked something.

Bill Spight · **#13**

FWIW, here is what I have worked out.

Go to move 250, OC.

Edit: Clarified the file a bit.

macelee · **#14**

I cannot see any apparent error from Bill's reading. White has one more ko threats no matter what.

Some technical details of the Mlily Cup final

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