I stumbled across the Japanese National Library site some years ago. I found this set by doing a search there for tsumego. The father was a 7 dan (awarded posthumously, I think); the son was a shodan. They have pages on SL. ( http://senseis.xmp.net/?KobayashiTetsujiro , http://senseis.xmp.net/?KobayashiKentaro )

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

A cook?

Here is the answer in Igo tsumekata to the easy problem.

Click Here To Show Diagram Code

[go]$$ Black to play
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . , . . . . . , . . . . X , O . . |
$$ | . . . . . . . . . . . . X . X O . . . |
$$ | . . . . . . . . . . . X . O O X X X 1 |
$$ | . . . . . . . . . . . . . O X O O O . |
$$ | . . . . . . . . . . . . X 3 X X O . . |
$$ | . . . . . . . . . . . . . . . X 2 . . |
$$ | . . . , . . . . . , . . . . . , O . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

It is, in fact, the only line of play shown in the text. Occasionally it shows a variation or two on the main line, but usually not. That has good and bad aspects.

Both of our solvers started with at 2. Was that a mistake, or was the problem cooked? The text is no help. (BTW, my impression is that cooks were not considered to be flaws in ancient problems. It is not unusual for go positions to have more than one correct line of play which transpose into the same result.)

With no failure diagrams or variations, the reader could, and, IMO, usually should, explore those possibilities. In particular, if a play is correct there should be an answer to every reply, not just the one in the main line.

Click Here To Show Diagram Code

[go]$$ Variation 1
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . , . . . . . , . . . . X , O . . |
$$ | . . . . . . . . . . . . X . X O . . . |
$$ | . . . . . . . . . . . X . O O X X X 1 |
$$ | . . . . . . . . . . . . . O X O O O 2 |
$$ | . . . . . . . . . . . . X . X X O 6 5 |
$$ | . . . . . . . . . . . . . . . X 3 4 8 |
$$ | . . . , . . . . . , . . . . . , O 7 9 |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

If , this rollup is familiar to experienced players.

Click Here To Show Diagram Code

[go]$$ Variation 2
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . , . . . . . , . . . . X , O . . |
$$ | . . . . . . . . . . . . X . X O 2 . . |
$$ | . . . . . . . . . . . X . O O X X X 1 |
$$ | . . . . . . . . . . . . . O X O O O 7 |
$$ | . . . . . . . . . . . . X . X X O 5 6 |
$$ | . . . . . . . . . . . . . . . X 3 4 . |
$$ | . . . , . . . . . , . . . . . , O 9 . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

fills at 5.

If , this rollup may be somewhat less familiar.

Click Here To Show Diagram Code

[go]$$ Solution 2?
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . , . . . . . , . . . . X , O . . |
$$ | . . . . . . . . . . . . X . X O . . . |
$$ | . . . . . . . . . . . X . W W X X X 3 |
$$ | . . . . . . . . . . . . . W X O O O . |
$$ | . . . . . . . . . . . . X 5 X X O 4 . |
$$ | . . . . . . . . . . . . . . . X 1 2 . |
$$ | . . . , . . . . . , . . . . . , O . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

This is the solution given by Ed and jeromie. In this variation threatens the rollup in variation 2. defends against that, and the wins the capture fight.

At first glance not only is the problem cooked, but this is a better solution than the one in the book. Why was that the answer given? Was it an oversight by the son, who was probably weaker than today's pros? Or is there some other reason?

Can the marked stones escape in this variation, because of Black's shortage of liberties after - ? Or can White exploit that shortage in some other way? These questions go beyond the scope of this position as a tsumego problem per se, but they are practical questions.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I've been meaning to answer this one for a while. Still haven't peeked at Ed's answer.

@Ed:

Kudos to jeromie for his work on the latest problem.

Click Here To Show Diagram Code

[go]$$W White to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . , . . . . . , . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | X X O . . . . . . . . . . . . . . . . |
$$ | . O O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Here is the main line, hidden in case anyone wants to still work on it.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Hi Bill, Thanks.

Well,

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

A problem from an ancient game, the game played for the gold-petalled bowls.

Click Here To Show Diagram Code

[go]$$W White to play and make jigo
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O . X . . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X . |
$$ | . . X , . . . X . , X O O O O O X X . |
$$ | . . X . . . . . . X X X X . . . . O . |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O . . . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

Territory scoring with a group tax. (Subtract two points from the territory of each independently living group.)

Black has captured one White stone, White has captured three Black stones.

Black won the game by 1 point, but White has a cool move or two for jigo. The first play is not ordained, as White has some forcing plays.

Enjoy!

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

On playing around

Here is an easy life and death problem. It may be familiar to you. It is kind of familiar to me, but I can't say for sure that I had seen it before I constructed it. Anyway, it's easy.

Click Here To Show Diagram Code

[go]$$B Black to play
$$ | . . . . . . .
$$ | . . . . . . .
$$ | . X . . . . .
$$ | . . . . . . .
$$ | . X X . X . .
$$ | . O X , . . .
$$ | O . O X X . .
$$ | . . O O X . .
$$ | . O . X . . .
$$ --------------[/go]

Now, I constructed it as a potential flashcard by playing around with this position.

Click Here To Show Diagram Code

[go]$$B Black to play
$$ | . . . . . . .
$$ | . . . . . . .
$$ | . X . . . . .
$$ | . . . . . . .
$$ | . X X . X . .
$$ | . O X , . . .
$$ | O . O X X . .
$$ | . . O O X . .
$$ | . . . . . . .
$$ --------------[/go]

This is one of those standard problems that people learn when they begin to study life and death. One of the things that you learn about this position is that death is not in the hane.

Click Here To Show Diagram Code

[go]$$B Life in the hane
$$ | . . . . . . .
$$ | . . . . . . .
$$ | . X . . . . .
$$ | . . . . . . .
$$ | . X X . X . .
$$ | . O X , . . .
$$ | O . O X X . .
$$ | . 2 O O X . .
$$ | . . . 1 . . .
$$ --------------[/go]

But what if White makes a mistake?

Click Here To Show Diagram Code

[go]$$B Strange thing on the 1-2 point
$$ | . . . . . . .
$$ | . . . . . . .
$$ | . X . . . . .
$$ | . . . . . . .
$$ | . X X . X . .
$$ | . O X , . . .
$$ | O . O X X . .
$$ | . . O O X . .
$$ | . 2 . 1 . . .
$$ --------------[/go]

OC, is a silly play, but playing around includes making silly plays.

Now, playing around is something that children do. That may be a big clue, because children are the best learners in the world.

When I was a kid I dealt out bridge hands, bid them, and played them out, imagining what each player would do if they did not know what was in the other hands, as I did. I am sure that I made a lot of horrible bids and plays, but I think that it paid off. I started playing occasionally in the local duplicate bridge club when I was 13 -- not on school nights, OC --, and in the summer after eighth grade I remember hesitantly playing a difficult two diamond contract. The local life master was kibitzing, and after that he told people that I was the best player in the club at the play of the cards. Looking back, he was probably right, except for him, OC.

When I was learning go in my early 20s I set up and played around with positions on the go board, mostly from my own games. Nobody told me that I was supposed to do everything in my head. I think I benefited from that. Later on, when I was president of the New Mexico Go Association, I ran four tournaments a year and put out a newsletter about a week after each tournament. In each newsletter I reviewed a game from the previous tournament, usually my own games but also others. Did I rely just upon my reading? Hell, no! I was writing for publication. I played variations out on the go board. I'm sure that I made some mistakes, but nobody complained. At that time I had no real competition, no better players to learn from. I was giving two stones to my nearest competitors. To my surprise, even as they advanced I kept two stone ahead of them. I think that doing those reviews helped me to do so.

Do you think that I relied only upon my reading for the endgame problem I just posted? Of course not. I saw a variation that I thought might gain one point, but I was not sure. The position is not simple. I played it out to be sure. Especially as a lot of pros have looked at this game over the centuries and have not apparently discovered the play.

I have praised jeromie for his work on the recent corner problem. Whether he did it all in his head or played it out on the board or computer, I don't know. In any event, he has done valuable work.

I especially encourage beginners to do as I did, to play around with positions from their own games. They can learn a lot by doing so.

Finally, let me end with this quotation from chess grandmaster Nigel Davies:


(Emphasis mine) From http://rlpchessblog.blogspot.com/2011/0 ... rtesy.html

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

In the spirit of playing around...

This might be referencing the recent thread about how we read go books, where I said:

That's a description of how I read go books, not a description of what I consider the right way to read go books. I think my method is fine, but it is not the only way. As much as anything, it's an indication that I'm too lazy to pull out a board and work through variations while reading a book. (I don't think Bill is addressing me in particular; I just thought I'd clarify my position.)



Thanks. I made generous use of the preview post button as I was making that reply, so I was looking at intermediate diagrams of positions I was considering.

I do use a board (usually virtual, since I play most of my games online) to explore positions from my own games. That's a big part of my self review: I search for a position where I think that I (or my opponent) could have gotten a better result and try out variations until I find something that works or convince myself there was nothing else that could have been done with the position. This often leads to interesting problems, and seeing various possibilities in the context of a game makes the moves more memorable and reinforces the concepts I've been exposed to through other reading.

I completely agree with Bill's position that play is an important part of learning; there is a world of possibilities that can be explored after the question "what if...?"

Hi Bill,

Thanks.

@ emeraldemon

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Analysis of the position from the game for the gold petalled bowls.

Click Here To Show Diagram Code

[go]$$W White to play and make jigo
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X W ? B ? a . O . . . O X . X ? ? |
$$ | . X O X X O O O O X O O O X X . ? ? ? |
$$ | . . . . . X X O X X X X O O X X O X ? |
$$ | . . X , . . . X . , X O O O O O X X ? |
$$ | . . X . . . . . . X X X X c ? ? ? O ? |
$$ | . X O X X X X . . X O X O O O O O ? ? |
$$ | . X O O O X O X X O O X . X X X O ? O |
$$ | . X X O O O O O O O . X . X ? ? X O ? |
$$ | X X O . . X O . . . O O O b ? ? X O X |
$$ | O O . O O O X O . X O X O O X X . X ? |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

There are three active areas of the board, indicated by "a", "b", and "c". "c" is the largest and most complicated. The local temperature in each is 1. Let us look at each of them, in turn.

Click Here To Show Diagram Code

[go]$$W "b" is positive for Black
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O . X . . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X . |
$$ | . . X , . . . X . , X O O O O O X X . |
$$ | . . X . . . . . . X X X X . . . . O . |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O 1 2 . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

"b" is positive for Black.

is a 1 point sente which carries a 3 point threat. Black gets the last local play, whether he answers or plays the reverse sente at 1 himself. That means that "b" is positive for Black. If "b" is the last area of play, Black will get the last play of the game.

Click Here To Show Diagram Code

[go]$$B "a" is also positive for Black
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 3 X 1 2 . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X . |
$$ | . . X , . . . X . , X O O O O O X X . |
$$ | . . X . . . . . . X X X X . . . . O . |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O . . . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

"a" is also positive for Black.

gains 1 point in gote, so Black gets the last local play if Black plays first.

Click Here To Show Diagram Code

[go]$$W "a" is positive for Black, II
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 2 X 1 . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X . |
$$ | . . X , . . . X . , X O O O O O X X . |
$$ | . . X . . . . . . X X X X . . . . O . |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O . . . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

If White plays first, Black can also get the last local play. That means that "a" is positive for Black, as well as "b".

But Black does not have to play last in "a".

Click Here To Show Diagram Code

[go]$$W Black tenuki
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 3 B 1 . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X . |
$$ | . . X , . . . X . , X O O O O O X X . |
$$ | . . X . . . . . . X X X X . . . . O . |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O . . . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

tenuki, at , at 3

- gains only 1 point, so is not sente. is ambiguous between sente and gote. (See http://senseis.xmp.net/?AmbiguousPosition ). It is called an Up. (See http://senseis.xmp.net/?Up ).

"c" is the most complex position. It is negative for Black (positive for White). If it were also positive for Black, Black would get the last play.

Click Here To Show Diagram Code

[go]$$B "c" is positive for White
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O . X . . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X 3 |
$$ | . . X , . . . X . , X O O O O O X X 2 |
$$ | . . X . . . . . . X X X X . . . 1 O 4 |
$$ | . X O X X X X . . X O X O O O O O C C |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O . . . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

is a 1 point sente, carrying a 2 point threat, as you may verify. Note that White gets only 2 points in the eye on the edge.

Click Here To Show Diagram Code

[go]$$W "b" is positive for Black, II
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O . X . . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X 4 |
$$ | . . X , . . . X . , X O O O O O X X 3 |
$$ | . . X . . . . . . X X X X 2 6 7 1 O 5 |
$$ | . X O X X X X . . X O X O O O O O C C |
$$ | . X O O O X O X X O O X . X X X O C O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O . . . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

If White plays the reverse sente, , he gets the last local play. Note that this way White gets 3 points in the eye.

The game sequence

Click Here To Show Diagram Code

[go]$$W How the game went
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . 1 O X . O X X X X . O X O X |
$$ | X O X O 2 X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 4 X 3 . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X 6 |
$$ | . . X , . . . X . , X O O O O O X X 5 |
$$ | . . X . . . . . . X X X X . . . 8 O 7 |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O . . . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

is a meaningless sente. plays in "a" with sente, and then White plays in "c" with sente, as well. That leaves "b" as the only active position on the board. "b" is positive for Black, which means that Black will get the last play and win by 1 point.

Now, the normal heuristic is to play where the opponent is positive.

Click Here To Show Diagram Code

[go]$$W Normal heuristic
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 4 X 3 . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X . |
$$ | . . X , . . . X . , X O O O O O X X . |
$$ | . . X . . . . . . X X X X . . . 5 O . |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O 1 2 . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

White starts with the sente in "b", and then switches to the Black positive region, "a". After only the White positive region, "c", is left. With the correct local play, , White gets the last play of the game, for jigo.

However, in this case the normal heuristic does not work with correct play by Black.

Click Here To Show Diagram Code

[go]$$W Black Zwischenzug
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 8 X 3 . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X 6 |
$$ | . . X , . . . X . , X O O O O O X X 5 |
$$ | . . X . . . . . . X X X X . . . 4 O 7 |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O 1 2 . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

As pointed out above, is not sente. Instead of answering right away, Black interposes the sente in "c", an in between play (Zwischenzug in chess parlance) and then gets the last play with .

Click Here To Show Diagram Code

[go]$$W White's best chance
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O . X . . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X . |
$$ | . . X , . . . X . , X O O O O O X X . |
$$ | . . X . . . . . . X X X X . . . 3 O . |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O 1 2 . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

After the sente in "b" White plays the reverse sente, , in "c". Since "c" is still positive for White, as you may verify, White has a chance to get the last play.

Click Here To Show Diagram Code

[go]$$Bm4 White gets the last play for jigo
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 0 B 2 . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X C |
$$ | . . X , . . . X . , X O O O O O X X 9 |
$$ | . . X . . . . . . X X X X 1 3 4 O O 6 |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O 8 O |
$$ | . X X O O O O O O O . X . X . . X O 7 |
$$ | X X O . . X O . . . O O O O X . X O X |
$$ | O O . O O O X O . X O X O O X X . X 5 |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

at , at 13

plays in "c", which is White positive. If Black played in "a" instead, that would leave only a White positive region on the board, guaranteeing that White would get the last play. plays in "a", the Black positive region, and then Black plays with sente. is a clever play, but White has an answer with the descent, , which is sente, threatening the jump attachment at the marked point, for a gain of 2 points. Black interposes with sente, but now Black must take gote with . Next, captures the stone and finally White gets the last play with .

A real battle! Who said the endgame was about counting points?

Click Here To Show Diagram Code

[go]$$Bm8 White mistake
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 7 X O . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X 3 |
$$ | . . X , . . . X . , X O O O O O X X 2 |
$$ | . . X . . . . . . X X X X X X O O O 4 |
$$ | . X O X X X X . . X O X O O O O O . . |
$$ | . X O O O X O X X O O X . X X X O 6 O |
$$ | . X X O O O O O O O . X . X . . X O 5 |
$$ | X X O . . X O . . . O O O O X . X O X |
$$ | O O . O O O X O . X O X O O X X . X 1 |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

If White plays the hane-and-connect with - , Black takes his sente and then gets the last play with .

Click Here To Show Diagram Code

[go]$$Bm4 White mistake, II
$$ ---------------------------------------
$$ | . O O O . . . . O X X X X X O . . . . |
$$ | O . O X O . . . O O X . O O O . . . . |
$$ | O . O X . O . X . O X . O X X O O O O |
$$ | . O X X . . O X . O X X X X . O X O X |
$$ | X O X O . X O O . O X . O . X X X O X |
$$ | . X . X X O O . . . O O . O O X . X X |
$$ | . X X O 8 B 2 . . O . . . O X . X . . |
$$ | . X O X X O O O O X O O O X X . . . . |
$$ | . . . . . X X O X X X X O O X X O X . |
$$ | . . X , . . . X . , X O O O O O X X 7 |
$$ | . . X . . . . . . X X X X 1 3 5 O O 4 |
$$ | . X O X X X X . . X O X O O O O O 6 . |
$$ | . X O O O X O X X O O X . X X X O . O |
$$ | . X X O O O O O O O . X . X . . X O . |
$$ | X X O . . X O . . . O O O O X . X O X |
$$ | O O . O O O X O . X O X O O X X . X . |
$$ | . . . . O X X X X X X X O . X X O X . |
$$ | . O . . O X . . . O X O O O X O . O O |
$$ | . . . O X X . . . . X X O . O . O . . |
$$ ---------------------------------------[/go]

at , at 11

White can live on the side in sente with , and White gets the last play with . However, as cuts the White group off, White loses by 2 points because of the group tax.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

On basic instinct and unconscious processing at go

The first paragraph below is from my response, viewtopic.php?p=204274#p204274 ,
to Uberdude's post here: viewtopic.php?p=204263#p204263 .

----

I don't think that this does justice to the massive parallel processing that goes on in the brain when playing go. It is not just a question of pattern matching. There is real computation going on. There is analysis, there is synthesis, there are feedback loops. Decisions may emerge through some process of competition in the cerebral cortex. OC, we are unaware of nearly all of this. Consider visual processing. The last time I studied any of this, we had discovered that the brain constructs at least 18 different images before synthesizing what we think we see. Consider language processing. We occasionally recognize ambiguities in language, but as we make sense of speech we eliminate hundreds of ambiguities per second, without conscious effort. This is not just a matter of pattern recognition, as we have to choose among a number of patterns that fit what we hear, and construct a meaningful interpretation (usually only one) as we go along, taking both context and non-verbal information into account. By comparison our conscious processing is linear, and painfully slow. But even our parallel processing is slow by comparison with computer processing. We may unconsciously process hundreds of possibilities while the computer is processing hundreds of thousands, or millions. If we weren't better at it, there would be no contest.

We tend to overvalue our slow, linear, conscious processing at go. Not that it is unimportant, but without the underpinning of our fast, parallel, unconscious processing, it would be hopeless. Much of our training is focused on conscious processing, but surely training our unconscious processing is important. The trouble is, how to do it? It's not like we know exactly what is going on. Reward and punishment is a way of training without looking into the black box of unconscious processing. Which, perhaps, is one reason for the advice to play a lot of games. Imitation is important. Remember Shusai's advice to play over 1,000 professional games.

Let me illustrate the training of unconscious processing, or, rather, the lack thereof, in my own case. The basic instinct page at Sensei's Library ( http://senseis.xmp.net/?BasicInstinct ) used to have as an example of basic instinct the extension as a reply to the hane of a single stone. My reaction was a vague sense of unease, not because that wasn't my first thought as response, but because I thought that maybe it shouldn't be. After all, the crosscut left a locally equal position on the board. It might not be right if it raised the local temperature and then gave the opponent the first shot at making a larger play than he could have made before, but it still restored equity. The results of a Kombilo search surprised me. The most frequent reply to the hane was neither of those two, but the counter hane. I had not even thought of that as a basic instinct play. Why not? Like the crosscut, it produced a locally equal position. It was obviously not a heavy as the extension, nor did it heat up the position like the crosscut. Often the opponent would connect his two stones, and you could tenuki. Why was the counter hane not my basic instinct?

Well, why not? I don't know. I had certainly seen it in pro play and in josekis, and I had played it myself a number of times. But I had always thought of it as some special technique that depended upon the local tactics. Well, of course it depends upon local tactics. What doesn't? But it is not special. It is normal. It should be basic instinct.

I had learned about extending from a crosscut and about playing hane at the head of two stones. Why had nobody told me about playing the counter hane?

I have become sensitized to the counter hane. I recently noticed how Michael Redmond played it in his commentary on the Lee Sedol - Alpha Go match, without comment. (Why comment? It's obvious, right? ) I make a conscious effort to consider it the default response. But I think that my game will always suffer from the lack of unconscious processing of the counter hane over the years.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Bill

In support of what you are saying, let me mention a rather similar experience I had had just a couple of hours before reading your post (I mention that detail to show I was not influenced by it).

I was transcribing a 1939 game and sat bolt upright when I saw Black play the triangled stone in the position below.



I have it engraved in my unconscious brain that A is the move to play, and I registered a reaction along the lines of: "I wouldn't have thought that the triangled move was even possible." But that was followed, as is usual for me with these not-quite-rare examples of seeing surprising but interesting moves, by another reaction that can be summed up as "That's why it's so useful to play over lots of pro games - you see ideas you wouldn't think of for yourself."

Now one other reason for my piqued interest in that position was that I quite often see A in my own games (on both sides of the fence) but I always have a frisson that translates into "isn't this a bit heavy?" The possibility of finding a new way of playing that wasn't heavy caught my attention. I should add that after a little bit of thought my conclusion was, nevertheless, "Nah, the triangle is heavy as well, and on top of that it leads to the bad shape of an empty triangle." I looked at the commentary. It said that A is normal, but the pattern with the triangle does exist. I still scoffed at that remark, then moved on.

But later, when I read your post, I re-visited this position via Kombilo. I found first that the triangled stone is exceedingly rare. There was only one other example in fact, but that was by Kitani in a high-profile 1934 game. That would be enough to explain the Kido comment about that move existing, I suppose. The whole cluster is still rare even when produced by other move orders, with just 7 examples.

By contrast the A form appears in well over 500 games. But then I started to wonder about B instead. My first impression was that this is not at all bad, but is actually not so common (presumably because it still leaves the opponent with an underneath attachment relevant to both players' bases). It turned out that my intuition was spot on: a little over 300 examples surfaced.

That got me on to thinking about the heaviness aspect. It is common to let the opponent cut at A. In the position above, for example, that would mean playing on the upper side, letting the opponent cut at A and then using the cut-off stone to force from the outside and make a nodule of incipient thickness. I have long been aware of that option, but tend to ignore it in my own play, and choose A, seeing that as denying the opponent not just territory and a base, but thickness too. Accepting a bit of heaviness seems acceptable for all of that. But simply in the process of thinking about that, I could feel myself tilting towards the "let him cut" option, if for no other reason to see how it pans out.

I think this goes some way to giving one answer to the question you posed about how to train unconscious processing. I infer that you need something substantial there (a neural network), in the unconscious, before you can start. You get that by playing over lots of games. You then "train" your unconscious processor by thinking explicity about something. I put "train" in quotes because I think that word tends to imply repetitive practice, but I have a feeling that that is not always necessary, or even desirable. Also, training tends to imply a measurable goal. I don't think that is always feasible either. What I think is going on with both of our examples is that our conscious thinking has put the unconscious processor on alert. We are telling it to switch on whenever it sees that sort of position in future, and to log the results. We will have no direct control over the results. The results will be nothing more than a revised set of weightings. In my particular example, I am assuming my unconscious processor will now leap into action whenever it sees a similar example, and especially of playing away and letting the opponent cut at A. It will evaluate those positions in various ways, some totally opaque to me, some reflecting the points I have already flagged up, such as heaviness.

Assuming all that is passably close to what is really going on, let me turn now to your question: "Why was the counter hane not my basic instinct?" My instinct is to say it is the fault of beginners' books. Most beginners' book give highlght examples only: in the case of your example let us say the crosscut answer to the hane. If you are a beginner you have a go-empty brain and such examples are seared into your brain. They become your basic instinct not because they are the commonest or the best instances but simply because they are the first you encountered.

I think it follows from that that beginners should avoid beginners' books beyond those that teach the rules, and instead should expose themselves to lots and lots of games, preferably pro games. The argument that "I don't understand what is going on in such games" should be brushed aside. You should not be trying to understand. You should be simply accumulating data. The argument that a little bit of theory can speed up improvement should also be treated as treacherous. Theory can help, but only after masses of data have been collected. Furthermore, even for theory I'm not sure that understanding is really the key: simple awareness seems more important, so that you know the right kind of questions to ask to help not 'you' (i.e. your conscious brain) but your subconscious. Again, to take my own example above, my awareness of the theory of heaviness is all I need to kickstart a useful process (I hope so, anyway!). I don't really need to know a definition of heaviness, or what kinds of heaviness exist, or how heavy is heavy.

I am not saying that beginners shouldn't read books. There are certainly beginners' books that do provide gentle "awareness" training and do not use the branding iron. I think the exemplar is Kageyama's "Lessons in the Fundamentals of Go." But more advanced books (or discussions with other players) are much safer to use because the player, once he is ready for them, already has a massive database in his head. The books/discussions then work with the database rather than against it.

One of the simplest but most useful ways advanced books can work is by repetition rather than tuition. I can illustrate that too from my own experience, and I believe this is also very relevant to Bill's fundamental question about how to train the unconscious processor. Something I am working on at the moment involves going through lots of commentaries that just happen to refer often to choshi - momentum-seeking moves. I have known about these for a long time, and in any case, even if I hadn't, the commentaries don't explain the concept, so I am not getting any new information directly from the commentary. What I am getting is the repetitive pounding that means this concept gets put high up on my unconscious processor's to-do list. I'm not sure of that to-do will ever turn into a ta-da moment when I can say I have learned something specific and can convey that precisely to others, but over the course of about 40 commentaries I have noticed already that I am starting to spot choshi moments even before I turn to the commentary, and I also feel I have a more rounded feel for the nuances - before I just "understood" choshi, in a chunky, clunky way. Now I "feel" it. I have to say "feeling" feels an awful lot better than "understanding", but is that not, after all, what basic instinct really means?

On the probability of winning the game

Now, in some sense go is not a game of probability. It is a game of perfect information and correct play, if known, leads to a certain outcome. However, as we know, if two players are evenly matched at a particular handicap and komi, we may say that the probability of either player winning a game is 50%. OC, that begs the question of how we know that the players are evenly matched.

Modern computer go programs, like AlphaGo, evaluate positions based upon the probability of winning the game. I submit that there is no such thing as the probability of winning the game, in general. A pure Monte Carlo program can estimate the probability that the current player in a position will win the game based upon random playouts. But, OC, the players do not play randomly. And pure Monte Carlo programs do not do very well. IIUC, most or all of the modern Monte Carlo Tree Search (MCTS) programs modify their playout procedures. What any program means by the probability of winning the game is anybody's guess. And how well it applies to the actual players is also anybody's guess. There is in general no accurate objective measure of the probability of winning the game from any position.

I do not mean to suggest that the probabilities that these programs produce are not good guides to play. The strength of the programs attests to that.

Humans do not have any good way to estimate probabilities of winning the game, in general. But in the endgame we have ways of evaluating local positions and plays in terms of territory or area, and sometimes whole board positions and plays. These evaluations, done correctly, are both accurate and objective. They provide good guides to play in the endgame -- not perfect, OC. Furthermore, they allow us to assess our chances -- not probabilities -- of winning. For instance, if we are ahead and have sente, and there are no kos now or later, we will win with correct play. Or if we are ahead by 7.25 points and the largest play gains only 5.5 points and there are no kos now or later, then we will win with correct play, even if the opponent has sente. Or similarly, if we are ahead by 5.5 points and the largest play gains 7.25 points and there are no kos now or later, and that is all that we know about the position, then we will -- ahem -- probably win, because the average gain for the opponent is 3.625 points, which is less than 5.5 points. We might even be able to generate a probability estimate from that information.

Endgame plays by MCTS programs often strike humans as silly. Perhaps that is human bias, but it may also be that such plays, or many of them, are suboptimal. How many MCTS programs have modules that have been specifically tuned to the endgame? If humans use MCTS programs for study, how good a guide are their suggested endgame plays? Just because the programs are strong does not mean that their endgame play is as strong as the rest of the program.

Here is Crazy Stone's assessment of an endgame play and position. See http://www.remi-coulom.fr/CrazyStone/an ... s-225.html . I got it via a recent post: viewtopic.php?f=10&t=13179&p=204299

Click Here To Show Diagram Code

[go]$$Wc White 255
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . O O X X O . |
$$ | . . X X O O . . O . O X O O X O O O O |
$$ | . . O O X X O . O , O O X X X X X O . |
$$ | . O . O O . O . X O X O X O O O . O X |
$$ | . . O X X O . O O O X X X O X O O O O |
$$ | . O X O X X O O X X . . X O X X X O O |
$$ | O X X O . X X X . . . . . X . X . X O |
$$ | . O X O O . . . . . . . . . . . X O O |
$$ | O . X , X X . X . , . . . . . X . X X |
$$ | . X . . O . . . . . . . . . . . X . . |
$$ | . X O O O X X X O X . X X . . . . . . |
$$ | . . X O X X O O X . X O O X X . . . . |
$$ | . . X X O O O X X X X . O X O X . X X |
$$ | . . X . X O . O O X O O . O O X . X . |
$$ | . . X X X O . O . O O O O X . X X O X |
$$ | . . . X O O O . . O . O X . X X O O O |
$$ | . . . X X O O O . O X O X X . O O O . |
$$ | . . . . X X 1 X O . . O . . . . . X O |
$$ ---------------------------------------[/go]

gains 1 point in gote.

Click Here To Show Diagram Code

[go]$$Wc Crazy Stone's suggestion
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . O O X X O . |
$$ | . . X X O O . . O . O X O O X O O O O |
$$ | . . O O X X O . O , O O X X X X X O . |
$$ | . O . O O . O . X O X O X O O O . O X |
$$ | . . O X X O . O O O X X X O X O O O O |
$$ | . O X O X X O O X X . . X O X X X O O |
$$ | O X X O . X X X . . . . . X . X . X O |
$$ | . O X O O . . . . . . . . . . . X O O |
$$ | O . X , X X . X . , . . . . . X . X X |
$$ | . X . . O . . . . . . . . . . . X . . |
$$ | . X O O O X X X O X . X X . . . . . . |
$$ | . . X O X X O O X . X O O X X . . . . |
$$ | . . X X O O O X X X X . O X O X . X X |
$$ | . . X . X O . O O X O O . O O X . X . |
$$ | . . X X X O . O . O O O O X . X X O X |
$$ | . . . X O O O . . O . O X a X X O O O |
$$ | . . . X X O O O . O X O X X 1 O O O . |
$$ | . . . . X X . X O . . O . b 2 . 3 X O |
$$ ---------------------------------------[/go]

takes away the Black point at "a" and threatens to connect underneath at "b" and gain 3 points. The game is close enough that that might matter. prevents the connection and threatens ko for the life of the White group. Locally, is a 1 point reverse sente, the same size as White's actual play.

Crazy Stone's suggestion is a good one, perhaps the best chance to win the game. Definitely not a silly play. But after the actual move at G-01 Crazy Stone assesses the probability that Black will win the game at 82%, and after its suggested play at P-02 it assesses the probability at 78%, for a delta of 0.059. In fact, it says that W255 was the second worst play in the game. Does anybody believe any of that?

In the actual game White got in P-02, and Black replied at P-01. What a surprise!

BTW, White may have enough large enough ko threats so that White is komonster for the ko in the bottom right corner, so that we can regard that group as alive, and then P-02 is White's sente, not Black's. The one point difference hardly matters.

Edit: Before the game has reached a scorable point, traditional go evaluation in terms of territory or area is fuzzy, in the technical sense. Finding the mean value of a position or of the whole board is a process of defuzzification. While it is possible to define fuzziness in terms of probability, fuzzy logic and probability are two different ways of looking at things which are undetermined. In the opening of a game of go, defuzzification of the whole board is usually intractable. However, it becomes practical in the endgame and we cannot assume that a probability based evaluation will be a superior guide to play at that point.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Komaster and corner invasions

I have already mentioned Professor Berlekamp's idea of komaster, and have addressed this kind of question in this thread: viewtopic.php?f=15&t=428&hilit=komaster

Informally, you can think of komaster as the player who can win kos, but technically it is more precise. The komaster can win a ko, but is unable to delay winning it. It is a kind of Goldilocks idea: the komaster has just the right number of (large enough) ko threats to win a ko, but no more and no less. OC, it is quite possible that the player who can win the ko has enough threats to delay winning it (i.e., is komonster) or that neither player is komaster. However, the idea of komaster is helpful in understanding complex kos such as approach kos and 10,000 year kos, because both the value of such ko positions and the value of ko plays in them are different, depending upon who is komaster. Those values for regular kos do not depend upon who is komaster.

As it turns out, endgame corner invasions often lead to such complex ko situations. Who is komaster may tell us when to make such invasions or defend against them, as well as which moves to make.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.