Life In 19x19

RobertJasiek wrote:Can you please show the calculation that the profit is not a number but a game?

We start with S and end up with 0. The profit is 0 - S. 0 - S = -S, which is a game.

OC, the mean value of -S is 0, so the average gain is 0. Hence the saying, Sente gains nothing.

It seems that I need to find out on my own why the count of S is not a number. Maybe I find time for this in a few months.

RobertJasiek wrote:It seems that I need to find out on my own why the count of S is not a number. Maybe I find time for this in a few months.

The count of S is a number. It's 0. S is a game. So is -S.

The profit is the value change from the count of S to the count 0. Why do you instead say that the profit is the change from the game S to the count 0?

RobertJasiek wrote:The profit is the value change from the count of S to the count 0. Why do you instead say that the profit is the change from the game S to the count 0?

What do you want to call the difference between S and 0? Oh, and 0 is the score, not just the count. {1 | -1} has a count of 0.

Bill Spight wrote:What do you want to call the difference between S and 0?

Call it "the difference between S and 0".

But "the difference between the count of S and 0 (which is the count of a leaf)" we call the "the negative of the [net] profit" aka "the negative of the gain", right?

RobertJasiek wrote:The profit is the value change from the count of S to the count 0. Why do you instead say that the profit is the change from the game S to the count 0?

In CGT a game is a value, and numbers are games. Non-numerical games are fuzzy values. The count of a go position is a number, which is the mean value of its game (adjusted in modern go according to the specific rule set).

You are the one to introduce the term, profit. If you wish to use it only for numbers, be my guest. But gain and loss, in English, are not restricted to numbers. One may gain understanding or lose confidence.

The gain from playing with sente from S to 0 is 0 - S, which is the game, -S, which is greater than 0, even though its mean value is 0.

If you want to say that the profit from playing S with sente is 0, that accords with the saying, Sente gains nothing.

Actually, you introduced 'profit value' for one move's profit and 'net profit' for the alternating difference of a sequence's profit values quite some time ago, although you did not provide such definitions explicitly, AFAIK. I have found these terms very useful when expressing the change from a starting count to a follower's count.

'Profit' used alone is also used in different, informal go meanings ("A player takes profit here, then tenukis."). Therefore, using 'profit value' and 'net profit' as the terms for CGT or endgame theory avoids ambiguity. Besides, 'profit value' reminds us of the close relation to the term 'move value'.

There seems to be no consensus yet on whether 'gain' might occur as another term. I hope that not because profit and gain are so similar to create confusion that is better avoided.

RobertJasiek wrote:Actually, you introduced 'profit value' for one move's profit and 'net profit' for the alternating difference of a sequence's profit values quite some time ago, although you did not provide such definitions explicitly, AFAIK. I have found these terms very useful when expressing the change from a starting count to a follower's count.

Well, your memory is better than mine on that score. (Edit: I did a search here and did not find that I used it here.) Possibly that happened on rec.games.go or, perhaps more likely, in the lost archives of Godiscussions before 2010. Back in the 1990s I pushed for Western players to learn and use miai values for moves instead of deiri values, in an attempt to help clarify evaluation. I seem to have caused more confusion, however. John Fairbairn has pointed out that the term, deiri in accounting refers to profit and loss. It could be that I tried the term, profit value, as an English equivalent to miai value. That seems to be how you are using the term. But eventually I decided to simply use the term, gain, despite some ambiguity. Unless you get really technical, you don't have to distinguish between the difference in counts and the difference in games. Here I was getting really technical, because I wanted to show that sente in the technical sense can gain something, just not points.

There seems to be no consensus yet on whether 'gain' might occur as another term. I hope that not because profit and gain are so similar to create confusion that is better avoided.

Yes, I see other people using "miai value", but neither "profit value" nor "gain" seems to have generally caught on yet.

Maybe on Sensei‘s? You used profit value in contrast to move value to describe the different behaviour of sente and the different values of starting a sente sequence or playing reverse sente. Precision is needed and I did some related proofs because I could not find such quickly from others, except that OC you paved the conceptual way.

Yet another post on Kano's Beauty
Kano's Beauty is A + D (normalized to have a count of 0). As we know, A + D = A - D < 0. Which means that White gets the last play in Kano's Beauty, no matter who plays first. It is rather interesting that the sum of two games that are confused with 0 is less than 0. But that is not all that unusual.

Here is something that I find interesting.

A < D, so
A + A < D + D = 0

So two copies of A is less than 0. Here is an SGF file that illustrates that. Note that when White plays first he could easily make a mistake.

Tsumego from an actual game

Click Here To Show Diagram Code

[go]$$Wc Status?
$$ --------------------
$$ | . . X . X X . . . .
$$ | . O O X X . X O . .
$$ | X . O X X X O X X X
$$ | X O . , O O O O . ,
$$ | O X O O O X X O X X
$$ | . X X X O O X O X O
$$ | . X . X . O X O X X
$$ | O O O X . O X O X O
$$ | . X X . X O X X X X
$$ | . X . , O O O X O ,
$$ | . O O O . X . X O O
$$ | . O X X X . X X X X
$$ | . O X . . X X . O O
$$ | . O O X X . X X O X[/go]

What is the status of the Black group on the left side? Can White to play kill? (The surrounding White stones are alive, OC.)

Enjoy!

speedchase wrote:

$$W1
$$ --------------------
$$ | . . X . X X . . . .
$$ | . O O X X . X O . .
$$ | X . O X X X O X X X
$$ | X O . , O O O O . ,
$$ | O X O O O X X O X X
$$ | 3 X X X O O X O X O
$$ | . X . X . O X O X X
$$ | O O O X . O X O X O
$$ | 2 X X . X O X X X X
$$ | 1 X . , O O O X O ,
$$ | . O O O . X . X O O
$$ | . O X X X . X X X X
$$ | . O X . . X X . O O
$$ | . O O X X . X X O X

Click Here To Show Diagram Code

[go]$$W1
$$ --------------------
$$ | . . X . X X . . . .
$$ | . O O X X . X O . .
$$ | X . O X X X O X X X
$$ | X O . , O O O O . ,
$$ | O X O O O X X O X X
$$ | 3 X X X O O X O X O
$$ | . X . X . O X O X X
$$ | O O O X . O X O X O
$$ | 2 X X . X O X X X X
$$ | 1 X . , O O O X O ,
$$ | . O O O . X . X O O
$$ | . O X X X . X X X X
$$ | . O X . . X X . O O
$$ | . O O X X . X X O X[/go]

$$W1
$$ --------------------
$$ | . . X . X X . . . .
$$ | . O O X X . X O . .
$$ | X . O X X X O X X X
$$ | X O . , O O O O . ,
$$ | O X O O O X X O X X
$$ | . X X X O O X O X O
$$ | 2 X 4 X . O X O X X
$$ | O O O X . O X O X O
$$ | 3 X X . X O X X X X
$$ | 1 X . , O O O X O ,
$$ | 5 O O O . X . X O O
$$ | . O X X X . X X X X
$$ | . O X . . X X . O O
$$ | . O O X X . X X O X

Click Here To Show Diagram Code

[go]$$W1
$$ --------------------
$$ | . . X . X X . . . .
$$ | . O O X X . X O . .
$$ | X . O X X X O X X X
$$ | X O . , O O O O . ,
$$ | O X O O O X X O X X
$$ | . X X X O O X O X O
$$ | 2 X 4 X . O X O X X
$$ | O O O X . O X O X O
$$ | 3 X X . X O X X X X
$$ | 1 X . , O O O X O ,
$$ | 5 O O O . X . X O O
$$ | . O X X X . X X X X
$$ | . O X . . X X . O O
$$ | . O O X X . X X O X[/go]

This seems to work pretty well. Anything I am missing?

Black has resources in the first diagram. Think about it before peeking!

A not so easy problem

Most of my problems and illustrations are easy. This one, however. . . .

Click Here To Show Diagram Code

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

No komi. White to play and win.

Enjoy!