Following the discussion, I decided to read a bit more seriously the book "Yose" by Dai Junfu and Motoki Noguchi (by the way, the last names are Dai and Noguchi). In that book, their method of counting is different than Bill's. Let me first summarize their method. Suppose we are given a position with a possible move for each player.

If the position is gote for both players

1. Play out the sequence starting from Black until Black ends in gote.
1.a. If there is no followup, count the score (i.e. number of points for Black minus number of points for white).
1.b. If Black has a sente move after that ("privilege" of Black), continue the second sequence until the end and count the score.
1.c. If both Black and White have a continuation after that, play out the two possible sequences and calculate the average of the scores after each sequence.

2. Do the same as in 1. above, but for White instead of Black.

3. Subtract the numbers obtained in 1. and 2.

If the position is sente for one player and gote for the other (position called sente/reverse sente):

Do the same, but multiply by 2 the obtained number.

Remarks.

• Some positions are sente for both players, but are not evaluated, no quantitative criteria are given to decide when to play them.
• The term "sente" is not defined by Dai, so the player is supposed to guess if a move is sente or not. This is obvious in most cases.
• Dai's evaluation is less scientific than Bill's, but looks reasonably precise for practical purposes. In examples I examined, it corresponds roughly to Bill's (value of Black's move + value of White's move). I don't know if it's true in general, so if someone has an example where there is a large discrepancy between these two numbers I would be interested.
• I didn't talk about kos yet, and I am confused about that point but won't discuss that in this thread.

Here is a double gote example (from page 77 of the book).

Click Here To Show Diagram Code

[go]$$B
$$ | . O O . O . . . .
$$ | . O X . . O O . .
$$ | O X X . X X O . .
$$ | . O X . . . X O .
$$ | . O X . X . X X .
$$ | . a . . . . . . .
$$ +-------------------[/go]

If White plays first, then White plays at "a" and ends in gote, but later White has the privilege to play so the final position is this:

Click Here To Show Diagram Code

[go]$$W White has four points in the corner
$$ | . O O . O . . . .
$$ | S O X . . O O . .
$$ | O X X . X X O . .
$$ | S O X . . . X O .
$$ | S O X . X . X X .
$$ | S O 1 2 . . . . .
$$ +-------------------[/go]

If Black plays first, then Black plays at "a" and ends in gote, but there are two followup diagrams. In the first one, Black captures 2 stones

Click Here To Show Diagram Code

[go]$$W Black has 7 points
$$ | . O O . O . . . .
$$ | . O X . . O O . .
$$ | O X X . X X O . .
$$ | . @ X . . . X O .
$$ | X @ X . X . X X .
$$ | S X S S . . . . .
$$ +-------------------[/go]

In the second one, White connects.

Click Here To Show Diagram Code

[go]$$W Black has 1 point.
$$ | . O O . O . . . .
$$ | O O X . . O O . .
$$ | O X X . X X O . .
$$ | . O X . . . X O .
$$ | . O X . X . X X .
$$ | . X . S . . . . .
$$ +-------------------[/go]

The average between the last two diagrams is 4 points for Black. The difference between "White plays first" and "Black plays first" is 8 points. To conclude, Dai's evaluation of "a" is 8 points gote.

Here is a sente/reverse sente example.

Click Here To Show Diagram Code

[go]$$W White plays first, ends in gote after 3 but has the privilege 5--8 so gets 10 points.
$$ | . . O . . . . . . .
$$ | . X X . . . . . . .
$$ | . O X X X . . . . .
$$ | M O O O O X X . , X
$$ | M M M M 3 1 2 8 . .
$$ | M M M M M 7 5 6 . .
$$ +---------------------[/go]

Click Here To Show Diagram Code

[go]$$B Black plays first in sente, White has 6 points and Black 5 points.
$$ | . . O . . . . .
$$ | . X X . . . . .
$$ | . O X X X . . .
$$ | M O O O O X X .
$$ | M M M 2 1 3 S S
$$ | M 4 M . . S S S
$$ +----------------[/go]

The difference between the two diagrams is 9 points reverse sente, which is equivalent to 18 points gote.

My question will follow in the next post.

Here is the question on page 64 of the book. Should white connect?

Click Here To Show Diagram Code

[go]$$B To connect or not to connect?
$$ | . . . X . . . . . . .
$$ | . . . . X X . . . . .
$$ | X X X X O . O . . . .
$$ | X O O O O . . O O O O
$$ | O a S . . . . . . . .
$$ | S S S . . . . . . . .
$$ +----------------------[/go]

If White plays first, then White gets the 4 marked points and ends in gote. If Blacks plays first then Black cuts, White ataris, Black captures and gets 1 point. Ignoring the possibility of a ko, the difference between "White plays first" and "Black plays first" is 5 points gote. Taking the ko into account, Dai's evaluation of the position "slightly more than 5 points gote". So far so good.

Here is another diagram on page 86. The question is the following: "after White's hane on the first line, if Black doesn't protect at 'a' and plays elsewhere, what is the price of this tenuki?"

Click Here To Show Diagram Code

[go]$$W
$$ | . . X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . X . . . . . . .
$$ | S S S . . X . . . O .
$$ | S S S X . X O O . , .
$$ | S S S X . O . . . O .
$$ | S a 1 X O . . . . . .
$$ | S S X O O . . . . . .
$$ +----------------------[/go]

The book's answer is the following:

"Of course, White cuts at . With the protection at a, Black would have kept 13 points.

Click Here To Show Diagram Code

[go]$$W White's privileges: White 5 pts, Black 2 pts
$$ | . . X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . X . . . . . . .
$$ | 4 6 S . . X . . . O .
$$ | 3 2 S X . X O O . , .
$$ | 5 1 . X . O . . . O .
$$ | M . O X O . . . . . .
$$ | M M Z O O . . . . . .
$$ +----------------------[/go]

If Black is not completely alive, White can play 1 and 3 in sente. The difference with White's yose is 16 points gote. However, this value can be different depending on the strength of Black's group".

Now I am confused. It looks like White has played twice in the last diagram, contrary to the first diagram of my post. Can someone help to clarify?

This is not contrary to your rule. We are at 2b. Black is supposed to tenuki whites cut at 1 after which the follow up is supposed to be whites sente/privilege. Under this assumption the count makes sense.
The assumption is not obvious to me though. Why is it obvious black would not want to tenuki again after the kosumi(in that case it wouldnt be whites privilege)?

The sente sequence in the diagram establishes a maximum value of the position for White after the original atari. That's implicit in the text, I think.

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

Visualize whirled peas.

Everything with love. Stay safe.

What I still don't understand is the difference between Diagrams 1 et 2 below. It looks like the comparison of the two cuts is unfair. Or does it have something to do with the assumption that "Black is not completely alive" in Diagram 2?

Click Here To Show Diagram Code

[go]$$B Diagram 1 : White responds to the cut
$$ | . . . X . . . . . . .
$$ | . . . . X X . . O . O
$$ | X X X X O . O . . . .
$$ | X O O O O . . O O O O
$$ | O 1 2 . . . . . . . .
$$ | 3 . . . . . . . . . .
$$ +----------------------[/go]

Click Here To Show Diagram Code

[go]$$W Diagram 2 : Black tenukis after the cut
$$ | . . X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . X . . . . . . .
$$ | . . . . . X . . . O .
$$ | . . . X . X O O . , .
$$ | . . . X . O . . . O .
$$ | . . 1 X O . . . . . .
$$ | . . X O O . . . . . .
$$ +----------------------[/go]

In this case, Black ended in gote and has no good sente followup.


In this case, White ended in gote and has a sente followup, which we assume she will get to play by your rule 1b.

In Diagram 2 the authors are assuming that is gote and that White's next play is sente. To justify the second assumption they assume that Black is not completely alive.

Apparently they do not address the question of whether, if White's next play is sente, is also sente?

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

Visualize whirled peas.

Everything with love. Stay safe.

Indeed they don't explain why is gote. This wasn't obvious to me, probably because I don't have a good intuition of what is sente and what is not, and I overestimated the difference between tenuki and not tenuki after the cut .

Do the authors ever prove that a play is sente?

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

Visualize whirled peas.

Everything with love. Stay safe.

If you hope your opponent tenukis your move was probably sente, if you hope they answer it was gote .

Click Here To Show Diagram Code

[go]$$W Diagram 3 : White sente sequence
$$ | . . X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . X . . . . . . .
$$ | S S S . . X . . . O .
$$ | S S S X . X O O . , .
$$ | . 4 2 X . O . . . O .
$$ | a 3 1 X O . . . . . .
$$ | . b B O O . . . . . .
$$ +----------------------[/go]

OK. Let's assume that White captures with sente. Later B "a" - W "b" is sente, leaving Black with 6 pts. of territory minus 1 pt. for the captured stone = 5 pts.

If Black connects at 1 she gets 13 pts. of territory, and if the position after is White's sente, it is worth 3 pts. to White, i.e., -3 pts. to Black, then the gote value of that position is (13 - 3)/2 = 5 pts. for Black. That's exactly the same as if Black replies to for a White sente.

That means that is ambiguous between sente and gote. Black gets to choose which it is. See https://senseis.xmp.net/?Ambiguous .

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

Visualize whirled peas.

Everything with love. Stay safe.

So you skipped one step, what is the count if black answers whites cut? I get black at +5 locally.

If black connects in dia. 1; he gets +13
If white cuts in dia. 2; he can A) answer and it at +5 or B) tenuki and end at -3

So preventing the cut and responding to the cut are both 8 point moves. I think it's possible but unlikely to reach this outcome with optimal play... still it's an interesting exercise.

There is some circular logic in these sorts of sente/gote evaluations. A move is sente if it must be answered, because the answer will be the largest gote play. A move is gote unless it leaves a larger gote follow-up, in which case it was really sente

You can recursively evaluate the continuations to determine the value of a gote move. In your example, W to play will cut. Is this sente? Evaluate two branches: B responds locally to limit damage; B plays elsewhere and W gets another move. If W gets another move, presumably W will one-space jump. Is this sente? Evaluate two branches .... When a branch is clearly sente, prune away the alternate branch. When a branch terminates with a set of finished positions, evaluate those positions, and assign the average value to the parent node. Continue this process back to the original node to determine the value of the W cut in the starting position.

Finally, the sente/gote decision for the original move depends on the value of moves on the rest of the board. So your example cannot be answered in isolation. If the rest of the board contains nothing but smaller gote plays, then the W cut is clearly sente. However, if other comparably large gote moves are available, then evaluating the value of the cut and its follow-ups is reasonable. After that you will know if its gote value was indeed really comparable, and you may be able to decide whether it is sente.

Clearly there are many approximations and simplifying assumptions involved in these yose calculations. The only exact answer is to figure out optimum play for both sides for the full board position. Then at any point in the playout where the cut becomes the best move, it is sente if the best follow-up is local and gote otherwise. Exact in theory but useless in practice

Only in the sense of being consistent. See my recent posts on the operational definition of sente, starting with viewtopic.php?p=234253#p234253 . As well as previous discussions, such as viewtopic.php?t=11167 .



The values of moves elsewhere is not the only consideration. Go is hard.

The question of whether White should connect in the first example indeed depends upon the whole board. But the question of the price of not connecting does not, given the assumptions of the authors. The price can be defined locally, and is. Whether it is worth paying, however, does depend upon the whole board.



If we can do that, we do not need any theory, nor do we need any definition of sente or gote.

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

Visualize whirled peas.

Everything with love. Stay safe.

Thanks to everyone for your contributions. The book indeed never proves that a move is or is not sente. To summarize, I was assuming that the cut was sente, the book was assuming it was gote, and the calculation shows that it is neither, but whatever the assumption, the cost of not protecting the cut is evaluated at 16 points gote (with the evaluation method given in my first post).