Evaluation through (hypothetical) play in the environment, III
Now let’s evaluate a slightly different position.
$$ Outer stones alive
$$ . . . . . . .
$$ . X X X X X .
$$ . . O . O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .
- Click Here To Show Diagram Code
[go]$$ Outer stones alive
$$ . . . . . . .
$$ . X X X X X .
$$ . . O . O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]
This is obviously a sente, but let’s not start with that idea.

$$W White first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .
- Click Here To Show Diagram Code
[go]$$W White first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]

elsewhere
As before, White gets 5 points locally and Black gets t0, for a result of t0 - 5.
$$B Black first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .
- Click Here To Show Diagram Code
[go]$$B Black first
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O . O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]

elsewhere
Now the result is v1 - t0, where v1 is the value of this follower.
Experienced players know that v1 = -2, and that t1 = 2. Black to play saves the

stones for a local score of 0, and White to play captures them for a local score of -4.
For the original position we have the equation,
t0 - 5 = —2 - t0
and so
t0 = 1.5.
Wait! t1 > t0 (2 > 1.5). That means that White’s reply gains more than t0, so White will reply instead of playing elsewhere.

is sente.
$$B Black sente
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O 2 O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .
- Click Here To Show Diagram Code
[go]$$B Black sente
$$ . . . . . . .
$$ . X X X X X .
$$ . . O 1 O . .
$$ . . O 2 O . .
$$ . . O B O . .
$$ . . O B O . .
$$ . . O O O . .
$$ . . . . . . .[/go]
The result after

is -4. That gives us this equation.
t0 - 5 = -4
and so
t0 = 1.
The reverse sente play gains 1 points.
The value of the original position is -4.

Note that we could have started with the assumption that the play was sente and confirmed that by the fact that t1 > t0 (2 > 1).
There is another way that we could have figured out that this was a Black sente, one I often used way back before I found out about solving for t0 and t1. I calculated the value of the position after

, which is -2 and used that to calculate the value of the original position as if it were gote. That comes to -3.5. The value if it is a Black sente is -4. White would certainly prefer it to be -4, and therefore will make it sente by replying to

.

As simple as the material in this note may seem, it is very important for understanding local sente and gote. It illustrates why we call this a one point sente. Not because, as it sounds, the sente gains 1 point, but because it tells us when each player is indifferent between playing locally or playing in the environment. (OC, in a non-ideal environment that may not be the case.

) It is the reverse sente that gains 1 point.
It also illustrates why we say that the sente player has the
privilege of playing the sente. When plays in the (ideal) environment gain less than 2 points and more than 1 point, Black may play locally with sente, while White has to wait until the plays in the environment gain 1 point or less.
It also illustrates why we say that sente gains nothing. The reverse sente gains 1 point with a play to a value of -5, which means that the original value is -4, the same as after Black’s sente and White’s reply.
The material in this note is also important because it shows us how to distinguish between local sente and gote. As I said, that was something that was never explained to me when I was learning. I had to figure it out for myself. Probably that was because there are other meanings of sente and gote, and so there was some confusion among the writers about their meaning. Before I figured out how to tell the difference, I did what I think most players do, I made an educated guess about whether a play was sente or gote and did the calculations accordingly. With some experience, that usually works, or the errors are small.
However, the calculated values in yose books are often wrong, and sometimes the lines of play are wrong, or if they are not wrong from the point of view of tesuji, they give the wrong impression of when to play elsewhere. I show an example on Sensei’s Library. here (
http://senseis.xmp.net/?YoseErrorsInMagicOfGo ) and here (
http://senseis.xmp.net/?TenukiIsAlwaysAnOption ). Very often the calculations are wrong because the play is misidentified as sente or gote. That suggests that the writer (often a strong amateur ghost writer) did not check, or did not know how to check. Now you do.

Even if the textbooks often get it wrong, that does not mean that strong players do. I remember once figuring out that a play that the textbooks said was sente was actually gote, and the next day I was playing over one of Sakata’s games, I think with Fujisawa Hideyuki, and the play came up. They played it as gote.
