Start by evaluating positions, not plays. The latter evaluations follow from the former.

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

Visualize whirled peas.

Everything with love. Stay safe.

Hi Tryss, Bill, Thanks.

On the value of "c"
(Hidden for convenience.)

_________________
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, Tryss,

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

Visualize whirled peas.

Everything with love. Stay safe.

@Ed, Bill, Tryss:

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

Visualize whirled peas.

Everything with love. Stay safe.

Hi jlt,

Hi Tryss,

You may have noticed that I did not assume that White's territory was negative in these notes. I did assume that the stones surrounding the corridor are alive.

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

Visualize whirled peas.

Everything with love. Stay safe.

@ Tami

This discussion has grown quite a bit. I didn't mean to hijack your thread. If you'd like, we can move this discussion elsewhere.

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

Visualize whirled peas.

Everything with love. Stay safe.

I don't mind. It was my own fault for asking the question I'm just trying to make sense of your reply, mathematics not being my thing. Thank you very much for taking the time. It might take me some time to understand fully.

_________________
Learn the "tea-stealing" tesuji! Cho Chikun demonstrates here:

Thanks.

The math is easy: count, add, subtract, divide by 2. The first example is about gote. Next comes sente, and that's it.

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

Visualize whirled peas.

Everything with love. Stay safe.

@Bill,

I'm off to bed soon, but let me just make a quick clarification or two.

First, the evaluation of go positions and plays does not produce a general theory of the endgame. Far from it. But it is a good place to start your analysis. Doing so gives you information that will usually tell you where to play. But not always.

Second, you can use probabilities to understand this kind of evaluation. The go books do not teach that, and it is not necessary, but it is one way of looking at it. You can think of the value of a position as a kind of expected value. But you can also think of finding the average value of a position as a form of defuzzification. Historically, however, go players figured out how to evaluate positions and plays without reference to either probability or fuzzy logic.

Third, you can view the evaluation of go positions in minimax terms. I redefined go evaluation in such terms 20 years ago in my paper on the evaluation of multiple kos, which I presented at a computers and games conference in Japan. But that definition depends upon concepts that you do not need for these evaluations. That definition is algebraic. As I mentioned to Tami, all we need here is arithmetic.

In any event, we do not need to know perfect play in any sense to evaluate positions. We can use every possible line of play in a position, alternating or not. For instance, instead of playing first at the mouth of a corridor, we could start at the other end. We would then eliminate such lines of play from consideration. It makes our job easier if we know that they are wrong in the first place, but it is not necessary. We can use evaluation to find lines of play that are in some sense, correct. We do not have to assume perfect play.

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

Visualize whirled peas.

Everything with love. Stay safe.

_________________
On Go proverbs:
"A fine Gotation is a diamond in the hand of a dan of wit and a pebble in the hand of a kyu" —Joseph Raux misquoted.

@Bill:

I am still under the impression that using minimax is equivalent to assuming perfect play, but let's not worry too much about that minor point. I am more interested in what you have in mind about sente; so far we only had gote examples.

Hi Bill,