Life In 19x19

The black follower can be a local gote, ambiguous, local sente or something else. The white follower can be a local gote, ambiguous, local sente or something else. The initial position of a local endgame can be a local gote, ambiguous, local sente or something else. This is so regardless of whether the black follower is a local gote, ambiguous, local sente or something else.

We know that our black follower is a local sente. We still have to determine the status of the initial local position BEFORE THE BLACK MOVE. You call the move Black 1, Bill calls it Black 4 and rushes ahead claiming it to be ambiguous. However, we need to verify that it is indeed ambiguous.

I'll give it a try. I'm sensing that I'm about to understand miai counting after all these years (or maybe I said so 10 years ago, I'm getting old in many ways)

Click Here To Show Diagram Code

[go]$$B
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O S O O X . O X X O X . X O O . . . . |
$$ | . O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X . |
$$ | C X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Let's first assume this move is local gote. We know Black's follower is a sente move with value 1. So we don't count the squared point for White while we do count the circled point for Black. The count of this position is +1

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O S O O X . O X X O X . X O O . . . . |
$$ | 3 O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X . |
$$ | 2 X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

We further simplify by assuming White needs to answer at . This time the count is -1 due to the squared point. The position has count 0 (taking the squared and circled point, here , into account) and the miai value is 1. In other words, is a 1 point gote.

Now let's check our assumption.

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O S O O X . O X X O X . X O O . . . . |
$$ | 5 O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X . |
$$ | 3 X X X O O O X X X X O . O X X X . X |
$$ | 4 6 . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

First consider that in itself was gote. The follower destroys 2 points in sente. So, Mg = (1-(-1-2))/2 = 4/2 = 2 while F = 2. So this is ambiguous. Black can choose to answer or not.

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O S O O X . O X X O X . X O O . . . . |
$$ | . O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X . |
$$ | 2 X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Next we must verify can remain unanswered, which would make a sente move. Black's follower, capturing is sente and Black can leave the ko behind. The value of that follower is 5/3 which would make White's move a 1 - 5/3 sente, which is absurd.

So, must be answered.

Click Here To Show Diagram Code

[go]$$B
$$ | . . . . O X . X X . . . X W . . . O . |
$$ | . . . O X . X O O X X . e . . , O . . |
$$ | . . . O X . O d O O . . . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | O S O O X . O X X O X . X O O . . . . |
$$ | . O X X X X O O X X X . X X O . . O O |
$$ | 1 X . . X O X X O . . O . X O O O X . |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Although technically ambiguous from White's perspective, I would call a 1 point gote, with the benefit of simplicity and not being essentially wrong.

And repeating my evaluation of F in the original diagram:

Click Here To Show Diagram Code

[go]$$W
$$ ---------------------------------------
$$ | . . . . . . X X . X 2 1 . . 7 5 6 . . |
$$ | . . . . O O O X X . X O . . 3 X 8 . . |
$$ | . . . O . O X . X X O O . . O X . . . |
$$ | . . . , O . b . . O . . O S O , X . . |
$$ | . . X . . . . O . O O O O . . X . . . |
$$ | . . . O . . . . O X X X . . . . X X X |[/go]

This is our reference, being sente and having a sente follower. We count 6 points for White here, the squared point depends on what happens in the middle.

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------------------
$$ | . . . . . . X X . X X O . . S C C . . |
$$ | . . . . O O O X X . X O . 3 1 X C . . |
$$ | . . . O . O X . X X O O . . O X . . . |
$$ | . . . , O . b . . O . . O . O , X . . |
$$ | . . X . . . . O . O O O O . . X . . . |
$$ | . . . O . . . . O X X X . . . . X X X |[/go]

Black makes 3 points here, destroying 3 of White's reference 6. The follower destroys 3 more and makes another point with 50% probability.

Mg = (6+3,5/2)/2 = 3,875, F = 3,5 so it is a 3,875 gote.

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------------------
$$ | . . . . . . X X . X . . . . . . . . . |
$$ | . . . . O O O X X . X O . . . X . . . |
$$ | . . . O . O X . X X O O . . O X . . . |
$$ | . . . , O . . . . O . . O . O , X . . |
$$ | . . X . . . . O . O O O O . . X . . . |
$$ | . . . O . . . . O X X X . . . . X X X |
$$ | . . . . . . . . X . . b . . . O O O X |
$$ | . . O . O . . . . . . X O O . . . . O |
$$ | . . . . O X . X X . C S X W . . . O . |
$$ | . . . O X . X O O X X c 1 a . , O . . |
$$ | . . . O X . O . O O . 2 . O . . . . . |
$$ | . O . O X X X O X O O . O . . . X . . |
$$ | . X O O X . O X X O X . X O O . . . . |
$$ | . O X X X X O O X X X . X X O . . O O |
$$ | . X . . X O X X O . . O . X O O O X . |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

In this reference position after Black's sente move of we count the circled point. Other border points like the squared one are likely to become neutral due to White's moves like B or C. Black's A is sente too.

Click Here To Show Diagram Code

[go]$$W
$$ ---------------------------------------
$$ | . . . . . . X X . X . . . . . . . . . |
$$ | . . . . O O O X X . X O . . . X . . . |
$$ | . . . O . O X . X X O O . . O X . . . |
$$ | . . . , O . . . . O . . O . O , X . . |
$$ | . . X . . . . O . O O O O . . X . . . |
$$ | . . . O . . . . O X X X . . . . X X X |
$$ | . . . . . . c . X . . b . . . O O O X |
$$ | . . O . O . . . . . . X O O . . . . O |
$$ | . . . . O X . X X . 6 5 X W . . . O . |
$$ | . . . O X . X O O X X c 1 S S , O . . |
$$ | . . . O X . O . O O . 2 . O . . . . . |
$$ | . O . O X X X O X O O 3 O . . . X . . |
$$ | . X O O X . O X X O X . X O O . . . . |
$$ | . O X X X X O O X X X . X X O . . O O |
$$ | . X . . X O X X O . . O . X O O O X . |
$$ | . X X X O O O X X X X O . O X X X . X |
$$ | . . . X X O . O O . X X . . . X . X . |
$$ | . . . X O O O . O X . . . . . . . . . |
$$ | . . . . X . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

If White forestalls Black's sente, she makes the 2 squared points, captures a stone and destroys the Black point circled in the previous diagram, here at Later, White C is also sente, so we can count the point under the captured stone too. The remainder of the border remains similar as in Black's sente position.

Hence this is not such a difficult move to evaluate: it's a 5 point move and Black's sente.

I found this topic yesterday. I find it hard to follow and there doesn't seem to be a clear conclusion.

It appears only Knotwilg tried to work it out. I don't mind calculating values but my critique is that calculating values for 7 different endgames is unrealistic, and for most people intuition or internalized principles are needed to reach a good conclusion. I think it is a good study so I gave it some thought too.

I'd consider this as my mainline candidate, probably informed by something I read above. Don't get your hopes up because my endgame is terrible but even worse outside of actual games, i.e. it is hard to get into the right mood and solving endgames one move at a time seems less error prone than posting sequences in chat or on forums.

Is this very wrong? Let me explain my thought process.