Life In 19x19

It would be easy to play the biggest move if we knew the value of each move. To help with this, I'm compiling a list of move values in the opening.

Naturally, this is only an approximation. I used the following method:
A situation is a board and a turn state, while a position is simply a board.
The value of a situation is the estimated score for black plus the komi.
Situation values are assessed by KataGo after adjusting the komi to make the win rate nearly 50% (I believe this results in better accuracy).
The value of a position is the average of the values of the situation with black to play and the situation with white to play.
The miai value of a move is the difference in value between the positions preceding and following the move.

This may differ from the standard definition of miai value. Let me know if you can think of a better method. I won't know for sure until actually compiling a list and trying it out, but I think this method does a reasonable job of satisfying these criteria:

The calculated value of a move is not affected much by seemingly unrelated parts of the board
Given two moves, each of which is KataGo's favorite move in its respective local region, KataGo should globally prefer whichever move has the highest calculated value

It's not obvious that will be true, since my calculation method discards information about the order of play. However, I believe this compromise was necessary in order to satisfy , which makes memorizing these move values practical.

I'll be slowly adding moves to this post. I'll also edit in any helpful contributions that may appear in responses.

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[go]$$Bc 15.69
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . 1 O . . . . |
$$ , . . . . X , O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 15.18
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . O X 1 . . . |
$$ , . . . . O , X . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 14.22
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . O O . . . |
$$ , . . . 1 X , . . . |
$$ . . . . . . . X . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 14.14
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . 1 X . . . |
$$ , . . . . O , . . . |
$$ . . . . . . . O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 13.94
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . 1 . X X . . . |
$$ , . . . O O , . . . |
$$ . . . . . . . O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 13.82
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . O . . . |
$$ , . . . . 1 , . . . |
$$ . . . . . . . X . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 13.64
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . 1 . . . . |
$$ , . . . . O , X . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 13.15±0.02
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . 1 . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 13.11
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . X O O . . . |
$$ , . . . 1 X , O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 12.99
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , 1 . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 12.83
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . O X X . . . |
$$ , . . . O O , X . . |
$$ . . . . . . . . . . |
$$ . . . . . . 1 . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 12.78
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . 1 . . |
$$ , . . . . . O . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , O . . |[/go]

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[go]$$Bc 12.75
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . 1 , O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 12.68
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . 1 . . . |
$$ , . . . . . , . . . |
$$ . . . . . . . O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 12.65
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . 1 . . |
$$ , . . . . . O . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 12.45
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |
$$ . . . . . . . 1 . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 12.36±0.10
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . O . . . . . |
$$ , . . . . . X . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . 1 . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 12.35±0.10
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . O . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . 1 . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 11.92
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . O . O . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . 1 . . |
$$ , . . . . . , . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . O . O . . |
$$ . . . . . . . . . . |
$$ , . . . . . X . X . |
$$ . . . . X . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ --------------------[/go]

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[go]$$Bc 11.89
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . X . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . 1 . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 11.83
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . X . . |
$$ , . . . . X , O 1 . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

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[go]$$Bc 11.82
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . 1 . . . |
$$ . . . . O . . . . . |
$$ , . . . . . X . . . |
$$ . . . . O . . . . . |
$$ . . . . . . . X . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

Click Here To Show Diagram Code

[go]$$Bc 11.78
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . O . O . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . 1 . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

"The value of a position is the average of the values of the situation with black to play and the situation with white to play."

No. This is so only for gote endgame positions.

"The miai value of a move is the difference in value between the positions preceding and following the move."

No. This is NOT the move value but it is the (absolute value of the) "gain".

Let's assume that we have a normal whole board position, P, with a mean value of m and a temperature of t. t is equal to the miai value of a correct gote or reverse sente. (The miai value of a sente is the same as the miai value of its reverse sente, but this can be confusing when people think that the sente gains its miai value. It does not.)

All calculations will be from Black's perspective.

The minimax result after Black plays first in P will approximately equal m + t/2, and the minimax result after White plays first will approximately equal m - t/2. The average of those two results will approximately equal m. The absolute difference of those two results will approximately equal t.

As we know, bots do not play to optimize minimax values, but to optimize winning percentages. IMO the best estimate of a minimax result is the one that produces the winning percentage closest to 50%.

So far, so good, but we have not addressed specific plays. If the miai value of the specific play is equal to the temperature of the whole board, there is no problem. What if a gote or reverse sente has a miai value, g, which is less than t? Then the minimax result for Black, starting with that play will approximately equal m + g - t/2, which is the sum of g and the approximate minimax result for White on the whole board. If the play is a sente, then the reverse sente will normally have a miai value less than g, which will also be the miai value of the sente.

What if a Black play gains more than t? If it is a sente, then normally the reply will gain the same amount, and the minimax result will be approximately m + t/2. If it is a gote or reverse sente which reverses and is not correct play, then it is uncertain what the minimax result will be.

But suppose that P is not a normal whole board position and after the initial play gains t0, the whole board temperature drops to t1 and the new board is normal? Such positions can happen. Then the approximate minimax result of the play will be m + t0 - t1/2, which will approximately equal the sum of its miai value, t0, and the minimax result for White after the initial play by Black.

I think that humans should try to come up with a theory that explains these values. Or at least in comparison to each other.

The key concepts are local shape, assuming high temperature forcing exchanges, with miai on the rest. And then include value of attack which depends on number of moves required to live and the value of attacking moves, with the more subtle mitigating defences.

For example, in the first example, the move is basically sente (as it threatens another say 8 intersections and mutual eyespace in reverse sente. We need to double for the gain as W turns into B). Then if we assume that the wall needs to make eyes, and subtract W's most severe attack, perhaps B expects no local territory (after discounting W's attack). Then if we just assume one line of "force field" around B has around 4 stones after connecting (due to endgame on the corner) and 6 neighbours. After a W move (in gote), these would basically be W potential because although a cut exists, W is very alive. Finally, we need to add the extra points on the right due to W not being alive. Basically W expects to add another tight 3rd line move which perhaps gains just a 2x3 block compared to the full value of a move which should be 14 stones. If this gote is halved, and the reduction of B's influence is added (say 2), perhaps this comes to another (14- 6-2)/2= 3 stones.

This is a total of 4+6+3=13 stones gain. I think the rest comes from the fact that B wouldn't be settled otherwise. Though that depends on whether your values come from territory or area scoring (passing makes a difference between these systems).

In the opening it is not about the biggest play. It is about steering the game.

I do not care to loose half a point, if I am able to play the game my way.