Place black stones on the second line, white stones on the third line, like so:
Check the evaluation from KataGo (recent 28b net, Chinese rules, 7.0 komi, black to move).
Move all the stones up one step and repeat.
Plot the data.
Before looking at the hidden results below, you could try to predict: what will this plot look like? It’s pretty clear that the second line board above is bad for black, and the opposite situation (with black on line 17 and white on line 18) will be very good for black. But what happens inbetween? Will the evaluation get better and better for black as the stones move upwards, or will there be some up-and-downs? Will there be one or more positions where the evaluation is equal?
Results
The evaluation gets better for black up until line 5, then it slowly drops back down until line 14, and then it goes back up again!
(1) you place any shape made of stones anywhere on the board
(2) in simulation it moves 1 step in all 4 directions and score is estimated for each
(3) it actually moves in the direction where position is the most even
(4) do (2),then(3) again and again…
it will peak for Black when Black is somewhere about the 4th or 5th line, and then go down to nearly even when White is on the tenth line, with White having a slight advantage there. Mirrored as you continue, of course
I really like playing with zero komi since it’s easier to count, so this kind of thing could be great for setting up fair games.
Especially on 9x9, I was thinking it would be cool to have a database of opening positions that would give balanced games at zero komi for various rating differences, and we could draw from these (instead of using the normal boring handicap stones with komi added to balance it out).
These rarely used openings waste some of the first move advantage and put black only 4 points ahead instead of 7 (according to a quick OGS review). So they might be appropriate for a 2-rank handicap game.
Maybe to give white more freedom, we could pick a bad black move and disallow any response that puts black less than 4 points ahead:
I think there was a funny tournament in which the board position is unusual but considered as even by AI, was it in EGC 2019? The website disappeared so I can’t check that.
a straight inward facing wall without any defects on the 2nd line is worth 1 point of territory per stone length. This is not surprising.
a straight inward facing wall without any defects on the 3rd line is worth 2 points of territory per stone length. This is not surprising.
a straight inward facing wall without any defects on the 4th line is worth 3 points of territory per stone length. This is not surprising.
a straight inward facing wall without any defects on the 5th line is worth 4 points of territory per stone length. This is not surprising.
in the early game, a straight outward facing wall without any defects is worth 3 points of territory per stone length. This is new for me and a bit surprising. I sort of assumed it would be closer to 2 points of territory per stone length, so the graph tipping points would be at line #4 and line #15. I think this heuristic is also in some older youtube lecture that discusses how to assess the value of influence for positional judgement in the early game.
in the early game, a straight inward facing wall without any defects at progressively higher levels of the 6th to the 10th line level gradually diminishes from 4 to 3 points of territory per stone length. Given #4 and #5, this makes sense, because the distinction between outward and inward gradually blurs when the wall is progressively further away from an edge.
It’s a bit abstract to understand why it works, kindof like how it’s a bit abstract to understand why pass stones work, but even if you don’t it just works
A problem with 0 komi in area scoring is that draws are unlikely, but that could be fixed with a 0.5 point button
Both sound like a renju-like nightmare I like simpler Pie rules like Swap-5 and Swap-2
To test this further, I asked KataGo how big black’s lead is when making a straight line of stones from the 3rd line on the left to the 3rd line on the right (so 15 stones long), and white just passes while black is doing this. (I’m using Japanese rules with 6.5 komi)
Sofar it seems quite consistent with my conclusions in that post:
Wall on the 3rd line => 75 point lead = 5 points per stone (2 on the inside + 3 on the outside)
Wall on the 4th line => 92 point lead ~ 6 points per stone (3 on the inside + 3 on the outside)
Wall on the 5th line => 105 point lead = 7 points per stones (4 on the inside + 3 on the outside).
Wall on the 10th line => 90 point lead = 6 points per stone (3 on both sides)
Though apparently the 5th line is the most efficient line to build territory by nobis, it doesn’t mean that the 5th line is the most valuable line to play on in the early game. 7 points per stone is not the maximum value per stone you can achieve. Nobis are overconcentrated when there is no need to play so solidly. Overconcentration means a reduction of the value per stone.
When you keep some distance between your stones, they seem to be worth about 10 points per stone in the early game (best on the 3rd or 4th line, even better when they are close to a corner).
But keep in mind that developing by one-space jumps on the 3rd line is still a bit overconcentrated, reducing the value per stone by ~1.5 points compared to one-space jumps on the 4th or 5th line, and still even by ~0.5 points compared to one-space jumps somewhere in the center.
The 9x9 net used to generate this book has explicit training on suboptimal openings as well, even if the book was not developed as extensively for non-main lines. If you download the special 9x9 net, it also has some training on 9x9 handicap games. For example if you run a game at ~75 komi and black starting with all the 3-3 points, although it’s not fully converged, combined with high playouts it thinks that white can live, but that a fifth black stone anywhere that’s not on the first line (even on a 2-2 point) is enough that white can no longer live and black owns the whole board.
Swap-5 followed by Uwate (handicap giver) passing n turns where n is the size of the handicap? that’s the naive solution, but that doesn’t make it wrong
I like simpler Pie rules like Swap-5 and Swap-2