As a (poor) Go player, linear growth rather than exponential sounds right to me. In chess, every piece you take is a piece your opponent no longer has—death is permanent. In Go, if you lose a piece, you can hope to make up for it later. You’re down one piece, but it’s not like losing a bishop—it can be replaced*. In Go, poorer play doesn’t necessarily lead to a collapse of a figure and its complete capture, but more usually leads to simply a smaller figure. Big figures, equivalent in value to a queen, say, are almost always alive (either because they’re big enough to have 2 eyes in their own right or because they can connect outwards) and can’t be lost.
* I ignore pawns advancing to the last rank; the promotion rule can matter a lot in chess, but it doesn’t pervasively affect the whole game and rise inexorably out of the game mechanics.
In go, I don’t think of mistakes as costing me stones; I think of them as costing me chunks of territory. A mistake that puts you one stone behind can turn a large group of stones from alive to dead.
A strong group of stones can’t move across the board like pieces can in chess, so winning is localized in go. Winning one corner of the board doesn’t have a huge effect elsewhere on the board; losing a rook in chess has a huge effect everywhere.
If you lose a stone in go (as opposed to sacrificing it), you aren’t only losing territory but the group that captures your stone gets an eye.
That eye gives the group strength that can be used to attack elsewhere.
If you capture a stone and don’t get an additional eye you probably not gaining a small advantage through that move but are doing an even exchange.
I think you are being too general. But discussions such as this should happen about concrete positions; it’s too easy to talk past each other when speaking in the abstract.
You don’t really need concrete positions to discuss what gets considered as general go theory.
To take the relevant proverb, ponnuki is supposed to be worth 30 points. Of course you can find examples where ponnuki isn’t worth 30 points, I however wouldn’t consider those relevant enough to drop the proverb.
My objection to your original statement was the specificity about gaining eyes. Yes, a ponnuki is strong, but it’s not necessarily a guaranteed eye. There’s more to strength than eyes. That’s what I was trying to say and apparently failed miserably at.
I am 1d AGA FWIW. Just for fun, I feel like guessing your level based off this conversation. :) I’m guessing you’re probably between 5-10k, but 10% chance you’re weaker than that, 20% chance you’re 1-5k, and 10% chance you’re same level/stronger than me. What level are you?
Okay, I accept that point. However the main point I wanted to make is that a mistake usually not only leads you to lose points locally but also leads you to lose strength.
If the mistake would only lead to the local loss of points than I would speak about linear development. The fact that you however also get strength when you are making points (especially through actions such as capturing stones) suggests to me that the effect is larger than linear.
What level are you?
As written above I’m 1 kyu in Germany. At least that was my ranking when I played regularly two years ago.
As a (poor) Go player, linear growth rather than exponential sounds right to me. In chess, every piece you take is a piece your opponent no longer has—death is permanent. In Go, if you lose a piece, you can hope to make up for it later. You’re down one piece, but it’s not like losing a bishop—it can be replaced*. In Go, poorer play doesn’t necessarily lead to a collapse of a figure and its complete capture, but more usually leads to simply a smaller figure. Big figures, equivalent in value to a queen, say, are almost always alive (either because they’re big enough to have 2 eyes in their own right or because they can connect outwards) and can’t be lost.
* I ignore pawns advancing to the last rank; the promotion rule can matter a lot in chess, but it doesn’t pervasively affect the whole game and rise inexorably out of the game mechanics.
In go, I don’t think of mistakes as costing me stones; I think of them as costing me chunks of territory. A mistake that puts you one stone behind can turn a large group of stones from alive to dead.
A strong group of stones can’t move across the board like pieces can in chess, so winning is localized in go. Winning one corner of the board doesn’t have a huge effect elsewhere on the board; losing a rook in chess has a huge effect everywhere.
If you lose a stone in go (as opposed to sacrificing it), you aren’t only losing territory but the group that captures your stone gets an eye. That eye gives the group strength that can be used to attack elsewhere.
captured stone != eye (not always!)
eye != additional strength (not always, anyway—only weak groups need eyes, and they only need two, a third one doesn’t make them stronger)
If you capture a stone and don’t get an additional eye you probably not gaining a small advantage through that move but are doing an even exchange.
In the end game you are right that additional strength through more eyes doesn’t really exist. In the middle game it however often does.
Beginner games are a bit different because beginners often overconcentrate their stones and then an added eye won’t do any good.
I think you are being too general. But discussions such as this should happen about concrete positions; it’s too easy to talk past each other when speaking in the abstract.
You don’t really need concrete positions to discuss what gets considered as general go theory.
To take the relevant proverb, ponnuki is supposed to be worth 30 points. Of course you can find examples where ponnuki isn’t worth 30 points, I however wouldn’t consider those relevant enough to drop the proverb.
By the way, what your Go ranking?
My objection to your original statement was the specificity about gaining eyes. Yes, a ponnuki is strong, but it’s not necessarily a guaranteed eye. There’s more to strength than eyes. That’s what I was trying to say and apparently failed miserably at.
I am 1d AGA FWIW. Just for fun, I feel like guessing your level based off this conversation. :) I’m guessing you’re probably between 5-10k, but 10% chance you’re weaker than that, 20% chance you’re 1-5k, and 10% chance you’re same level/stronger than me. What level are you?
Okay, I accept that point. However the main point I wanted to make is that a mistake usually not only leads you to lose points locally but also leads you to lose strength. If the mistake would only lead to the local loss of points than I would speak about linear development. The fact that you however also get strength when you are making points (especially through actions such as capturing stones) suggests to me that the effect is larger than linear.
As written above I’m 1 kyu in Germany. At least that was my ranking when I played regularly two years ago.