No, that doesn’t sound right at all. You make it sound like there is linear growth and that all moves are sort of the same. When I hear small advantages escalate, I imagine something more like exponential growth. Small moves, early on, compound throughout chess and can lead to bigger and bigger advantages. From what I understand of go, this is not the same. Small mistakes early on are unlikely to be crippling.
Actually, as your total advantage is growing consistently, even more slowly than linearly, you should be able to say that small advantages accumulate. And similarly, they escalate as long as the growth is accelerating. In calculus terms, small advantages accumulate while the derivative remains positive, and they (also) escalate while both first and second derivatives remain positive. So now I think that my original usage suggestion is too restrictive.
Of course, if you really have a precise mathematical idea about growth, then you could just say that! So don’t read too much into anything that I say.
I think this difference is just a misstatement. One thing pounded into me from Go was how a small difference in skill can produce a dominating effect. The handicap system shows the immense differences in ‘strength’ possible—no other game lets you give up first mover advantage AND several moves and still play on a fair level on a regular basis.
Playing Go feels to me like walking a tightrope, and I’m not even dan-level yet. I would characterize it as ‘small advantages escalate’, but the score only measures a relative difference in play quality. Thus it looks linear.
Small mistakes are unlikely to be crippling for two reasons. First, at a lower level, the other player doesn’t realize how to effectively punish it, so you can get away with your mistake. At a higher level, you don’t make blatant errors (too big of an error and you resign anyhow), so when you do make an error, you have enough skill to play flexibly and partially nullify the relative effect of your opponent’s punishing moves.
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.
I didn’t realize “escalate” implied exponential growth. I am now torn as to whether advantages scale linearly or exponentially in go. It may depend on how strong the players are. (i.e., do you actually know how to punish that?) It can easily scale exponentially if the player with the slight disadvantage tries something crazy to catch up.
I don’t think early mistakes in go are less severe in an absolute sense than mistakes in chess—but go gives you more time to recover (and more time for your opponent to screw up), so relatively speaking they might be.
9x9 go is more similar to chess in that a single mistake is most likely game ending.
EDIT: having thought about this further, I think advantage in go scales linearly. Having a small advantage does not make you more likely to gain additional advantages. Assuming correct play from opponent, etc..
I don’t think that’s an improvement. As I said in another comment just now, I think that in go having a small advantage does not make you more likely to gain additional advantages.
Then why does handicapping work? Giving someone 3 stones on star points at the start of a game will have a much larger impact than giving them 3 stones on star points at the end of the game.
I finally saw your point—moves are more valuable at the beginning of the game, mistakes come at a more or less constant rate, therefore the margin of victory shouldn’t be divided up evenly into every move of the game. Yes.
I tried to put a blanket disclaimer in my post that started this thread (“There are some problems with averaging things like this which I probably don’t need to point out to you all...”) in the interest of brevity but perhaps that was a mistake.
There are problems with my calculation that yours does not solve. Namely, mistakes do not tend to be small and come at a constant rate. If I lose by 10 points it’s entirely possible that I made a single 20 point mistake and my opponent made 10 single point mistakes. (well, for example only. In reality amateurs make a lot more mistakes than that)
That said, now that I understand why you suggested it, your calculation does represent the situation more accurately.
The escalate/accumulate/linear/exponential discussion threw me off, as did the fact that I was looking for an answer expressed in points (it’s easier to visualize what that means), and the fact that I have seen this calculation done by stronger players than I am. Obviously an answer expressed in points can’t be constant throughout the game, and I should have seen that.
No, that doesn’t sound right at all. You make it sound like there is linear growth and that all moves are sort of the same. When I hear small advantages escalate, I imagine something more like exponential growth. Small moves, early on, compound throughout chess and can lead to bigger and bigger advantages. From what I understand of go, this is not the same. Small mistakes early on are unlikely to be crippling.
Suggested usage:
Exponential growth: small advantages escalate.
Linear growth: small advantages accumulate.
That makes sense to me. Upvoted.
Does it make sense to talk about chaotic growth?
Small advantages bounce around?
Actually, as your total advantage is growing consistently, even more slowly than linearly, you should be able to say that small advantages accumulate. And similarly, they escalate as long as the growth is accelerating. In calculus terms, small advantages accumulate while the derivative remains positive, and they (also) escalate while both first and second derivatives remain positive. So now I think that my original usage suggestion is too restrictive.
Of course, if you really have a precise mathematical idea about growth, then you could just say that! So don’t read too much into anything that I say.
I think this difference is just a misstatement. One thing pounded into me from Go was how a small difference in skill can produce a dominating effect. The handicap system shows the immense differences in ‘strength’ possible—no other game lets you give up first mover advantage AND several moves and still play on a fair level on a regular basis.
Playing Go feels to me like walking a tightrope, and I’m not even dan-level yet. I would characterize it as ‘small advantages escalate’, but the score only measures a relative difference in play quality. Thus it looks linear.
Small mistakes are unlikely to be crippling for two reasons. First, at a lower level, the other player doesn’t realize how to effectively punish it, so you can get away with your mistake. At a higher level, you don’t make blatant errors (too big of an error and you resign anyhow), so when you do make an error, you have enough skill to play flexibly and partially nullify the relative effect of your opponent’s punishing moves.
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.
I didn’t realize “escalate” implied exponential growth. I am now torn as to whether advantages scale linearly or exponentially in go. It may depend on how strong the players are. (i.e., do you actually know how to punish that?) It can easily scale exponentially if the player with the slight disadvantage tries something crazy to catch up.
I don’t think early mistakes in go are less severe in an absolute sense than mistakes in chess—but go gives you more time to recover (and more time for your opponent to screw up), so relatively speaking they might be.
9x9 go is more similar to chess in that a single mistake is most likely game ending.
EDIT: having thought about this further, I think advantage in go scales linearly. Having a small advantage does not make you more likely to gain additional advantages. Assuming correct play from opponent, etc..
Try redoing the calculation with geometric averaging: 300 moves, 150 of which are yours, suppose the final score is 80 to 70:
x^150 = 70, x = (exp (/ (log 70) 150)) = 1.028728
y^150 = 80, y= 1.029644
y / x = 1.00089
I don’t think that’s an improvement. As I said in another comment just now, I think that in go having a small advantage does not make you more likely to gain additional advantages.
Then why does handicapping work? Giving someone 3 stones on star points at the start of a game will have a much larger impact than giving them 3 stones on star points at the end of the game.
I finally saw your point—moves are more valuable at the beginning of the game, mistakes come at a more or less constant rate, therefore the margin of victory shouldn’t be divided up evenly into every move of the game. Yes.
I tried to put a blanket disclaimer in my post that started this thread (“There are some problems with averaging things like this which I probably don’t need to point out to you all...”) in the interest of brevity but perhaps that was a mistake.
There are problems with my calculation that yours does not solve. Namely, mistakes do not tend to be small and come at a constant rate. If I lose by 10 points it’s entirely possible that I made a single 20 point mistake and my opponent made 10 single point mistakes. (well, for example only. In reality amateurs make a lot more mistakes than that)
That said, now that I understand why you suggested it, your calculation does represent the situation more accurately.
The escalate/accumulate/linear/exponential discussion threw me off, as did the fact that I was looking for an answer expressed in points (it’s easier to visualize what that means), and the fact that I have seen this calculation done by stronger players than I am. Obviously an answer expressed in points can’t be constant throughout the game, and I should have seen that.