That some “horns” have a threshold beyond which the standard diminishing returns formula is the wrong way to think about it, and that once this threshold is crossed you open up a whole slew of new parameters to toy with, as if you’d just started on something entirely new (which is often the case in some sense).
(paragraphs 1-2) This idea that there’s a transition point where suddenly returns start increasing appears nowhere in the physical instance of a powder horn (when you finally turn it over, do you get even more powder than your first easy scoop?) which even implies that returns will hit zero the instant after you turn over the horn (because now the horn is completely empty).
(paragraphs 3-4) OP then claims that some things aren’t horns because there is some transition effect where returns suddenly start increasing with more investment. But the claim comes off completely flat because exactly one example is given, and a pretty dubious one at that.
Basically, the guy who stopped trying to learn more about poker rules because he saw diminishing returns and never pushed forward enough to “get” the things that lead to counting cards and deception and metagame will have missed out on the point of poker entirely.
Those may be interesting and complex, but your description matches up fine with diminishing returns.
At least, if I’m interpreting the main article correctly, there are some fields of knowledge which behave in a similar fashion, and we might benefit from having good heuristics for figuring out which fields will behave like this so that we can improve our research efficiency… or something.
At this point in the discussion, I think we would benefit more from establishing that there are such fields at all.
Yes, all good points, but one minor bump when I read your comment:
Those may be interesting and complex, but your description matches up fine with diminishing returns.
I don’t quite understand what you mean. Given that an agent values having the kind of fun given by playing poker on more advanced levels, I do see a point at which poker suddenly starts generating more fun-returns for each unit of learning-to-play-poker, just before which diminishing returns still applied.
Then a bunch of increments give high value before diminishing returns start being apparent again, at which point there may or may not be more deviations from the standard pattern (I’m not aware of any personally, I have some minor evidence that there might be one more “boost” point).
So yeah. If you’d care to explain how this actually matches with standard diminishing returns theory, I’d be curious to learn about it. If I imagine plotting what I observe of poker-learners on a graph and what a standard diminishing returns model would predict, I don’t see the same curves at all.
Diminishing returns doesn’t mean that you can’t get more out of additional investment—that’d be ‘zero returns’, after all. But the returns you get out of each additional increment of investment will be less than the previous returns. The thrill you get from your first poker game where you successfully bluffed your way to victory is greater than the ‘return’ you get millions of hands later from noticing that you are bluffing a decimal point too often, or whatever. (I don’t play poker, so I don’t know what the relevant examples would be.)
Besides utility, you could also express it in terms of expected value or winning probability; since poker is partially random, there’s always going to be a limit on performance where even the best player will lose, and initial skill gains will move you closer to that limit than later refinements of computer modeling or whatever. Think Pareto.
Hmm. I’m not sure whether I’m confused about this, or whether I didn’t adequately express the theoretical value unit I was picturing.
If I naively picture the cost as a flat “number of rules or tactics learned”, and the returns as an ideal “fun-value per hand played”, then for most people there’s going to be a “spike” at some point where the fun-value-per-tactic goes up much faster than it should at that point in the graph, almost as fast (if not faster) as the first few increments at the very beginning.
Depending on how saturated the new player is with low-complexity gameplay value (and the diminishing returns thereof), it might even be that the curve actually accelerates up to that spike, and after the spike finally starts looking more like a diminishing returns graph.
I suppose there could be spikes like that—if one knows n-1 rules of chess, it’s not fun at all, while at n rules one can actually start playing. But I don’t know of any games where this spike would come after, say, months or years of practice.
Any game where increased playskill changes the shape of the tactical space, I’d think. For example, Street Fighter 2. Yeah, the arcade game.
It’s easier to show than tell, but basically there’s a strategy, made up of grabs and weak attacks, that’s easy to execute but hard-ish to defend against. Two players who are skilled enough to use that strategy but not skilled enough to defeat it will find the game degenerate and boring, but once they’re skilled enough to get past that gate they’ll find a space of viable tactics that’s a lot broader and more engaging.
Yes, this is a very good example. The street fighter games change completely in landscape once you get past several key difficulty walls, each of which can require months of training or more for people not already adept at the genre.
fezziwig gives a pretty good example; the Street Fighter series in general can be considered to have an uncommonly high number of instances like this.
However, with that said, I agree with your earlier statement that the question is whether there really are any fields of knowledge that behave like this (and would be useful to us), or if it’s dependent upon key patterns of game logic and none of those patterns are present in nature, or some other explanation that makes these cases too limited in scope to be worth exploring the way I thought the OP was suggesting.
(paragraphs 1-2) This idea that there’s a transition point where suddenly returns start increasing appears nowhere in the physical instance of a powder horn (when you finally turn it over, do you get even more powder than your first easy scoop?) which even implies that returns will hit zero the instant after you turn over the horn (because now the horn is completely empty).
(paragraphs 3-4) OP then claims that some things aren’t horns because there is some transition effect where returns suddenly start increasing with more investment. But the claim comes off completely flat because exactly one example is given, and a pretty dubious one at that.
Those may be interesting and complex, but your description matches up fine with diminishing returns.
At this point in the discussion, I think we would benefit more from establishing that there are such fields at all.
Yes, all good points, but one minor bump when I read your comment:
I don’t quite understand what you mean. Given that an agent values having the kind of fun given by playing poker on more advanced levels, I do see a point at which poker suddenly starts generating more fun-returns for each unit of learning-to-play-poker, just before which diminishing returns still applied.
Then a bunch of increments give high value before diminishing returns start being apparent again, at which point there may or may not be more deviations from the standard pattern (I’m not aware of any personally, I have some minor evidence that there might be one more “boost” point).
So yeah. If you’d care to explain how this actually matches with standard diminishing returns theory, I’d be curious to learn about it. If I imagine plotting what I observe of poker-learners on a graph and what a standard diminishing returns model would predict, I don’t see the same curves at all.
Diminishing returns doesn’t mean that you can’t get more out of additional investment—that’d be ‘zero returns’, after all. But the returns you get out of each additional increment of investment will be less than the previous returns. The thrill you get from your first poker game where you successfully bluffed your way to victory is greater than the ‘return’ you get millions of hands later from noticing that you are bluffing a decimal point too often, or whatever. (I don’t play poker, so I don’t know what the relevant examples would be.)
Besides utility, you could also express it in terms of expected value or winning probability; since poker is partially random, there’s always going to be a limit on performance where even the best player will lose, and initial skill gains will move you closer to that limit than later refinements of computer modeling or whatever. Think Pareto.
Hmm. I’m not sure whether I’m confused about this, or whether I didn’t adequately express the theoretical value unit I was picturing.
If I naively picture the cost as a flat “number of rules or tactics learned”, and the returns as an ideal “fun-value per hand played”, then for most people there’s going to be a “spike” at some point where the fun-value-per-tactic goes up much faster than it should at that point in the graph, almost as fast (if not faster) as the first few increments at the very beginning.
Depending on how saturated the new player is with low-complexity gameplay value (and the diminishing returns thereof), it might even be that the curve actually accelerates up to that spike, and after the spike finally starts looking more like a diminishing returns graph.
I suppose there could be spikes like that—if one knows n-1 rules of chess, it’s not fun at all, while at n rules one can actually start playing. But I don’t know of any games where this spike would come after, say, months or years of practice.
Any game where increased playskill changes the shape of the tactical space, I’d think. For example, Street Fighter 2. Yeah, the arcade game.
It’s easier to show than tell, but basically there’s a strategy, made up of grabs and weak attacks, that’s easy to execute but hard-ish to defend against. Two players who are skilled enough to use that strategy but not skilled enough to defeat it will find the game degenerate and boring, but once they’re skilled enough to get past that gate they’ll find a space of viable tactics that’s a lot broader and more engaging.
Yes, this is a very good example. The street fighter games change completely in landscape once you get past several key difficulty walls, each of which can require months of training or more for people not already adept at the genre.
Thanks for the good example.
fezziwig gives a pretty good example; the Street Fighter series in general can be considered to have an uncommonly high number of instances like this.
However, with that said, I agree with your earlier statement that the question is whether there really are any fields of knowledge that behave like this (and would be useful to us), or if it’s dependent upon key patterns of game logic and none of those patterns are present in nature, or some other explanation that makes these cases too limited in scope to be worth exploring the way I thought the OP was suggesting.