On Mon, 2007-01-29 at 23:17 -0600, Matt Gokey wrote: > > 1. Game playing skill is a function of time. > > > > 2. Memory (or knowledge) can proxy for time - saving enormous > amounts > > of time in many cases. > > > > 3. "Technique" is a function of knowledge and how it's organized - > > which translates to a big time savings indirectly. This is really > > the ability to apply knowledge. > > > > 4. Because these various aspects of game playing ability can be > mixed > > and matched, you are sure to get very interesting intransitives. > > > > (snip) > > > > I agree this is quite reasonable and very well said. The intransitive > nature of ratings for players in complex games is evident. Much of > what > you are describing accurately reflects my understanding and explains > in > another way what I was trying to express earlier. > > Let me take this reasoning a little further. Rating systems - yes > they > are one dimensional whereas reality strength is very much > multi-dimensional. Ratings are not perfect, but do pretty good job > especially for widely disparate ratings which rarely exhibit > intransitivity. Where "widely disparate" could be defined as > whatever > rating difference is needed to achieve a, let's say, 99% win rate > between the higher and lower rated player.
It would be interesting if it would be possible to construct a 2 dimensional model statistically. A 2 dimensional system would not be a perfect fit either, but would simply be a better approximation. So in some way a players "strength" could be expressed by 2 numbers instead of 1, and the 2 numbers together would predict your chances of beating another (2 dim) player more accurately that a 1 dimension system could. And of course you could extend this. But I don't have a clue how one would construct such a system or if it's even possible - but it seems like more information should be better than less. > #1 - I completely agree with this; it is only the curve that is > different and in question for each type of player and individual > player. > > #2 & #3 - These are exactly what I was referring to and especially I > think apply in Go to a significantly greater extent than many other > games. This is primarily because there is no relatively simple and > reliable evaluation method in conjunction with the huge branching > factors and deep play. Other games mentioned such as Chess, > Checkers, > Armimaa, Othello for example have simpler evaluations that work. > > #4 - I completely agree. > > Now with regard to #2 and #3, if these can be substitutes for enormous > amounts of time, which usually must be learned over whole games and > real > experience (this is what I understand as 'enormous amounts of time'), > doesn't this support my position? When you say 'enormous amounts of > time' are you talking about a few doublings of thinking time over one > move or more like weeks or months of practice and experience and > study, > etc.? With humans, a few days of studying a position probably leads directly to becoming a better player with permanent benefits. However, I would prefer to isolate this from the picture. An inflexible but scalable program might improve with thinking time, but it doesn't benefit permanently. In other words, it won't help the program play the next game better. (But I will conjecture that a properly designed "god" program probably would be picking up skill every time it makes a move.) I believe that "in principal" you play a complete game better on the average with more thinking time and this scales naturally. Of course I went to great lengths to make the point that even in a human lifetime you don't have very many doublings to work with (that allow you to play a single game) so you cannot expect to be able to play pro level if you not just a few stones away already. And I believe that this is even worse because of the scaling properties of different algorithms, including the various human algorithms (where stronger players have a different playing algorithm in some sense of the word.) It's even stronger with computer go (and even computer chess it's true.) In computer chess, programs that run faster tend to be significantly stronger than other programs, but they seem to improve a bit less against humans. I believe there is a mathematical way to model this. I have considered trying to build a pseudo game simulation where I could specify all these factors to get a better feel for this. It wouldn't be a real game, but it would have some number of moves, a probability of making an error and a variable to determine the seriousness of the error and perhaps I could divide game playing skill into 100 different categories, so that you could abstractly create players with different degrees of skill in different areas of the game (perhaps phases of the game for instance.) A purely mathematical system where I could create intransitives and run matches etc. Perhaps some insights could be gained here. > The scalability experiment you are doing is very interesting. Though, > like I mentioned a couple times I was not characterizing any > computer-go > engines. > I wrote: > > In computer-go where there are so many wildly different > techniques > > being used, some scalable to some degree or another and some not, > it > > doesn't make sense to make generalizations. Whether a specific > > program's scalability results in any improvements (linear or > otherwise) > > with time-doubling depends entirely on the algorithms and > techniques > > in use. > > Of course we all know many computer-go programs don't scale extremely > well. MC Go (and variants) scale fairly well but probably need a lot > more knowledge and probably other methods built into them to become > good > as MoGo is showing. But this doesn't really say anything about human > play. In fact, since Go would not succumb to standard game-search > techniques, most computer-go programs used fairly simplistic models, > pattern matching, combined with some reading - roughly attempting to > emulate certain aspects of human play. But I disagree with this, Go programs DO succumb to standard game-search techniques. All the pattern matching, reading and other clever techniques are simply putting the effort where it's currently the most beneficial. Current go programs are at a stage where it's better to make the evaluation smarter and slower than to add 1 ply of search to it. If you mean they haven't got to Dan level using these techniques, of course you are right and of course go program have not succumbed to these other techniques either. It's a classic trade-off that EVEN CHESS programmers have in recently years discovered, and chess program actually started to search less deeply for a while because we realized there was more to be gained by focusing on quality evaluation. Go programs are already at the stage where the best programs have some level of global searching, so I'm not sure what you are talking about. > So I thought of another way to express some of what I was thinking. > Humans play kind of like GNU Go only lots better and can think beyond > what they've learned and learn as they play. GNU Go can't get > dramatically better by thinking longer, only modestly better. > Instead > GNU Go must learn (i.e. be programmed with knowledge/techniques - #2 > and > #3) to get that much better (no offense to the GNU Go team). To some > extent, humans are similar and may require #2 and #3 to improve > playing > skills dramatically and thus challenge a player with a "widely > disparate" rating. I think in general if you have more knowledge you scale better and more universally across styles. A brittle game program always scales wonderfully with even 1 extra ply of search, but not very well against more robust styles of play (but still better even if slight.) > So I still question the premise about doubling thinking time for > humans. > But this is just a hypothesis also - I don't know the answer, but > as > I said before simply wanted to introduce some reasonable doubt, which > any good scientist should always have... > > However, I don't think this is a pointless discussion. Something > might > be gained by understanding whether Go is by its nature in some > qualitative way different from other (perfect information) games > because > then we might use this to help focus program design on these > challenges. > _______________________________________________ computer-go mailing list [email protected] http://www.computer-go.org/mailman/listinfo/computer-go/
