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Topic: Rating of a perfect chess player (Read 6523 times) |
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Fritzlein
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Re: Rating of a perfect chess player
« Reply #30 on: Aug 4th, 2008, 9:39pm » |
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One should never be "sure" of anything. I wouldn't bet that I was right at odds of 10 to 0, so in that sense I agree with your challenge of the boldness of my statement. But (if there were any way to test it) I would bet at odds of 10 to 1. Whatever a 23x23 board would do to the influence/territory tradeoff, I seriously doubt it would make each of the 300 decisions more obvious, i.e. less conducive to separating the more skilled from the less skilled. If anything, I suspect it would not only create more decisions, but make each of those decisions more telling, if only because there would be more choices for each play. But even if the discrimination represented in each decision were less, I could still win my bet about there being more levels of skill overall in the 23x23 game.
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| « Last Edit: Aug 4th, 2008, 9:42pm by Fritzlein » |
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aaaa
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Re: Rating of a perfect chess player
« Reply #31 on: Aug 4th, 2008, 10:18pm » |
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From what I've gathered, the mechanics actually work in the other direction; that is, as the board size increases beyond 19x19, human comprehensibility of the game (as a whole) quickly plummets to the point that between roughly equal players, it becomes much more a question of luck who wins such a game, meaning a more compressed potential skill range.
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Fritzlein
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Re: Rating of a perfect chess player
« Reply #32 on: Aug 5th, 2008, 5:18am » |
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That could be true at present without being true inherently, simply because the 19x19 game is what everyone has studied. The game of 23x23 Go might initially have fewer ranks because it is a new game, just like Arimaa didn't have many ranks in the first year it was released. Looking at some early Arimaa games you might be tempted to say the outcome was largely a matter of luck, but that was a function of our collective inexperience, not of the game per se.
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aaaa
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Re: Rating of a perfect chess player
« Reply #33 on: Aug 5th, 2008, 6:58am » |
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Don't tell me you're thinking the at-first-sight intuition about a brand new game is in any way comparable to the amount of expertise of masters of an ancient game that can be transferred to a different size with that game already having shown itself being flexibly played at different sizes in the first place?
On the one hand, the evolution of Go has shown itself to have been progressive enough to the point of the standard size having been changed from 17x17 to 19x19, while on the other, the long time that has passed since then suggests that there may be something intrinsically preferable about the current size. Although a mystic connection has been made about the closeness of the number of squares on the board to the number of days in a year, this strikes me as an ad hoc justification.
With chess on the other hand, having undergone significant changes much more recently, I think one could well make the argument that the preserving nature of modernity may well have short-circuited any potential, beneficial changes to the game as popularly played. In fact, the fact that people like Capablanca, Fischer and to a lesser extent Lasker, all legends of the game, proposed drastic changes to the game, is strong supporting evidence in this regard.
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Fritzlein
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Re: Rating of a perfect chess player
« Reply #34 on: Aug 5th, 2008, 10:46am » |
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You could easily persuade me that there is something intrinsically preferable about the 19x19 board, and that is why Go is usually played on a board of that size. But that preference probably is not an attempt to maximize the number of player ranks as defined by 75% winning chance. I wouldn't be surprised if even at a 17x17 board size the game felt rather long, and the increase to 19x19 was reluctantly made to add depth at the cost of making a too-long game even longer. Perhaps the current size is a balance between being "deep enough" but "not too ridiculously long". Just a guess.
If you ask master Go players why they don't play on a 23x23 board, and they say that there would be less strategy (incidentally, I'm curious to see your reference for this), I would indeed expect that they say this because their skills and insights don't completely transfer to the larger size, not because all of their expertise remains applicable and there would be an inherent lack of insights and skills to be attained.
I once read a quote from a Go expert who said that playing on a 21x21 board would be very difficult, i.e. openly admitting that he wouldn't know what to do. To my mind the fact that experts can be baffled doesn't show that the larger game would inherently be beyond human comprehension; on the contrary it strongly undermines the notion that the Go community somehow knows perfectly well that 19x19 creates the most strategic game possible.
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aaaa
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Re: Rating of a perfect chess player
« Reply #35 on: Aug 5th, 2008, 12:01pm » |
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It's not a question of whether amongst the best players one can set oneself apart from the others when it comes to playing larger sized boards. The question is, whether this is enough to offset the considerably confounding effect there would be on players over the entire range of possible skill levels, whose ranges between them would in terms of the players that dwell there metaphorically stretch. That is, it would become harder to improve to the point of reaching a certain winning percentage versus a fixed reference player.
It depends on your point of view whether you consider such a change to make the game more strategic or not.
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| « Last Edit: Aug 5th, 2008, 12:02pm by aaaa » |
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Fritzlein
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Re: Rating of a perfect chess player
« Reply #36 on: Aug 5th, 2008, 12:07pm » |
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My contention is the that "confounding effect" is due to inexperience only. You might as well ask a beginning player whether a 9x9 board is more strategic than a 19x19 board. Just because play on a 19x19 board is totally opaque and confusing to a beginner does not mean the larger board size is inherently incomprehensible. Therefore I believe that
Quote:| That is, it would become harder to improve to the point of reaching a certain winning percentage versus a fixed reference player. |
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would simply not be true.
Indeed, I would still offer 10:1 odds to the contrary. 
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| « Last Edit: Aug 5th, 2008, 12:09pm by Fritzlein » |
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lightvector
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Re: Rating of a perfect chess player
« Reply #37 on: Aug 5th, 2008, 11:05pm » |
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If we measure ranks purely by win percentage, then I tend to agree with Fritzlein that a larger board almost certainly means more ranks. Consider if you will, the game of N-iterated Go - play N regular games of 19x19 Go, and the winner is the player who wins more in total. Purely by virtue of involving a greater total number decisions, this will magnify any win percentage differences between players potentially many times if N is large. Essentially, we are doing a statistical sampling. A larger board size should do the same thing. More space, a longer game, more local fights, will give more room for the slightly stronger player to overcome variation and chance.
Of course, if we want to talk about levels of strategy and understanding, then this is quite unsatisfying. It is hard to argue that N-iterated Go has a greater "strategic depth" than regular Go.
In the case where we do want to measure levels of skill in terms by levels of understanding and strategic ability (whatever that means!), I wouldn't go so far as to say a slightly larger board (like 23x23) would be incomprehensible. Shape knowledge, life and death, local tactics, extensions and stone relationships, etc, would all remain completely unchanged. In fact, the great majority of playing ability is determined by 2 things: local, group-level tactics/shapes, and the ability to judge their relative urgencies.
Even larger-scale decisions remain similar - the fact that there's a few extra lines of space way *over there* shouldn't too greatly affect how one decides to handle an invasion, or extend from a wall, or secure a large area *over here*.
Together, these account for almost all of a player's strength, and none of it is fundamentally affected by board size.
A larger board would, however, radically change the flavor of whole-board evaluation and the influence/territory balance, which makes it a little hard to tell.
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| « Last Edit: Aug 5th, 2008, 11:07pm by lightvector » |
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clauchau
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Re: Rating of a perfect chess player
« Reply #38 on: Aug 6th, 2008, 3:36am » |
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There might be the same quasi-transcendental leap between 19x19 Go and, say, 723x723 Go as there is between 3x3 Go and 19x19 Go.
Someday someone will study Go on much bigger boards, probably through computers experiments. Surprising concepts and beautiful patterns may emerge. 1459x1459 Go might even be quite different from 1460x1460 Go due to some harmonics. Who knows yet.
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Janzert
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Re: Rating of a perfect chess player
« Reply #39 on: Aug 6th, 2008, 7:23am » |
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Chris Fant did a few experiments with very large board sizes last year. Here you can see the result of a random playout on a 1600x1200 board (the final single point eyes are filled in with the owners color for display). It also generated a fair amount of discussion on the computer-go list. If I'm recalling correctly there are some more playout result images buried in that thread as well.
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99of9
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Re: Rating of a perfect chess player
« Reply #40 on: Aug 6th, 2008, 4:37pm » |
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Great picture.
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Fritzlein
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Re: Rating of a perfect chess player
« Reply #41 on: Aug 6th, 2008, 5:16pm » |
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on Aug 6th, 2008, 4:37pm, 99of9 wrote:
Elmo and I just spent fifteen minutes finding faces, animals, and sundry objects in it. Do you see the camel?
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99of9
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Re: Rating of a perfect chess player
« Reply #42 on: Aug 6th, 2008, 6:13pm » |
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on Aug 6th, 2008, 5:16pm, Fritzlein wrote:
No, because I didn't spend 15 minutes finding animals in it.
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clauchau
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Re: Rating of a perfect chess player
« Reply #43 on: Aug 7th, 2008, 12:28am » |
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lol.
Cool. They do mention Go experts find 21x21 less interesting. Maybe the bigger the board, the more drawish the game, avoiding NP-complete endgames.
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omar
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Re: Rating of a perfect chess player
« Reply #44 on: Aug 7th, 2008, 9:52am » |
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on Aug 4th, 2008, 8:01pm, Fritzlein wrote:
I think the drawishness of chess does indeed crimp its depth as measured in Elo points. If we define rank as a 75% chance of winning, then we can guess how the scale would expand if chess were drawless. Between chess players who have 50% draws, but the better player wins 75% of the decisive games, it comes out to a 62.5% score, or only 89 Elo points difference instead of 191 Elo points different. So the upper end of the chess range would probably expand to have twice as many ranks if draws were eliminated. The lower end of the chess rating scale would expand less because draws are less frequent there, but it too would expand somewhat.
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Thanks for your insights on this Karl. The implications of what you have said here are really amazing.
First this mean that if draw games are included in the rating of players then the shape of the "Rating vs Draw Percentage" should start curving up very quickly and perhaphs get close to 100% at even lower rating then 4000. Only if draw games are not included in the ratings will the graph be more linear.
But perhaps the most serious implication of this is that chess ratings which include draws don't fit the ELO model. I have always thought that 200 rating points meant about 75% winning changes for the higher player. But what you are saying is that though this might be true between 1000 vs 1200 players where the draw percentage is low, a 200 point differece between a 2600 vs 2800 is actually much higher than 75% winning chance for the higher rated player. Very interesting.
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All in all, I think the assertion that Go is deeper than chess is a bit overblown. Go might be more subtle and amenable to deep insights of the human mind than chess is, but the measuring stick of ranks of depth is not as precise as we pretend. |
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So perhaps we would see much more than 13 ranks in chess if draws were not included in the ratings.
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