Life In 19x19

jts wrote:Anyway, there are few things that could be less interesting than the arcana of how a website rejiggers its rankings to keep them interesting and the resulting discrepancies, but I looked into it anyway, so there's your answer.

I can tell you: you're not the only one that looked into it

hyperpape wrote:Actually, 100 EGF is 20 kyu. AGA ranks go past 30 kyu. The systems aren't perfectly calibrated, but they're close enough that it's clear that there's a range of 20 kyus that the EGF lumps together in a single category of "players with rating 100".

An AGA 30 kyu is roughly an EGF -1000.

You can quibble about the exact numbers, but it does seem that Go has slightly more range.

If your argument that go has a greater depth than chess hinges on the 30k-20k range, then that's just not very impressive. The "depth" required to get from 30k to 20k is surely not a big selling point compared with the overall complexity of both chess and go.

Another argument: 30k-20k and 1k-9d have the same difference in ELO rank. Does that mean there's as much depth in the 30k-20k range as in the 1k-9d range?

Winning probability statistics just aren't related to depth at all.

The thing is that you're making a really selective adjustment. The 30k-20k ranges are pretty quickly passed, but so are the 300-1000 range of chess!

I would never argue that the depth of a game, measured this way, is a good measure of its goodness as a game. But it is measuring something real and important. The depth of both go and chess are extraordinary: each of them has a great many levels, such that a player of a higher level knows more (or plays better) than a player of the previous level.

That's all that it shows, but that is important, even conceding the obvious points that it's not close to being the most important thing about a game, and Herman's point that you can artificially distort the measurements, if you're enough of a smartass.

palapiku wrote:

hyperpape wrote:Actually, 100 EGF is 20 kyu. AGA ranks go past 30 kyu. The systems aren't perfectly calibrated, but they're close enough that it's clear that there's a range of 20 kyus that the EGF lumps together in a single category of "players with rating 100".

An AGA 30 kyu is roughly an EGF -1000.

You can quibble about the exact numbers, but it does seem that Go has slightly more range.

If your argument that go has a greater depth than chess hinges on the 30k-20k range, then that's just not very impressive. The "depth" required to get from 30k to 20k is surely not a big selling point compared with the overall complexity of both chess and go.

Both chess and go have blunder-ranges. I agree you don't learn much go between 30k and 20k, but that is probably true of chess between 300 Elo and 1000 Elo. (I don't know that much about the lowest ranks for chess - 1000 is still super-blunderer, right?)

More importantly, as you learn more about a game, it becomes harder and harder to improve your game sufficiently to squash your peers. In almost any game of skill, beating someone who just learned the rules 90% of the time is not at all hard. Beating that person 90% of the time takes very little familiarity with the game. Beating that third person 90% of the time requires some experience. And we go up and up and up, to the point where beating someone 90% of the time takes years and years of effort, which most people will never put in. -- So hyperpape and I don't think it's the first 1000 Elo points (which take a week or two) that are impressive, but the last 1000 Elo points, which build on three previous blocks of difficulty, each one speaking to greater depth of gameplay than the previous.

palapiku wrote:Another argument: 30k-20k and 1k-9d have the same difference in ELO rank. Does that mean there's as much depth in the 30k-20k range as in the 1k-9d range?

Winning probability statistics just aren't related to depth at all.

If I'm every going to get an intelligent answer to this, it's going to be on L19. How can this be possible? How can a game be deep without that depth translating into people more familiar with the depth pwning noobs? I'm happy to admit that a very deep game might be brand new (Redstone, anyone? ) and lack the player-base to sufficiently explore the depth. Or you could add arbitrary elements of luck into a game to make a new game with a narrower Elo range. Lots of other contingent factors like that are possible. But assuming a game has been adequately explored for a sufficiently long period of time, how could depth not translate into winning?

I'm just having trouble picturing a game where you explore the depth, learn more about the depth, have some quantitative sense of how much depth you've plumbed, but don't think that knowledge will help you improve at the game.

(Maybe we could relate this to the recent Fairbairn-Spight exchange over endgame theory. I took JF's point to be that if miai counting and all the rest don't help you win games, knowledge of miai counting is just a trivial redescription of Go (like that guy who wanted to catalog all possible dango shapes), rather than an exploration of one of its deeper caverns. It looked to me like everyone who participated in that conversation shared that premise, and disagreed about whether miai counting was an understanding of the game that leads to better play.)

Damn, succinctly ninja'ed by hyperpape.

jts wrote:Both chess and go have blunder-ranges. I agree you don't learn much go between 30k and 20k, but that is probably true of chess between 300 Elo and 1000 Elo. (I don't know that much about the lowest ranks for chess - 1000 is still super-blunderer, right?)

I've heard 1000 Elo described as a bright beginner. Maybe 17/18k EGF perhaps.

I can imagine a game that is very deep in terms of ELO score, but not interestingly deep in the relevant sense. Consider a game where people compete to do mental multiplication of very large numbers. I presume it would have a wider ELO range than even Go or Chess, but there's still something formulaic about it.

Could there be a more typical game with that feature? I'm not sure.

By the way, I earlier promised Boidhre I would do a direct FIDE-EGF translation.

As we said, Chess has approximately 26 levels where at the player at one level beats a player at the next 35% of the time (from 300 to 2800). The EGF system is slightly annoying in that they are vague about the exact value of one the variables they use in GoR, but the table from which Boidhre got 29.5% per 100 pts suggests that we're talking ~35% per 70 pts. So about 58 levels at 35%.

There are still many, many extra wrinkles. Do we adjust for draws? Do we give Chess an extra 5 levels for Rybka? But I think the basic comparison between two rating systems for different games that share a similar mathematical basis is not hard.

jts wrote:

palapiku wrote:Another argument: 30k-20k and 1k-9d have the same difference in ELO rank. Does that mean there's as much depth in the 30k-20k range as in the 1k-9d range?

Winning probability statistics just aren't related to depth at all.

If I'm every going to get an intelligent answer to this, it's going to be on L19. How can this be possible? How can a game be deep without that depth translating into people more familiar with the depth pwning noobs?

Sure. The issue is that rank is related to what we think of as "depth" in an essentially logarithmic way. Applying the same level of effort that got you from 20k to 19k will only get you from 10k to 9.9k and from 1d to 1.001d or so.

Here's a simple mathematical model. Your "strength" is some number. Your "relative strength" compared to someone else, which is related to winning probability, is your strength divided by theirs. So if your strength is 100, you are twice as strong as someone whose strength is 50. If both of you increase in strength by the same amount, you will no longer be twice as strong. Your chance of winning against them will decrease.

This model is obviously oversimplified, but if you imagine that "strength" represents, for example, the number of hours spent studying go, then it's not that far off. The point is that additional strength gives a smaller advantage when you are already strong.

So we are talking about the essentially linear "depth", but all the evidence we have is from the essentially logarithmic ranks. The same range in ranks may correspond to very different ranges of depth. The problem with converting from one to the other is that we don't have reasonable endpoints. Near the very beginning of the scale, every tiny increase in strength corresponds to gigantic increases in rank, so it's very hard to establish the starting point for rank. This is the reason some go ranking systems start at 30 and others at 20 - both numbers are more or less arbitrary. The number of 100 or 300 for a beginner in chess is just as arbitrary.

At the other end of the ranking scale, we have the opposite problem. Every tiny increase in rank corresponds to gigantic increases in strength and depth. There may be incomprehensible depth between 10d and 10.0001d, and we'll never know.

So simply comparing the rank ranges means ignoring two problems - one, the rank systems don't have a good starting point. Two, we need really good accuracy to capture the depth that's mostly contained at the upper end of the ranking range.

Okay, I misunderstood your point. I'm mainly interested in whether it makes sense to compare games (as in, "I know Go sounds like random game with simple rules, but it's actually much deeper"). I understand that the first step in what you call "relative strength" involves absorbing much less information/ trivia/ experience etc. than the last step. But this is (presumably) true for all games. So comparisons between them all assume something equivalent (that a game is being credited both with an initial level of depth where players avoid blunders, and a final level of depth where players get very close to knowing everything a human being can know about the game).

As for the question about where in the learning curve of a game we find the most depth doesn't really interest me, partly because it seems bound to be muddled up, partly because I'm skeptical that what you call "strength" (and which I might call "effort" or something like that - strength as an absolute quality is a pernicious idea) has such a strong connection to depth.

You might compare the effort of learning a game and the game's depth to the effort of preparing for a mountain trip and the elevation. The difficulty of mountain climbing may go up faster than linearly as you try to climb to higher elevations, but it would be perverse to call your position on the mountain "relative elevation" and the amount of work that went into the climb "elevation".

jts wrote:So comparisons between them all assume something equivalent (that a game is being credited both with an initial level of depth where players avoid blunders, and a final level of depth where players get very close to knowing everything a human being can know about the game.

Maybe you need to clarify what exactly do you mean by depth. Otherwise I interpret this as follows: at one end of the scale you have complete beginners. At the other end, you have extremely talented people who have dedicated their lives to the game. Since the extremely talented people are still far from perfect play, the game itself is not the bottleneck as far as depth goes. Therefore, all such games (this certainly includes go and chess, but also almost every other board game) have the exact same depth, which is simply the general human analytical capacity to comprehend board games. The extra depth which may be inherent in the game is irrelevant, as it's not accessible to humans.

What's depth?

jts wrote:The EGF system is slightly annoying in that they are vague about the exact value of one the variables they use in GoR

http://senseis.xmp.net/?EGFRatingSystem is pretty comprehensive.

HermanHiddema wrote:

jts wrote:The EGF system is slightly annoying in that they are vague about the exact value of one the variables they use in GoR

http://senseis.xmp.net/?EGFRatingSystem is pretty comprehensive.

Thanks! Embarrassingly, all those values of a are also on the EGD page, as well. It seems they use the formula a=205-(GoR/20), but it's not clear whether they think this formula extrapolates below 100 or above 2700.

Recalculating, we get ~48 levels of depth at 35%, or 40 levels if we assume that a should be as high as 255 and as low as 60.

palapiku wrote:

jts wrote:So comparisons between them all assume something equivalent (that a game is being credited both with an initial level of depth where players avoid blunders, and a final level of depth where players get very close to knowing everything a human being can know about the game.

Maybe you need to clarify what exactly do you mean by depth. Otherwise I interpret this as follows: at one end of the scale you have complete beginners. At the other end, you have extremely talented people who have dedicated their lives to the game. Since the extremely talented people are still far from perfect play, the game itself is not the bottleneck as far as depth goes. Therefore, all such games (this certainly includes go and chess, but also almost every other board game) have the exact same depth, which is simply the general human analytical capacity to comprehend board games. The extra depth which may be inherent in the game is irrelevant, as it's not accessible to humans.

What's depth?

In general, the depth of something is how many measuring-units deep something is, from the surface down. A pool might be 10' deep, the Marianas Trench is 11km deep, and so on. Now, obviously we aren't talking about physical depth - if we were, go would be deeper on a floor board than on a table board, and Herman's 3-go might be as many as 18 sun deep! I assume we are talking about depth of strategy or of game play.

A shallow or superficial game is one where a line of play that appears reasonable to someone who knows nothing about the game other than the rules actually is reasonable. (And likewise, the lines that appear unreasonable actually are unreasonable.) A game is less shallow if, lurking below the line that appears reasonable from the surface, there is another line that appears reasonable to another player who has thought more about how to win, and the more such lines that are hiding under one another, the deeper the game is. As I've probably made clear, I think the proper measuring-unit is bands of mastery such that there is a constant winning percentage between people at the top of one band and the top of the next band.

As you say, the maximum amount of effort someone can devote to any game is (a good chunk of) a human life. I don't think this has too much to do with depth. This would be sort of like measuring the height of a mountain by the weight of a hiker's backpack, or the depth of swimming pool by the number of rungs leading up to its diving board. You can see a connection between these things, but just as you can overpack for hiking, you can lavish effort on a comparatively shallow game. I can see the point that learning to play a ladder-breaker is a comparatively dull accomplishment compared to some of the exquisite tesuji that pros find, but I think it's equally important to realize that a high-dan player knows dozens of things about the game that collectively contribute less to his finding winning sequences than a 15k's shaky grasp of ladders and nets contribute to his.

jts wrote:A shallow or superficial game is one where a line of play that appears reasonable to someone who knows nothing about the game other than the rules actually is reasonable. (And likewise, the lines that appear unreasonable actually are unreasonable.) A game is less shallow if, lurking below the line that appears reasonable from the surface, there is another line that appears reasonable to another player who has thought more about how to win, and the more such lines that are hiding under one another, the deeper the game is.

Sorry, but this tells me very little. It also doesn't seem to contradict my point above, which is that depth is limited by the human ability to "see more lines".

As I've probably made clear, I think the proper measuring-unit is bands of mastery such that there is a constant winning percentage between people at the top of one band and the top of the next band.

This, on the other hand, is awfully specific. You don't show how or why this is related to what you say above. You also ignore a number of arguments people in this thread have brought up against using ranks (which is another word for "bands of constant winning percentage") for anything more than ranks. By this point I'm not sure that you really mean to say what you are actually saying. Let me restate the arguments:

* So you think there's the same depth between 30k and 20k as there is between 1k and 9d?

* Consider a new game, Go 2.0. In Go 2.0, we first play a game of go, then half the time the winner of the go game actually wins, and the other half we just flip a coin to determine the overall winner. This game has much fewer "constant winning probability bands" than Go does. So you think it is much less deep than Go?

* Consider a game where everyone in the world is randomly pre-assigned a number from a vast range. Whenever two people meet, they just ask a computer and it picks a winner with the probability based on the ratio of their numbers. That's all there is to this game. Because the numbers chosen can be very different, there's a large number of "constant winning probability bands". Do you think this game has a large depth?

With your definition being as specific as it is, you can't just brush these arguments aside. I suggest you think more about what you think depth is and why it should or shouldn't be related to winning probability. Personally I see no reason why winning probability is at all related to something like what you are describing above about lines lurking beneath the surface.

palapiku wrote: Since the extremely talented people are still far from perfect play, the game itself is not the bottleneck as far as depth goes. Therefore, all such games (this certainly includes go and chess, but also almost every other board game) have the exact same depth, which is simply the general human analytical capacity to comprehend board games. The extra depth which may be inherent in the game is irrelevant, as it's not accessible to humans.

This really says it all to me. It's meaningless to try and compare the depth of things that are far deeper than we're capable of comprehending.

jts wrote:As you say, the maximum amount of effort someone can devote to any game is (a good chunk of) a human life. I don't think this has too much to do with depth. This would be sort of like measuring the height of a mountain by the weight of a hiker's backpack

It would be more like measuring the height of a mountain by how high up it hikers can get. Saying a game is deeper because it has a wider ELO range is like saying a mountain is taller because hikers get higher before giving up/dying.