palapiku wrote: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:
I mean what I say, and say what I mean!
First: You may be slightly mislead by how we were reckoning things with the Elo scores above. The depth bands aren't linear in points (under the EGF system). 30k to 20k would cover 8 EGF bands of 35% probability of winning, assuming a=200 for every rank; it would cover even fewer bands if we calculated it for an average a= ~225 (the a you would extrapolate for 25k). 1k to 9d would cover 18 bands of 35% probability, at an average a=82.5. So the the latter range you chose covers about 2.25 times as much distance, whether we call that distance depth or something different.
I may be responsible for this confusion, since I'm the one who started talking loosely about the first 1000 Elo points and the last 1000 Elo points earlier in the thread. But this is, imho, an advantage of using quantitative models: even if they are not perfect, they force me to be consistent, and indicate how I should change my understanding when I get more information. In the case of the EGF, I should compare the first 2200 points to the last 1000 points (but in the FIDE system, the points are linear and a direct comparison is appropriate).
("a", for people following along casually, is a variable the EGF uses to make ranks tighter at the top and looser at the bottom.)
But anyway, I understand that your point is broader than this. "Is there the same depth between (some equivalent range at the beginning of a go player's progression) as there is between 1k and 9d?" And I would say, if we are talking about the contribution each range makes to the total depth of the game, both ranges contribute the amount amount. If we are asking whether one range is deeper than the other or if they are at the same depth, then I would say that every single point in the second range is deeper than any point in the first range, so of course the second range is deeper than the first. Is there any other coherent way of rephrasing your question about "the depth between point A and point B" that doesn't boil down to one of these?
Second: yes, I agree it's a less deep game then Go. If we treat getting more points on the go board as the moral equivalent of winning, then of course we're just playing Go (fun! deep!) and then flipping a coin at the end for no apparent reason. But if we actually care about winning go-2, and winning by a flip is as good as getting more points on the board, which is hard to imagine but that's the thought experiment you set up, then go-2 would be less deep. There would be a lot of information to assimilate, but it would be relatively less interesting than go to the tune of it not mattering in 25% of games.
(Side question: what is n such that n-go-2 is equivalent in depth to 1-go-1?)
Considering the following two games. Game one is the board game Olympics: You play one game each of go, chess, and then three other games of strategy which aren't particularly important to the example; best of three wins. In game two, you play go and chess and then you play three luck-games that are equivalent to coin-tosses. If you really think the goal is to win, which game do you consider deeper?
Third: I don't really consider that to be a game. No strategic interaction, and person-specific starting positions. Sort of like roulette salted in with feudalism. I think there should be descriptions of hypothetical games that challenge my position in various ways, though.
To answer your very first point, about seeing more lines: again, I don't think the raw number of lines or the number of lines humans can see matters if they don't translate into any ability to beat other people.
