krv?: I wonder if the common handicap system is adequate.
If a 1k plays with a 2k then the 2k has the first move with no komi. If the game is even, then it is fair to "share" the first move right between the partners - to throw a die, or one partner pays komi to the other. Thus it seems like this is only a handicap of half a stone. Also, 2 stones handicap is really 1.5 worth and so on. A handicap system is used on the internet servers (IGS, KGS) to calculate ranks.
Having this in mind, to make the handicap system proper, we can use reverse komi or adjust the probability of winning (if a 1k plays with a 2k and the 2k has the first move and komi is 0.5 points for white, then the probability of winning is more than 0.5 for white - but less than if they played an even game with a komi of 6.5 points).
Another question - can anybody collect stats from any server to analyze it and check if this is right?
What do you think about it?
Harleqin: Yes, this is a known issue, and at least the KGS system does indeed take this into account. I don't know about the other servers.
Velobici: AGA tournaments make use of both reverse komi and 0.5 point komi when deemed appropriate by the WinTD (Chuck Robbins) pairing program. Don't know if PyTD (Chistopher Sira) uses reverse komi and 0.5 point komi as well or not. See Tournament Directing Software.
axd: Is the assumption "2k against 1k equals no komi" correct? Where are the stats that show that the komi should be zero in that case? (And I'd like to see those stats for smaller boards too, see Handicap For Smaller Board Sizes.) Personally I'm more and more convinced that the handicap system is flawed - or only valid for a specific band of ratings (eg 30-10k? no idea.) We now do have several servers that tote thousands of games each whose outcomes could be analysed statistically to determine the correlation between ranks and komi, not only between equal-rated players; that should also confirm the existing value (5.5 - 6.5 - 7.5 ?). One of the reasons to know how far this system is correct, is to be able to say to anyone "go has an interesting handicap system that guarantees equal games" and know that is a true statement; now all I can say is "it is written so, it is believed so, someone says so". axd I begin to think that any system that takes the player ranks as inputs and then computes/outputs the number of handicaps, will equilibrate itself over time. But the system is only really good if "transitivity" works (if A receives X handicaps from B, and B receives Y handicaps from C, the system is stable if it correctly computes the number of handicaps A receives from C).
togo: The system is more than equilibrating: The level differences are defined by the handicaps. What is equilibrating is change in basic factors over time, or change from a deliberate level assignment.
The most important basic factor is the average Go-ability when playing the first game. This depends on age, education, general intelligence, other strategic games played before etc. This factor (together with some minor contributions) defines the zero point.
A second factor is the distribution of given handicaps (only zero-komi, one stone, two stones, ...). This correlates to the question tackled on this page, the inherent non-consistency, or the facet you mentioned, the transitivity. This factor equates to a mathematical scaling factor.
Please note that from a mathematical point of view komi would be the better type of handicap, because it is finely adjustable and does not change the game itself (like giving stones does). On the other hand concrete stones on the board give something to work with, are a guidance, pre-partition the board, and thus have some training capability.
Also important is the distribution across game types (for-the-win, best-play, one-hour, several-days, ...). This factor contributes to the mathematical scaling factor (and a bit to the zero point).
Another, ubiquitous, "factor" is lots of random noise from being different people and the fitness when playing a concrete game. This factor is averaged away. All-in-all it is a simple linear equation.
It might be considered an important factor at which percentage you increase your level, but that's not really relevant: You have to come around to the same percentage on the next level, so only the first level jump (or rather the average winning percentage when doing it) has some influence and it is only a minor contribution to the zero point.
The question of consistency across handicaps (non-komi, one-stone, two-stone ...) is important when the distribution changes over time, because it changes the whole scaling of the system. It might also be seen as nuisance when thinking about the right handicap for a concrete game, but in the end a concrete single handicap bias is smothered by random noise anyway far into the professional dan range. However, there might be some use in considering the type of game when choosing a handicap.
On a side note, the complete system in reality is only very loosly coupled, because not everybody plays with everybody else. This can be seen for example with the level differences between national gaming communities, which can reach several steps.
On another side note, the schemes which assign levels according to winning percentages effectivly act as a deliberate misassignment, if they are not adjusted according to winning percentages for given handicaps.