Is there any formula or rule ( or table ) for determining a komi between two players of any strength? Assuming that no handicap is used. The players might be 15kyus or dans or pros. I'm looking for a way to get a competitive game, regardless of relative strength, using only komi.

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I don't think so, and it depends very much on time controls.

My experience is 15 points in blitz, 10 points in non-blitz real time games, and 6 or 7 in correspondence based games per stone difference in strength.

My limited non-blitz experience has 10 points/stone being about right as well.

I believe it is not possible to trade handistones with komi.

With territory rules:

Dan difference Reverse komi
-------------- ------------

1 6.5
2 20.5
3 34.5
4 48.5
5 61.5
6 74.5
7 87.5
8 99.5

I wouldn't trust anything beyond that, and I would not expect precision, anyway. As komi increases, the difference per dan reduces, but nobody really knows how.

Also, komi should reduce with the strength of the White player, but nobody really knows how.

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I think that it is logically necessary that this is true. If player A plays player B with no handicap, there will be a result, and that result - assuming nobody resigns - can be quantified. That quantity is komi. As a practical matter, large numbers of games could be played to get a good average.

If you mean that it is not possible to trade at a fixed ratio, I'd agree.

I'm not suggesting that it is a simple formula, that we could say that "one handical stone = 14 komi". A stone may be worth 15 points when a pro uses it, less when you or I use it, and totally squandered by a 30K. I strongly suspect that such a formula would not only have to take into account the relative strengths of the players, but their absolute strength also. ( That is why the initial question mentions a table )

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In Kage's chronicles of handicap go, both players make comment (Kogeyama and his opponent for most of the games) agree a 3 stone handicap would be expected to lead to a 30 point difference. Their 5 stone games left me with the impression that 50 was about accurate - there isn't much data to go with here, but I suspect it isn't 15 points per stone equivalent at professional level if these games are anything to go by.

Everything depends on probability of winning given two ranks. That's how things work in tournaments with handicap games since ranks themselves are based on probability of winning. A "proper" handicap in theory would make probability of winning equal 50%. I think that's the best you can hope for with reverse komi. Because it is a probabilistic thing the formula will never be correct for any particular pair of players. We all know of people who can force weaker players to take a higher handicap than the rank difference would assign. It is also recognized that stone handicaps aren't really linear with rank difference.

The only way to get an approximation formula would be to have a database of thousands of even games, played out to a numerical result, between players of all different ranks. Even games because the reverse komi is supposed to compensate for rating difference in even games. With such a database some kind of multivariable regression or contingency table analysis might yield a useable formula. The trouble is in general we don't play even games when ranks are very different and in practice too many of these games would end in resignation.

You cannot simply average the score outcomes, because the playing style is dependent on who is leading and by how much. You need to set a komi before the game, then play a large number of games to gather the winning percentages; set a different komi, repeat.

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A good system naturally covers all corner cases without further effort.

And if you have two pairs of players which are evenly matched with n handicap this does not mean they are evenly matched with m komi. It depends a lot on the play style.

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Note that Jonas' location is Germany, so English is probably not his native language. I don't think we can take that statement literally in English. I think that he means that it is not possible with a simple ratio.

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The estimate of 10 pts. per stone dates to the time when komi was 4.5. Each stone difference is approximately worth twice komi, at least at first. Now that we know that komi is larger, so is the approximate size of the difference.

Edit: Back in the 70s I analyzed some pro-pro handicap games (admittedly a small sample) and found an average difference per stone of about 13.5 points through 9 stones. That's when I predicted a komi of 6.5 by the turn of the century. Almost!

BTW, I once gave 100 pts. reverse komi instead of giving 8 stones. I won by about 100 points.

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I expect it is quantifiable. Between two particular players, the ability, usually black's, to take advantage of the advantage may differ, but so does the ability to use handicap stones.

I simply think it is not a useful idea. Fun perhaps, but not useful.

If a weaker player wants to work on even game opening - then play an even game opening. An opening where a strong player is trying to make up 50 points is not an even game opening.

If a weaker player wants to work on fighting - then fight with handicap stones - the techniques learned are valid in even games. You still have to deal with strong attacks on weak stones, but you also get to attack from strength against strong responses - something you cannot set up in an even game.

Playing to coast out a huge komi teaches you very little, certainly not as much as other methods.

It can teach you how to count, I think. For players that usually don't count, knowing they have a reverse komi advantage might make them start counting.

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The score is the score, if they do not count in games when they receive normal komi, why count when you have reverse.

Better to tell the weaker player - "If we finish and count a game and you are losing by more the 20 - then (insert punishment). In a club when weaker players are competing to play the local strong guy, this method of encouraging timely resignation teaches counting and adds efficiency to the teachers time.

Sry I hadn't much time when I wrote my posting You're right, my choice of words wasnt the best.
I think it is very problematic to allocate a certain komi value to a handicap stone, because (afaik) there is no reliable data available. I'm sure the value of a handicap stone differs from person to person and it would need a large-scale analysis to determine the correct values.

I've visited many go clubs in germany in the last two years and every club seems to have different "rules" when it comes to the trade handistones - komi.
F.e. my local club in Osnabrück plays with 8 Komi for each handicap stone, the results show that this (sometimes more sometimes less) fits. Another club I visit rarly is located in the Ruhrgebiet (urban center in west germany) and there a 12 point komi, decreasing every stone by 1 point, is familiar.

If take the normal handicap rules the first handicap stone reduces whites komi to 0 or 0.5, which means the first european handicapstone has a value of 6 or 6.5, an american handicap stone has a value of 7 or 7.5 etc.

Personally I find it very hard to win by more then 50 points while not killing anything super big. I've played many 5 or 6 handicap games which I won without giant-killing, but I'm pretty sure that I wouldn't win with more then 30 points if I play a serious game against one of my opponents, simply because my play calms down when I see that I'm leading. The other option is, that I try to kill as much as possible without thinking that I've already won the game which results in a win by more then 80 or 90 points (have tried it at my local go club), because the missing security of the handicap stones enables me to kill half of the board.

Hmmm this leads to a rather complicated discussion ^_^

A few thoughts:

1) Most strong players I talk to say that the point amount by which win/lose is meaningless and says nothing about respective strength. I also think so.

2) Like with handicap, beyond certain rank-difference threshold, I don't think such considerations are meaningful. Say I can probably kill every stone on the board in an even game against a 15k for example. Same thing against every player of lower rank. Where does this leave us?

3) I can probably beat a 1d player as consistently as I can beat a 3k player in even games. And possibly by the same margins.

4) I can consistently beat one player by a different margin that I consistently beat another player of the same rank. Its a matter of personal 'style' for the lack of a better word.

5) The big difference between handi and komi is that handi has a much greater influence on determining your strategy than komi. So its hard to apply formula to convert one to the other.

6) Rank is defined by handicap, not komi, so this also presents a challenge once we agree that these two systems are not necessarily strongly related. It might be possible to devise a system based on komi instead., I dunno...

7) Even rank based on handicap can be very inexact, especially when dealing with two distinct groups of players.

8) At different levels, the size of the result is more or less random. A pro beating another pro by 20 points might mean something. A 10k beating another 10k by the same 20 points might mean nothing at all.


What does this all mean?
Well... it means that I don't have a formula, complicated or not.
It also means that I do not think finding a decent formula is possible.

Other than this, I'd give about 30 stones for each 2 levels of difference and see what happens.
As with handicap, you can add/subtract 10 or 5 points after each game depending on the result, so eventually you'll find your range against a specific opponent.

PS. Why not just play with proper handi?

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Well, then why don't we start out with this and if people want to experiment with it it can be adjusted based on experience:

W rank Komi/stone (rank difference) equivalent
30k-20k 8
19k-1k 10
1d-3d 11
4d-9d 12
1p-9p 13
4p-9p 14

Note that this is intended for 2+ stones. 1 stone (rank) seems to be handled decently by no komi.

This is based just off of W's rank since they'll be the one needing to make up the difference (change the sign however you see fit). Also based on rough estimates of "standard" equivalent in my area, Bill's pro v pro fingures above, and trying to remember what it was like with handi stones back when I was 20+k. To do this really well, you'd need to account for both W & B's rankings and the fact that lower kyu games will have many more blowout scores (100+ point wins) than higher ranks.

Comments, willing testing volunteers, mocking laughter, etc?

Bruce "Motion tabled" Young

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Yes.
As you say - nothing is perfect. This is why we need to play games rather than simply determining the result by looking at the ratings.



I am not sure if big komi or negative makes the game more 'stimulating' to stronger players. Maybe it does.

Personally, I like the idea I call 'Irish Handicap'.
It involves stronger player making some suboptimal or outright bad yet intriguing moves until he feels the game is interesting. Can be applied many times during the game. The advantages of such systems which I like are that the game can easily be taken out of the book and that the flow of the game can be adjusted multiple times if needed. What I don't like is that it all depends on the stronger player being comfortable with that and not minding potentially losing a nominally 'even' game. Also, it is very nice way to play 'teaching' games.

I play a lot of games like that, and its fun.
Its my personal invention such 'Irish Handicap' - handle with care!!

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WARNING: This post might contain Opinions!!