Handicap for smaller board sizes
(For the placement of handicap stones , see Handicap stone placement on smaller boards)
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Handicaps and komi for smaller boards
Theoretical value of a stone according to Goban size
The following table gives just the value of 1 stone - if we acknowledge that this value is purely proportional to the size of the board (which is debatable...).
Size Total Stone value 19x19 361 1 18x18 324 1.1141 17x17 289 1.2491 16x16 256 1.4102 15x15 225 1.6044 14x14 196 1.8418 13x13 169 2.1361 12x12 144 2.5069 11x11 121 2.9835 10x10 100 3.61 9x9 81 4.4568 8x8 64 5.6406 7x7 49 7.3673 6x6 36 10.028
For example 7 grade strength difference should mean roughly 7/4.4568=1.57 stones on a 9x9 board.
DragonGoServer uses a different formula: Value of a handicap stone = 256 / (boardsize-3)^2
Size Total Stone value 19x19 361 1 18x18 324 1.1378 17x17 289 1.3061 16x16 256 1.5148 15x15 225 1.7778 14x14 196 2.1157 13x13 169 2.56 12x12 144 3.1605 11x11 121 4 10x10 100 5.2245 9x9 81 7.1111 8x8 64 10.24 7x7 49 16 6x6 36 28.444
Here, a 7-grade difference would mean roughly 7/7.1111 = 0.984 stone on a 9x9 board.
First possibility
Regarding handicap games, the following table gives one possible way of allocating handicap and komi on 13x13 boards. First column: Strength difference on 19x19 goban, second column, handicap on 13x13 goban, third column, komi to white.
Difference 13x13 Komi Difference 13x13 Komi 0 0 5.5 10 4 5.5
1(*) 0 5.5 11 4 2.5 2 0 2.5 12 4 0.5 3 0 0.5 13 5 5.5 4 2 5.5 14 5 2.5 5 2 2.5 15 5 0.5 6 2 0.5 16 6 5.5 7 3 5.5 17 6 2.5 8 3 2.5 18 6 0.5 9 3 0.5 19 6 -3.5
could someone please explain 6/-3.5 here? I'd rather say 7/5.5
xela: Some people (including myself) feel that putting more than six handicap stones on a 13x13 board (or for that matter, more than four on 9x9 or more than 9 on 19x19) gets a bit silly. Dieter: Quite so. People whose ranks differ 20 or more stones, are either unlikely to meet on the board at all or should not engage in a game beyond 9x9, unless for pure teaching purposes, in which case a correct handicap doesn't really matter.
(*) In the case of a one stone difference in strength, the weaker player takes black and plays first.
Second possibility (Tim Hunt)
On RGG, Tim Hunt posted his recommendations
Grade 13x13 board 9x9 board Difference Handicap Komi Handicap Komi 0 1 6 1 6
1 1 2 1 4 2 1 -2 1 2 3 2 4 1 0 4 2 0 1 -2 5 2 -4 1 -4
6 3 2 2 4 7 3 -2 2 2 8 4 4 2 0 9 4 0 2 -2 10 4 -4 2 -4
11 5 2 3 4 12 5 -2 3 2 13 6 4 3 0 14 6 0 3 -2 15 6 -4 3 -4
See also ![[ext]](images/extlink.gif)
http://www.timhunt.me.uk/go/handicaps/
(Dead link. Archived in the Wayback Machine: “Go Handicaps on Small Boards” https://web.archive.org/web/20080112004009/http://www.timhunt.me.uk/go/handicaps/)
Third possibility (AGA)
There is a list of handicaps for small boards used by the American Go Association at AGA Handicaps.
Fourth possibility (RobertJasiek)
I have attended the small board tournaments at European Go Congresses since 1993 and watched many of the finals games. From that, I have observed that 8.5 komi for 13x13 and 6.5 komi for 9x9 (the latter is also currently used by Japanese professionals) frequently lead to strategically demanding 0.5 games. Whatever the handicap table is, these komi values are essential, unless one lets the players bid for the komi. Let me suggest some tables nevertheless, where handicap stones can be placed either freely or at the usual fixed patterns, which means 4x4 hoshis also on the 9x9. Free placement is significantly stronger in theory but still only very few players know to use that well.
Grade 13x13 board 9x9 board Difference Handicap Komi Handicap Komi 0 0 8.5 0 6.5 1 0 6.5 0 5.5 2 0 4.5 0 4.5 3 0 2.5 0 3.5 4 0 0.5 0 2.5 5 2 8.5 0 1.5 6 2 6.5 0 0.5 7 2 4.5 0 -0.5 8 2 2.5 0 -1.5 9 2 0.5 0 -2.5 10 3 8.5 2 6.5
etc.
Theoreticians notice that, according to the standard assumptions of the relation between komi and handicap, this is not linear. It works well for championship games in practice though. If Black does not know how to use his handicap (e.g., if he is an ordinary club player rather than well prepared for European championship level), then the system favours White.
Note by Herman on linearity: the standard assumption regarding komi and handicap is that normal komi is worth half a handicap stone. At 8 komi, every handicap stone is worth 16 points. In the above system, the black player gets 2 extra komi every rank, except every fifth rank, where he suddenly gets the equivalent of 8 points.
axd: ... but the staircase progression is still linear in average?
tarvaina?: The EGC 2010 13x13 tournament was played with the above handicaps (up until 24 grade difference, after which the maximum handicap of 5 stones and 0.5 komi (for white) was used). Out of 184 handicap games 35 (about 20%) were won by black and 149 by white. Here are the results by rank difference.
Rank diff B+ W+ 1 1 6 2 7 21 3 1 11 4 4 19 5 6 10 6 2 19 7 3 5 8 4 10 9 1 4 10 1 12 11 2 2 12 1 6 13 1 1 14 0 5 15 0 3 16 0 2 17 0 1 18 1 2 19 0 1 20 0 1 21 0 0 22 0 3 23 0 1 24 0 0 25 0 0 26 0 1 27 0 0 28 0 1 29 0 0 30 0 1 31 0 0 32 0 1
In conclusion, it looks like these handicaps are too small for a full-handicap amateur tournmanent. -- Antti Tarvainen
tapir: what was the reasoning for a base komi 8.5? (how were results in even games with 8.5 komi?) interestingly all other proposals have higher differences in komi for one stone on 19x19, this model only 2. (the japanese recommendation 5, timhunt 4, jewdan also 5, aga also 5)
Herman: What was the reason for choosing this system on the EGC? As already mention above, it is not linear, which means it is broken by design.
tapir: Well, he said it is for free placement of handicap which is supposed to be more efficient. The main point should be the 2 point komi per rank difference and 5 ranks per handicap stone which is absurdly low regarding to all other proposals. (Maybe a go server can help with data.) But wasn't the very system used last year at the EGC as well, Herman?
Herman: The broken aspect of the system is the jump from "even, 0.5" to "2 stones, 8.5" (and from "2 stones, 0.5" to "3 stones, 8.5". Theoretically, that is an 8 point jump, where each previous step was 2 points. The effect is noticeable in the above stats at the 4 vs 5 rank difference point, where black's chances suddenly jump up. I have no idea what system was used last year, actually, but it is quite likely this one, since Robert Jasiek organized that side event and it is his system.
tapir: It is not clear that it is a 8 point jump (without making any hidden assumption about the value of the handicap stone being 16 - which is of course indicated by the base komi of 8.5 - you can't say it is not linear. if the value is assumed as 10 then jumping from 0.5 to 8.5 + additional handicap stone may as well be linear though systematically 3-4 points off). Isn't there historical data from these side events?
Herman: I think it is reasonable to make the assumption that the even game handicap is (close to) fair. Theoretically it is indeed possible that the designer thought the value of a handicap stone to be 10 points, and decided to give white 3-4 extra komi in even games, but I can't imagine anyone would design a system that way. There is no logical reason for it. There is little historical data available online on the rule details for side events, as they are not always held, nor always held in the same way. You would have to find someone who has collected the congress bulletins and flyers/posters from all congresses, I guess, and see if they have the original announcements for the side events, with details on the system.
tapir: As RJ participated in those events, he probably knows the used rules best. (seems to be 8.5 komi and 5 or 4 ranks per handicap stone, acc. his page here) I would not mix the design intentions with the result. The problem with a handicap system may be the initial komi, the lack of linearity and the gradient of the function or a combination of all of them. Also in many tournaments you use reduced handicap (or the McMahon tournament system tends to minimize handicap anyway -> preferring equal opponents with handicap acc. to McMahonScore), e.g. an initial komi of 6.5 in an otherwise identical system with the provision handicap reduced by one (rank) would give very much the same result. The results of the even games are not given though. My guess: the slope is not sufficient and should be twice as much + there is no reason to believe a move one 13x13 is worth significantly more or less than one on the big board (relevant for komi) + less space on the board makes it harder to recover the handicap (reduce handicap stones per rank acc. board size = so 2.5 rank difference = 1 stone seems reasonable, for convenience say 3).
- The handicap system is not mine. In 2000 and 2009, I copied it from Anton Steininger's organization of the 1993 (my first) EGC 13x13. IIRC, in some other years it was also used.
- The EGC 2010 13x13 tournament was not played with the system but was played with almost the system. The difference was: In round 1 (the round when the strongest player in every group had to give the greatest handicap when playing the weakest opponent in his group) the stones were placed on 3x3 points, in all subsequent rounds on 4x4 points. (However, some groups did not know about these fine details at all...)
- The EGC 2010 statistics are interesting but what do they mean? Some of you read them as if a great deviation from 50% winning of each colour would show the system to be wrong. I read them as confirming my opinion that most black (kyu) players are not properly prepared to use their handicap well. They make many basic, fundamental, easy mistakes that they ought to know how to avoid. Wisdom like "Connect your handicap stones so that fewer groups need to survive!". It is knowledge that each 15 kyu in a 13x13 EGC ought to have but many don't have it. That is not a fault of the handicap system but a fault of such black players. Black players knowing these basics will win (almost) every game! I have seen that from well prepared kyu players from 20k to 1k (and applied it as a 3 kyu in 1993 myself, making 9x9 second place and 13x13 quarter finals). If you give greater handicap to kyu players, then they will continue to play badly instead of learning the basics.
- Being non-linear by standard theory does not imply being broken by design because in practice handicap stones themselves are not as linear as they pretend to be. One stone more on a small board has a huge effect. It is unclear how that compares to a great komi change.
- For the reasoning of 8.5, see my initial explanation. If you have better data about 13x13 EGC even games in KOs (all rounds) than my memory about the played / observed games (incl. quality of strategic choices) in all the years 1993 - 2010, please provide it! 8.5 not only means 0.5 games but also rather frequent global exchange and ko threat counting for huge semeais to get a 0.5 result.
Cambridge club
The Cambridge club (see http://www.cam.ac.uk/societies/cugos/ for more details) uses a different system for its end-of-term 13x13 handicap competitions. These are played with fast time limits of 10 minutes each. In that case
2.5 grades = 1 handicap stone
Old Japanese Recommendation
Around 1985 there was an article in the Japanese magazine Igo Kurabu by Ishikura Noboru (now 9p) on komi and handicaps for both 9x9 and 13x13 boards. His recommendations were based on the results of many pro-pro games on these boards. Here is a table summarizing his recommendations:
Difference in strength 9x9 13x13
handi komi* handi komi*
0 1 5.5 1 5.5
1 1 3 1 0
2 1 0 1 -5
3 1 -3 2 5
4 1 -6 2 0
5 2 3 2 -5
6 2 0 3 5
7 2 -3 3 0
8 2 -6 3 -5
9 3 3 4 5
10 3 0 4 0
11 3 -3 4 -5
12 3 -6 5 5
13 4 3 5 0
14 4 0 5 -5
15 4 -3 6 5
16 4 -6 6 0
17 5 3 6 -5
18 5 0 7 5
19 5 -3 7 0
20 5 -6 7 -5
21 6 3 8 5
22 6 0 8 0
23 6 -3 8 -5
24 6 -6 9 5
25 7 3 9 0
26 7 0 9 -5
27 7 -3 10 5
28 7 -6 10 0
29 8 3 10 -5
30 8 0 11 5
*komi given by Black, so negative number means reverse komi.
Jewdan's Handicap System
Jewdan?: I developed a handicap system for 19x19, 13x13, and 9x9 boards that takes into account complaints I have read about the handicap system and math I have seen regarding calculating stone values and handicap stone ratios for different board sizes. It tries to account for differences in territory and area counting, too. The complete tables are pretty large, so I won't paste them here. Please check the system out at Jewdan's Handicap System.
Rule-of-thumb
- Jeff: At the start of a 13x13 with someone, I hand them 6 prisoners (komi) plus 4 per rank difference. I then let them use ten stones to buy one handicap stone. I let them do this as many times as they want until their number of prisoners becomes negative. Similarly with 9x9: 6 prisoners plus 2/rank
(axd) This corresponds to
size start diff H-price 13 6 4 10 9 6 2 10?
Where:
start = number of W prisoners given to B diff = additional number of W prisoners for each rank difference H-price = number of W prisoners to return for each handicap
axd: todo: sizes 5,7,19
Switching over to larger sizes
It can be handy to have an idea when to switch from a smaller board to a larger board when playing against (much) weaker players. This allows to present an attractive learning path for beginners, that might otherwise stick too long to a small board size or switch too soon to larger sizes when playing against stronger players.
Maximum handicaps
An option is to switch to the larger size once the strength difference equals the maximum number of handicaps that are usually given on the larger size
from H to H rank diff ------- -- ------- -- ---------- 9x9 3 13x13 6 approx. 14 13x13 4 19x19 9 9
Notes
- from 13 to 19 would be at 5H according to AGA Handicaps, 4 according to Tim Hunt table, 3 according to 'First Possibility' table.
- to add: 5x5 and 7x7 boards
Maximum komi (less usual)
Rather than play with handicaps, as handicaps and komi are in relationship with each other, whenever Black manages to win without handicaps but with a specific (negative) komi, (s)he is "promoted" to a larger size board.
By lack of a better rule-of-thumb, following values are solely based on linear extrapolations (proportional to area) from 9H=140K on 19x19 - anyone with a better idea, feel free to improve.
from K to ------ ---- ------ 5x5 9? 7x7 7x7 19? 9x9 9x9 31? 13x13 13x13 65? 19x19
(to develop)
see also forum:komi
Links
- Rank And Handicap/Discussion: the smaller the board, the more subjective handicap stones become?
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