I wrote a genetic algorithm for determining the advantage a player gains from handicap stones, what the correct komi should be, and the the winning chance against different strength opponents. The dataset used was first half of this years KGS high dan games. The ratings provided by KGS were NOT used, instead they were deduced from the wins and losses. I decided to use twoeye as an anchor (pun intended) with a rank of 7.25dan. The benefit from 1 handicap and 2 handicaps where locked in place when attempting to find the optimum for the other variables. The result is..

Komi 9.5

Over the 9000 games played, games with no handicap between equal ranked players (as per KGS) with komi 7.5 showed black winning 52.6% of the time which is probably why the genetic algorithm resulted in such a high value for komi. The actual explaining might be either that high dans are not quite pro level yet so the value of those extra points differ. Or it could just be that a sample size of 9000 games isnt quite enough.

Value of handicap (compensates for how many ranks) :
1 : 1.0
2 : 2.0
3 : 3.1
4 : 3.3
5 : 5.1
6 : 6.5

Third handicap stone helps a bit more than just 1 difference in rank, where as the 4th and especially the 5th stone bestow very little help. 6th stone is again extremely useful compared to only having 5 handicap. Almost all handicap games are based on japanese handicap placement.

Probability of winning when x ranks stronger.

1 : 73.6%
2 : 85.7%
3 : 94.4%
4 : 94.5%
5 : 98.7%
6 : 99.9%

Here is an actual rank based on these calculations for some KGS players followed by the rank given by KGS.

smartrobot 9.9 9
MilanMilan 9.8 9
Korondo 10.1 9
eku 9.9 9
mysterious 9.3 9
Hutoshi4 8.5 8
kghin 8.4 8
roln111 8.3 8
lovebirds 7.8 7
twoeye 7.2 7
Cornel 7.2 7
foxy 6.6 7
michi2009 5.9 6
ThunderGod 5.2 6
Dcugel 5.3 5
jackoneeye 5.3 5
qwest 4.6 5
You can see that they correlate rather well, atleast in order, but KGS ranking system underestimates how much more often a stronger player wins against a weaker player.

So if you want to boost your rank on KGS. Play against players 5 stones weaker than you, with 5 handicap. KGS estimates you should win 50% of the time, when in actuallity you end up winning a 59% due to the 5 handicap stone effect, add in the fact that what KGS thinks as 5 ranks difference is in fact closer to 10 ranks difference in strength.

Very cool!

A few questions:

How many games total? (i.e., is this statistically significant)

I'd expect, e.g. the value of a handi stone, to vary with the strength of the players. Did you make an attempt to split it out by rank at all? I'd be really interested to see the same sort of analysis on low dan, low kyu, and ddk games!

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very interesting statistics, thank you

i wonder, did you include that traditional handicap system is actually off by half a rank?

what were the winning statistics in even games for black/white? i suppose you found the 7.63 number from that. but i am not 100% sure if you can decide which komi is proper when you only have sample with 6.5 or 7.5 (and different rulesets could also mess with it). i would think you can only safely compare komis for which you have data

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Spilling gasoline feels good.

I might be wrong, but probably not.

9523 games total.



Maybe if I feel up to writing a spider for downloading the KGS archives I could do just that. But I couldnt find them as an easily downloaded package as of yet.

Aren't these two statements contradictory?

My calculations were based on the assumption that with 2 stone handicap and 2 difference in rank should result in a fair game, with each player winning 50% of the time. All the other numbers where derived from that. Hence the first statement. Notice the second statement is NOT based on rankings derived by my calculations, but those provided by KGS, proving in a very clear way that on KGS 2 stone difference in strength does not equal to 2 stone handicap.

That's not quite correct-- with the normal handicap system, black would actually need komi to make the expected result 50%.

I.e.,

no komi is actually a 1/2 stone handicap
two stones, no komi is actually a 1.5 stone handicap

et cetera.

_________________
That which can be destroyed by the truth should be.
--
My (sadly neglected, but not forgotten) project: http://dailyjoseki.com

If thats the case, I probably need to go back to the drawing board

does this pseudo code look correct in that case?

handicap_in_ranks = handicap_stones + 0.5 - 0.5 * komi / correct_komi

if( handicap_stones > 0 )
handicap_in_ranks-=1 // due to black getting first move..

Anyways, fixed, and I updated the first post to reflect the changes. There is one curiosity, I got a very high value for komi. 9.5, so I analyzed all the games with equal ranked player, no handicap and 7.5 komi and noticed that black won 52.6% of those. Which explains the reason the algorithm resulted in the high value for komi.

i've just made a quick search on my GoGoD database. i filtered games only by komi. by these results it seems that 6.5 value is correct to make an even game under territory scoring

7.5 komi:
B+ 139 (51.87%) / W+ 129 (48.13%)

6.5 komi:
B+ 7322 (50.41%) / W+ 7202 (49.59%)

5.5 komi:
B+ 10970 (52.91%) / W+ 9762 (47.09%)

4.5 komi:
B+ 1395 (55.07%) / W+ 1138 (44.93%)

i included the 7.5 komi only after a short consideration, because most (probably all) of those games were played with area scoring while for other values i suppose territory scoring. 5.5 could be also influenced by mixing both subsets together. i think it would be preferable to sort the data and analyse them separately, but i didn't do it for i don't know a way in programs packed with GoGoD. similarly i would add results with 0 komi, but that would require to exclude handicap games

_________________
Spilling gasoline feels good.

I might be wrong, but probably not.

Urgh, silly simulation keeps running into local optimums, need to improve on it more to get better results...

I added another 6 months of KGS high dan games. Now its 19k games. Its been running for several hours and this is the current result. Cant but wonder whats going on with the 3 & 4 stone handicap to rank values, they seem really weird.

rank to probability :
0 : 50.0%
1 : 69.6%
2 : 83.9%
3 : 91.4%
4 : 95.4%
5 : 98.7%
6 : 99.9%

handicap to rank :
0 : 0.0
1 : 1.0
2 : 2.0
3 : 2.6
4 : 2.6
5 : 4.5
6 : 6.0

komi : 7.78

smartrobot 10.0 9
MilanMilan 10.1 9
Korondo 10.3 9
eku 10.0 9
mysterious 10.2 9
Hutoshi4 8.5 8
kghin 8.4 8
roln111 8.3 8
lovebirds 8.0 7
twoeye 7.2 7
Cornel 7.4 7
foxy 6.6 7
michi2009 6.0 6
ThunderGod 5.0 6
Dcugel 5.4 5
jackoneeye 5.2 5
qwest 4.7 5

That is a false assumption. Traditional handicaps give an advantage to White, as your statistics indicate.

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Everything with love. Stay safe.