The komi value that achieves winning ratios by Black and White that are as close to each other as possible can be either an integer or a half integer.

In 9x9 it seems the right value (with area scoring at least) is 7. Computer tournaments use that value because 7.5 turns out to be a bit too much.

Of course, with an integer komi, ties are possible. So I was wondering if using a simple tie-breaker like first passer wins ties or Button Go would keep win ratios basically the same or if one of the colors would be inherently favored.

I once wrote this proposed solution: http://senseis.xmp.net/?ResolvingJigoByKoThreats

Very nice!

EDIT: An inconvenient of both rules is that they force players to capture dead groups, I think. A player who lost the pass fight can force game resumption by disagreeing on the status of their dead groups so that their opponent is forced to capture them and pass last (or not pass first).


That's true, but it's perfectly possible that a fractional value works best in practice. The score difference in a game played perfectly needn't correspond to the komi value that brings the most statistical balance in games played imperfectly.

Of course, this can be solved by cancelling only the last pass in the event of a resumption. This means that whoever passed last plays first after a resumption.

Button Go achieves something similar as taking the button doesn't count as a pass and is therefore not cancelled in the event of a resumption.

I actually prefer "One player chooses (half-integer) Komi, the other one chooses sides." the most

I don't think there will be any 100% "fair" value for komi as long as we make it tie-breaking, no matter it is breaking by fraction value or by extra rules.

Let's assume two Gods play Go in a minimax manner (because Gods have infinite computational power so they can brute-force the whole game tree), and the games are played with the super ko rule (because Gods have perfect memory and don't feel any difference in simple ko and eternal life). In such case, each game they play will always end with the same score difference no matter what kind of scoring method they choose. Now we set that score difference as the komi value. This will be the "fair komi" for Gods or perfect players, which allow Gods to declare their games a draw.

Any other definition of "fair komi" will be subjective to the players' intelligence, and increase/decrease when people find new ways to play stronger as black or as white.

Yes, but seemingly it still happens to be the same in practice, since AFAIK all current data shows that 6.5 is a bit too small, and 7.5 is a bit too high. Which is not surprising considering how close current top levels are (supposedly) to perfect play. From a fairness perspective ddk komi is more practical problem.

No question about that.

I think a better way of phrasing my original question would be: if a certain integer komi value yields equal win rates for Black and White plus a number of ties, will adding the button as a tiebreaker on top of that still yield equal win rates for Black and White?

Reddit's AMA reveal that DeepMind's Julian Schrittwieser experiment and think komi 7.5 (probably with Chinese rule) favor White with 55% winrate. (Confirm what everyone's afraid of)

But the most interesting thing actually come from DeepZen's Hideki Kato that said Zen think komi 6.5 (Japanese rule) slightly favor white. (I talk to him in KGS room)

Combine with contrasting statistics from 8D+ game of GoBase data in 2008 that black win a little bit more (50.58%) in Japanese rule with komi 6.5, we can roughly conclude that Japanese rule is more fair than Chinese rule.

And 6.5 komi under Japanese rules is almost equivalent to 7 komi plus button under Chinese rules. The message is clear...

Agree, but I'm still standing my statement.
In Chinese rule both statistics and AI agreed that white has advantage with 7.5 komi.
In Japanese rule DeepZen also agree that 6.5 komi favor white but statistics says otherwise (black slightly win more), thus making it more fair.
Now the reason behind what's make black win more in Japanese rule is to be discussed. Both rule should give similar result, isn't it?

I don't understand. Black wins more in Japanese rule compared to what?

Compare to Chinese rule.
Black only win 49.51% in Chinese rule

source https://senseis.xmp.net/?Komi%2FStatistics

I see. Well, that's because 7.5 komi under Chinese rules is more than 6.5 komi under Japanese rules.

As I said, 6.5 komi under Japanese rules is nearly equivalent to 7 komi plus button under Chinese rules, which is less than 7.5 komi without button under Chinese rules.

It's also not surprising that White's advantage with 7.5 komi under Chinese rules is more apparent in AlphaGo games than it is in human games, as AlphaGo is closer to perfect play.

Hmm.... DeepZen is not strong enough for me to trust its own statistics as heavy as human stats. A person can be stronger in black or stronger in white. Same for AI.

I read my own comment and see many weakness

Let me try again... how about this evidence!

Macelee post the following message on Go4Go forum last year https://www.go4go.net/go/node/54875



Since fair is more about perception than mathematics solution, Japanese rule is more fair than Chinese rule. I'm wonder if this is better argument than the last one

PS. If Macelee is reading this, do you have the latest statistics now?
The latest you give is as of 2016-03-08.

The rationale of Chinese counting rule can't use 6.5 komi never make sense to me. Even after reading https://senseis.xmp.net/?WhyChineseKomiShouldIncreaseBy2PointSteps, although it does convince me 5.5 komi and 6.5 komi are "closer" while 6.5 and 7.5 are "wider" under Chinese counting rule, so what? As long as 6.5 komi in Chinese counting rule compensate to white more than 5.5 komi while compensate to white less than 7.5 komi, what makes it so unthinkable as a komi value? Or is it because I am too weak in playing Go so I will never get the mystery of that??

There is no reason not to use 6.5 other than the fact that it's virtually the same as 5.5, which has been proven to be less balanced than 7.5.

The reason why 6.5 is virtually the same as 5.5 is that the sum of both player's scores will almost always add up to 361, an odd number, which means that the winner's score will be an odd number of points higher than that of the loser. If Black wins by 5 on the board, they lose with either komi value, and if Black wins by 7 on the board, they win with either komi value.

6.5 komi only gives a different result than 5.5 komi if there is an odd number of empty points in seki, which happens quite rarely.

Note that 5.5 komi and 7.5 komi are about equally "unfair" according to the statistics. Both are about 2.5% away from 50%.

Under Chinese style rules, if the "correct" komi is 7, then any B+7 on the board should be jigo. In that case, it is logical that 5.5 and 7.5 are about equally unfair, because under 5.5 komi all the B+7 on the board results are awarded to black, while with 7.5 all the B+7 on the board results are awarded to white, and under Chinese style rules B+6 results are very rare (as are any even score results).

So apparently, there is about a 5% zone of B+7 on the board in the middle of the professional stats, and whoever you award those to gets an advantage.

Herman's explanation further strengthen my suspicion that 6.5 komi may be a reasonable komi value for area scoring, while Luigi's explanation repeated what I learnt from the Sensei wiki I linked.

6.5 komi may be less "fair" than 7.5 komi, maybe not. But assuming 6.5 komi is exactly as fair/unfair as 5.5 komi sounds strange, as professionals fine tune their game play in accordance to komi value, maybe 6.5 komi games will contain seki more often? If statistics really shows that 5.5 and 7.5 are about equal, as said by Herman, there's a chance, however slight, 6.5 may be fairer.