# What is Fair and Perfect Komi for Stone Scoring?

Using Stone Scoring what is Fair Komi (komi value which maximizes the chances of a draw) and Perfect Komi (komi value which minimizes the statistical advantage for either player (draws count as ½ win))?

For reference for those who don’t know, here are the Fair and Perfect Komi values for Area, Territory, and Stone Scoring:

Fair Perfect
Area 7.0 7.0
Territory 6.0 6.5
Stone 7.0 7.0

EDIT: inserted hypothesized values for Stone Scoring now that empirical data has backed up rational conclusions

I would conjecture that since Stone Scoring is equivalent to Area Scoring except for the Group Tax (whether you use Group Tax or play out all the stones manually doesn’t change the result and thus is not a different Scoring method, just a different Counting method), and the Group Tax would reasonably be believed to not significantly favor either color, and Group Tax penalties would generally be even and thus not alter the less granular nature of Area Scoring, that Stone Scoring would share the same values for Fair Komi and Perfect Komi that Area Scoring has. Is this logic correct?

I am open to either rational or empirical (or both) arguments for certain values; either one could convince me in the absence of evidence pointing contrariwise

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Sorry, how can you have draws since the values for Perfect Komi include a half point?

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Perfect Komi does not by fiat include a half point, but you did alert me to a typo I made in my post, which I have now corrected: Perfect Komi in Area Scoring is 7.0, not 7.5

But even if all Perfect Komis included a half point, that wouldn’t change that the definition does not mandate that, so the definition needs to define what a draw is worth

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fair komi 8.0
perfect komi 8.5

I think group tax somehow benefits black. Because first move advantage, black is able to build faster, thus white is often the player who needs to to invade and aim for many small groups around the board. So to make it as even as possible, white would need bit more komi

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I think group tax would bias toward Black. At least on 9x9, it is much more likely to see a game where White has two groups than Black has two groups.

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Do you think that advantage continues to be worth the same as the board size increases, or does it peter out to about even? Area Scoring Fair Komi goes from 25.0 on 5x5, to 9.0 on 7x7, to 7.0 on 9x9 and up. It does not seem prima facie unreasonable that any advantage group tax gives to Black might also reduce on larger board sizes

What’s the formal reasoning for this finding? I find it highly suspect that fair komi would not be an odd integer in Stone Scoring

Regarding “perfect komi”, assuming a komi of 10 gives the following results: 50 % of games are wins for black, 49 % are wins for white and 1 % are draws. Then the komi of 10 slightly favors black. But by making it 10.5, all the draws become wins for white, so both players have the same chance of winning.

Thinking about it like this, draws matter, even if the perfect komi turns out to prevent draws, right?

Ah yeah, thats a good point! I didnt think it thru, i just went for a gut-feeling that group tax would favor black little bit, so i increased area scoring komi by 1 ^^

But maybe it should be 9?

My intuition would be that this effect would largely disappear on larger boards, but at most would be no more prominent than on 9x9

On 9x9 1 extra group for White on average seems like an upper bound, not an expectation, so the question more explicitly is, is it enough to tip fair komi up to 9.0? What about perfect komi?

My intuition is that because White has alternate approaches on 9x9 besides making 2 groups to Black’s 1, the advantage would be significantly less on average than the full penalty for multiple groups, since White has a lot of resources available to work around the issue, and that thus Fair Komi and Perfect Komi would remain the same, though you might get a very slightly higher winrate for Black at high-level play, especially on 9x9, but that’s not really a concern as Area Scoring Perfect Komi favors White slightly according to AI anyway, so if anything a miniscule shift in favor of Black would make it more balanced without adjusting komi

You know, you can investigate this in KataGo if you like. It’s highly trained on stone scoring rules.

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I don’t have a computer that can run katago. Honestly, I expect someone on this forum has already done this and knows the answer anyway

I let KataGo think for ~10k visits from the empty 9x9 board with 7.0 komi.
(0.05 wideRootNoise, recent-ish 28b-network)

Chinese rules:

Stone Scoring:

(click on the images to make them bigger)

The images to the right show the respective principal variations: the first few moves have a lot of visits and can be trusted to be good moves, while the later moves may contain mistakes. However, for Stone Scoring the PV is settled on early and stays stable. Playing it out move by move and letting KataGo think deeper about each move, it still wants to go into the same sequence.

Note that the 4-5 and 4-4 points do not become worse opening moves under stone scoring, instead it is 5-5 that becomes better. In Chinese rules when black opens on tengen, it is quite common for white to end up making two groups. According to KataGo, it is still possible for white to maintain the draw while only making one group, but it seems like the path to doing so is quite narrow. Therefore black gets an “easy” draw by opening on tengen, in the sense that white is more constrained than she would be under Chinese rules (which is reflected in the fact that the principal variation is so stable).

Same stuff for 19x19, with 20k visits:

No significant difference in winrate or score here.
(fun to see that weird opening moves like Q10 only lose ~0.3 points under stone scoring rules - however it should be noted that Q10 only loses ~0.5 points under Chinese rules, so it’s not that unviable there either)

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That result seems to support my reasoning that stone scoring Fair Komi and Perfect Komi would be equal to that for Area Scoring (7.0 for both), and that the advantage conferred thereby to Black would be minor even on 9x9

That said, it also seems to propose a new hypothesis that the strategic viability of White making multiple groups in 9x9 is integral not to the balance of 9x9, but to the strategic depth of it, and that we ought thus to prefer sticking to larger boards when using Stone Scoring even though 9x9 is indeed balanced

EDIT: edited OP to reflect this data supporting the rational arguments engaged in so far in this thread

the only “fair” komi is a komi through negotiaion or bidding.
Just like a fair price is always through an open market, not by central planning by the government.
I propose a bidding system where players bid for the first move. It’s so simple I don’t know why it’s not implimanted

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That’s just semantics. I did not come up with the terms “Fair Komi” and “Perfect Komi”, but I find them very useful so I will continue using them

Komi bidding or Komi Pie or Coupon Go are extant variants, but most people (including myself) see them as not adding any value in terms of balance given that we have strong AI which has given us the values

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FWIW, the models I’ve trained on beginner games appear to think komi should be smaller at lower ranks. I’ve not investigated this specifically, but I noted that setting komi to 1.5 on 19x19 resulted in the model thinking the game was about equal. I don’t have too many games with non-standard komi in the training set so I wouldn’t trust the specific value too much, but I’m more sure it’s right about the direction.

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Yeah, common wisdom says that 5.5 Territory Scoring is more balanced than Perfect Komi for weaker kyus on 9x9, but whether or not that means we should take player strength into account when determining komi (I am not here speaking of reverse komi, but rather a reduced komi impartial to which if either of the two players is weaker), is a question of philosophy, not of what Fair or Perfect Komi are

For the record, I am of the opinion that we should use either Fair Komi or Perfect Komi even if we’re not strong enough to use that Komi to its fullest potential, because I’d rather know that I’m playing a fair game, than know that I’m playing an unfair game which happens to give more even results at my level

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Only 10% of my games were decided by less than 10 points either way, so it makes sense that the specific value of komi doesn’t hold too much weight on predicted game outcome.

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10% of all games, including timeouts and resignations?

Or 10% of those games that are scored?