Strategic differences due to group tax

[lightvector]

Today I played around a little bit to see how group tax or not affected KataGo's suggestions.

For those unfamiliar - group tax means that the two eyes that a group needs to live are not counted as points, so effectively it's -2 points for every independent group, except for seki groups, where they just lose only the points for whatever eyes they do have. Or, a cleaner way to think of it that makes it clear that this isn't just some arbitrary rule - if you do this on top of normal area scoring, this basically gives you stone scoring - your score is simply how many stones you can actually fill on to the board (and counting and subtracting two for each group is simply a shortcut to doing this instead of actually placing all the stones). Ignoring the actual rules history, which is a bit more interesting and I don't claim to be an expert on, and just "morally" speaking: you can think of this as sort of where Japanese "no points in seki" comes from - in addition to the territory vs area difference, the specific bit about "there is no territory in seki" can be thought of as a holdover from group tax rules, where the 2 points tax for living groups was discarded but the seki bit remained.

Anyways, KataGo plays about 20% of its self-play games using such rules, so in theory it should have extensive and superhuman-level practice with the strategic implications. Players should be more eager to connect on a large scale and make fewer groups, and to try to split the opponent's groups apart. And indeed it does seem to make a noticeable strategic difference in many opening positions. If you're one of these people who like center-oriented large-scale coordination play and find it disappointing that moves like 3-3 invasion are all the rage nowadays, you might like to play with group tax rules. Because with group tax, if you trust KataGo now 3-3 invasion becomes a pretty disfavored move, and also a lot of center-oriented cutting or covering moves become emphasized.

Maybe we can get OGS to implement these rules.

I'm posting some screenshots just for fun, other people should feel free to also try. If you want to compare, easiest way is if you can have two instances of Lizzie or your favorite review program open, each one set to different rules, and make moves in both at the same time, but also if you want to do it within just one instance, in a GTP console it's 'kata-set-rule tax all' to turn on group tax and 'kata-set-rule tax none' for Chinese style all-territories-count and 'kata-set-rule tax seki' to tax just territory in seki, like in Japanese rules.

The below are also with analysisWideRootNoise 0.04 to encourage evaluating more moves. All winrates and leads are from Black's perspective.

Normal - we see the usual bot preference for 3-3 invasion, but close behind are the approaching moves and developing the 3-4 corner stone.

withoutgrouptax2.png (732.45 KiB) Viewed 18950 times

With group tax - now 3-3 invasion is entirely off the radar, and developing 3-4 is the clear winner.

withgrouptax2.png (722.45 KiB) Viewed 18950 times

[lightvector]

Normal - in response to white's pincer, there's a preference for dodging into the corner, leading to a pretty usual joseki, although other moves are possible.

withoutgrouptax3.png (749.53 KiB) Viewed 18948 times

With group tax - now dodging into the corner is barely considered and black prefers the more global splitting move that moves out into the center, for the upper left fight.

withgrouptax3.png (771.28 KiB) Viewed 18948 times

[lightvector]

Normal - black prefers to pincer the white stone, which was also the move in the real game.

withoutgrouptax.png (776.49 KiB) Viewed 18945 times

With group tax - although the pincer is still very good, now a covering move also becomes very good too, which should be more likely to result in fewer groups. Also, black is noticeably behind here, due to having the isolated group in the lower right from the earlier 3-3 invasion, wheres white does not have any fully isolated groups yet.

withgrouptax.png (786.62 KiB) Viewed 18945 times

[Bill Spight]

Verrrrrrry interesting, lightvector. Thanks.

Before the virus altered my life expectancy, and hence, my priorities, one project I had in mind was developing a bot to play no pass forms of the Capture Game. It is possible to score those games, and it turns out that they use territory scoring with a group tax. Capture-N, as N increases, approaches the ancient Japanese form of go, with territory scoring and a group tax.

My guess is that a strong capture game bot would value the center, strategically, because of the group tax, and would also be good at semeai, given the fact that winning a semeai could win the game by sudden death. One large enough capture would be enough. OTOH, it might be very good at avoiding semeai. Quien sabe?

[mhlepore]

Hi lightvector,

All of your examples are Black to play, and with a group tax, Black prefers to have more large scale development.

Would it be true that White prefers small groups with a group tax, since komi is more likely to matter?

[lightvector]

No, I'm quite sure that white prefers the same things black prefers - white should avoid early 3-3 invasions, and should prefer to connect and cut stones on a large scale, such as slightly favoring central groups that enable global connectivity and slightly disfavoring invasions that live isolatedly, compared to normal go. Playing white isn't going to suddenly reverse the preference. Having numerous small groups as white instead of fewer groups still means you get taxed more... which is bad, not good!

"Komi is more likely to matter" seems to me the wrong way to think about it. It's just normal go, but you're going to sometimes get +2 or +4 points compared to normal, and sometimes -2 or -4, based on the different of number of groups relative to the opponent. And of course, in Japanese rules which have a 1-point granularity, this will smooth out in between as well due to choices and trades (e.g. a line that gives you an extra group being 2 points worse perhaps means that instead you opt for a line that is 1 point worse compared to normal Go, so then group tax net would change the result by 1 point, which is not a multiple of 2). Komi shouldn't be really either more influential or less influential than usual, because to a first approximation there shouldn't be much special interaction between the value of komi and the number of groups you end up with, except for the fact that they add up.

KataGo seems to judge having group tax as about +1% winrate for black relative to normal rules in both Japanese 6.5 komi and Chinese 7.5 komi variants, meaning that black starts out a little less behind than before. This is consistent with an intuition that black should find it slightly easier to have fewer groups than white, due to being a move ahead. And since early opening positions are seen millions of times in self-play, before the game develops into its own unique state, such differences, although well below the normal error margin that one would consider to be trustworthy for later in the game, probably do reflect real differences in the empirical frequency of wins versus losses between these rules at the bot's current level of play in training games.

But 1% also seems very slight (slighter than I might have expected), and being ever so slightly harder on white shouldn't cause white's preferences to reverse. White of course wants the same things, even if slightly harder.

If you have KataGo working, you can try it all yourself.

[johnsmith]

This is just brilliant, lightvector!

[Knotwilg]

Truly original work.

Myself I'm a firm believer that the game originated as stone counting and area counting was just practical. Group tax was probably discarded as a matter of elegance and because it didn't matter all that much in times when even komi was not a practice. Speculative I admit. Although that's now what the game has become, I can't help but feeling that group tax would stay truer to the original game. As you have proven, the cosmic style would highly benefit from it, which is another romantic reason to favor it.

Thanks a lot!

[Uberdude]

I remember watching/reading a commentary (EDIT: viewtopic.php?p=213010#p213010) on an ancient Chinese game, where the point was made white would play this checking move from outside rather than 3-3 like we would now because of the group tax:

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$$ . . . 3 . 2 . . . . . . |
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$$ ------------------------+

Click Here To Show Diagram Code

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[mhlepore]

Thanks for the response lightvector, Based on what you said, I think I didn't state my question as clearly as I could have.

(bolding is mine)

...Having numerous small groups as white instead of fewer groups still means you get taxed more... which is bad, not good!

...there shouldn't be much special interaction between the value of komi and the number of groups you end up with, except for the fact that they add up.

I was not trying to say that it should be white's goal to create as many small groups as possible, irrespective of what black is doing. What I was saying is that, in games that occur where *both sides* end up with numerous small groups, that the margin of victory tends to be small, and komi is therefore more likely to matter, favoring White


But I certainly defer to KataGo. Thanks again.

[RobertJasiek]

Granularity is the wrong word because it is 1 for territory, area and stone scoring.

Instead, you mean the smallest score difference under the assumptions of a 'constant seki parity' and possibly 'no asymmetrical seki'.

[Bill Spight]

Truly original work.

Myself I'm a firm believer that the game originated as stone counting and area counting was just practical. Group tax was probably discarded as a matter of elegance and because it didn't matter all that much in times when even komi was not a practice.

According to Ing, stone scoring persisted in parts of China into the 20th century. When the group tax was dropped from Japanese territory scoring, I don't know.

Speculative I admit. Although that's now what the game has become, I can't help but feeling that group tax would stay truer to the original game. As you have proven, the cosmic style would highly benefit from it, which is another romantic reason to favor it.

I like the idea, too. Bring back the group tax!

[iopq]

I'm not so sure, on 9x9 often you have black with one big group and white with two small groups. I'm not sure 7 komi is still accurate with group tax. It might be, but I haven't researched it.

[jann]

Myself I'm a firm believer that the game originated as stone counting and area counting was just practical. Group tax was probably discarded as a matter of elegance and because it didn't matter all that much in times when even komi was not a practice.

Wasn't group tax abandoned after the logical leap was made to territory? It makes little sense after that. (AFAIK area was only a very late invention.)

I can't help but feeling that group tax would stay truer to the original game. As you have proven, the cosmic style would highly benefit from it, which is another romantic reason to favor it.

This may be true for pros, but this could also break the game at amateur levels. It's already too easy to win mindlessly dropping random high stones, weaker players cannot play well against influence. The balance is delicate.

[Bill Spight]

Myself I'm a firm believer that the game originated as stone counting and area counting was just practical. Group tax was probably discarded as a matter of elegance and because it didn't matter all that much in times when even komi was not a practice.

Wasn't group tax abandoned after the logical leap was made to territory? It makes little sense after that. (AFAIK area was only a very late invention.)

John Fairbairn can correct me, but the oldest known description of weiqi suggests stone counting, while the oldest existing scored game records appear to have used territory scoring with a group tax. Berlekamp showed that no pass go with prisoner return may be scored with territory scoring with a group tax. (I have shown that other forms of no pass go may be scored with territory scoring with a group tax, depending on the definition of territory. ) It is quite possible that some precursor of ancient go as we know it was a form of no pass go. In any event, it is not necessary to assume that territory scoring was derived from area scoring, or vice versa.