# Group Count Go

I was thinking about the “shape game”:

In the shape game, as soon as you (as White) make a single live group you win. So you only have to count to 1, which is a lot easier than counting hundreds of points of territory/area in a normal game.

In fact, counting the live groups in a game is usually pretty easy even when there are more than one. Wouldn’t it be nice if that’s the only kind of counting we have to do?

So I’d like to propose a variant called Group Count Go:

• Starting position: empty board.
• Gameplay: normal.
• Score: number of live groups at the end.
• Komi: maybe 1 or 0.5?

Has this been done before?

There could be some strange consequences, for example with dame:

Should this count as 2 White groups and 2 Black groups or just 1 of each?

Do the marked stones count as live groups?

(If so, White should invade to force some connections.)

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A case of group psychosis perhaps?

Edit:

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I like the idea, but a rigorous definition of group is needed. Here is my proposal:

A maximally connected set of empty intersections is called territory of a colour, if it is exclusively adjacent to stones of this colour.

To determine the groups of a colour, imagine removing all intersections occupied by other colours and all empty intersections, except territory of this colour. Then the rest of the board decomposes into connected components, which we call groups of this colour.

With this the whole board is partitioned into dame points and groups. Similarily to area scoring, it is necessary to remove dead stones at the end of game (but can be short cut with mutual agreement).
This would mean that in your first example, both white and black have two groups. In the second example white has two groups and black has 4 groups, but only until the border gets closed, which white should force black to do.

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I think that @martin3141’s definition is pretty good for counting, but we still need to consider some possible issues with defining life and death.

Clearly, we need to either first agree on which stones are dead and remove them, or play out an “encore” phases to the capture dead stones that we wish to see removed, since we’d want to avoid counting lone dead stones as a group.

However, it is possible to have positions where one wants their opponent’s stone(s) to be alive, while the opponent wants them to be considered dead!

Imagine the following position (if we do not allow suicidal moves)

Black would want their own stone at tengen to be declared dead, while White would wish to contend that it is alive! If we call it dead and remove it before counting, White would only have one group while Black has three. However, if we call it alive, then White would have three groups and Black has four. If komi is “1.5 groups”, then this dispute would decide the game.

It seems that one possible resolution would be to allow suicidal moves, such that Black could continue play to settle the dispute by removing their own stone.

Overall, this variant seems to have weird pathologies in that players would try to create territory as inefficiently as possible and sometimes wish to suicide their own stones to cause their opponent to connect.

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When this was discussed on lifein19x19 a while ago, lightvector made a very similar diagram

(The variant proposed there was negative group tax go, which means that we add some group bonus to the usual territory. I think giving some value to regular territory is a good idea, to get a deeper game. The relative importance can be easily scaled by changing the size of the group bonus.)

I’m not sure this variant can be turned into a game I would enjoy, but just to contribute something, would it be possible to modify the rules to get closer to what we normally think of as “independent groups”?

Let’s say we’ve reached the end of the game and the players need to agree which stones are dead and alive. In normal go, there is only one way to disagree: the player that owns the stones in question thinks they’re alive, while the opponent says they’re dead. To settle this question we could do a hypothetical playout, then return to the original position when the life/death question is settled.

But in this variant the roles could be reversed, as in @yebellz’ diagram above. White says that the black stone is alive, and black says that it is dead. So then black says to white:

Prove it! Let’s switch colors, I’ll play the white stones, you play the black stones. I will demonstrate that I can kill the black stone.

(one fine detail left to decide is which side should move first in that scenario)

What would be the consequences of allowing reversed roles like this for hypothetical playouts? I feel like there probably is some obvious flaw here, but I’ll let someone else point that out.

One thing to note about the definition of group given by @martin3141 (which I agree with) is that if black plays E1 here, A1 and B2 count as separate groups. So black is one point better playing B1 and capturing the two stones - then he ends up with only one group, but white lost two groups. White playing first can prevent this by playing E1, killing all the black stones.

All in all, this corner is a 1 point double gote

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What happens in a position like this?

No territory, but all of the empty points are dame, resulting in 7 groups for Black and 6 groups for White.

I guess the players could continue to potentially capture some opposing groups, but that also comes at the cost of merging their own groups.

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Could you not adopt a tromp Taylor type scoring rules where you can score any position.

Something really simple like, every (directly) connected set of stones is a group and when both players pass those are counted as points.

It means any groups you don’t want to give your opponent points for you have to capture. Is that something people want? I don’t know but it is simple.

I think white should continue playing - she would be happy if she can kill all the black stones:

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It depends on how you wish to define a “group”. You seem to be describing it as each chain being a distinct group, however, a potentially undesirable consequence of that is that players should fill their own territory with lone, unconnected stones to artificially create more “groups”. @martin3141 suggested an alternative way to define group, which maybe better matches our intuitive sense of what is a group and is still general enough to apply to any board position. It essentially boils down to saying that dame and opposing stones separate chains into distinct groups, but territory unites chains into the same group.

One simple way to resolve the issue of determining life and death (in the Tromp-Taylor manner) is to simply say that all stones on the board after both players pass are considered alive, and then apply @martin3141’s group counting rules. Hence, players should first capture any stones that they find advantageous to remove, before passing to end the game.

However, the pathological thing is that there exists positions where you want your opponent’s stones to be considered alive, while your opponent’s wishes that they were considered dead and removed. If suicide is allowed, the owner of such stones should self-capture them before the end of the game. If suicide is not allowed, then a player should refuse to capture their opponent’s seemingly “dead” stone(s) to maximize their advantage. See my example above.

It’s not that hard to select a properly-defined ruleset, but the tricky part is whether any particular rules leads to a strategically interesting and subjectively pleasing game design, and exploring what curious phenomenon might emerge from the rules.

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Here is a case where both players would like to claim that their own stones in the center are dead, but it’s not possible to suicide:

The result of my “role reversal encore” idea would be that both chains are dead: black can demonstrate, as white, that the black stones are dead, and vice versa. Both chains are removed from the board, all that space is dame, the score is 2-2.

That is if the killing side gets the first move - if we instead say that when black wants to prove the black stones dead, playing white, white gets the first move as black, then white will kill the white stones and thus the black stones live. (everyone following along? ) In that scenario, both chains live and the score is 3-3.

Not sure which version is preferable. The second one agrees (in this particular case) with the easier Tromp-Taylor version without any hypothetical nonsense. But also either way the score difference is the same in this case.

Is there another case where hypothetical playouts will lead to a different score difference than Tromp-Taylor with suicide?

I feel somewhat tricked into thinking about something I don’t even like… this variant is horrible and deserves none of my time

Edit: Oh and one more thing, I’m starting to think that maybe dame should count as territory for both sides, so that kosumi’s, bamboo joint’s etc. are connected. Would that bring us even closer to what we normally think of as “one group”? Any bad side effects?

To clarify, that would mean that this diagram from the OP is just one group each:

(and neither side should connect - not because it connects, but because it cuts)

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I don’t see why one couldn’t just score every stone as a group. If noone wants to play the hypothetical variant anyway it doesn’t matter if it sounds like it’ll be tedious to have to make a bunch of ponnukis in order to get points. Or that one could try to tactically reduce the territory into shapes where the opponent can’t play ponnukis. Call it ponnuki go if you want to

I’m not sure that’s really undesirable any more than having to come up with convoluted rules to deal with all the edge cases of groups that aren’t connected but are more or less “connected” and disputes about a player wanting their own stones counted as dead but the opponent(!) wanting them alive. You may as well be playing a game where you lose points for every capture you make

You take this position, both players pass it’s 2-2. If both players try to make ponnukis to gain points it’ll probably be a draw because the second player can mimic the first. If they play in each others area it’s much more interesting, and I don’t know the outcome. (Because the groups aren’t unconditionally alive, if white blindly mimics black every move there’s a chance that Black can use their first turn advantage say to capture a group)

What if White or black tries to suicide one of their corner groups, then they could suicide the center group. In this specific case it would still be a draw, but to be honest the possibility of tactics like that isn’t very go like.

This variant would be to Go as antichess Antichess • Lose all your pieces (or get stalemated) to win the game. • lichess.org is to Chess.

In the sense that if you don’t think you can win you can always try to kill all but one of your groups and then get a draw since the opponent has the rest of the board.

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There are some details that could be argued back and forth, but…

That’s problematic indeed! I felt from the start that this variant would never be much fun to play, but this insight really shows clearly the contradictory nature of this win condition.

Regular scoring + large negative group tax could still be playable in theory, but I don’t think it has much going for it other than being technically possible…

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If you have exactly one group, the rest of the board decomposes into opponents groups and dame points. So the opponent can still have more groups than you, just needs to leave neutral points inbetween.

//Edit: I tried to compose an example and see a potential problem.

Black has three groups vs whites one, but white can just play on dame points (A) to create more groups and eventually force black to connect their groups. To disable this, we could perhaps say that stones only qualify as a group if they are adjacent to territory somewhere.

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I was surprised by this comment. Aren’t both sides supposed to honestly evaluate the status of groups, and so shouldn’t the opposite kind of disagreement be possible? It would be a particularly amicable one, but especially under Japanese rules I thought that in the rare situation where your group is dead, but your opponent doesn’t agree, you should still try to convince him.

Another way, probably equivalent to what you had in mind, would be group scoring with a regular scoring tiebreak. Either way, killing off all but one of your own groups to create a group count tie would almost certainly cause you to lose in scoring.

Unfortunately I think this might just end up like normal go but with the players being careful to leave a big dame region in the middle, keeping the group count even.

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Good point! I was thinking in terms of self-interested players in a ruleset where it can never hurt you to try and claim the “wrong” status of a group in your favor. But besides the issue of courteous play, maybe in Japanese rules you could even turn a winning position into “both players lose” by wrongfully claiming the status of some group?

What I really wanted to convey with my comment is that in regular go, regardless of the ruleset, you always want your groups to live, and the opponent’s groups to die. In this variant, the opposite can be true.

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