# Fractional Multicolour Go

Inspired by fractional colourings of graphs, which is the subject of my bachelor thesis, I would like to introduce a new variant of multiplayer go where stones have multiple colours.

Capture Rule

The colours of a stone not only change how the game looks, but also have relevance in the rules. For each colour the chains are determined individually. After every move, chains with no liberties are captured. Note that chains of a specific colour can include stones of different players, if they share this colour. Letâ€™s look at an example:

Here we have (at least) four players placing stones of colours (Red | Yellow), (Blue | Green), (Yellow | Green) and (Red | Blue). The (Red | Yellow) stone is surrounded, but both the corresponding red and yellow chains do have liberties. The chains are indicated in the following pictures:

Note that the (Red | Yellow) stone is associated with two distinct chains. Hereâ€™s how the yellow chain might get captured:

â†’

I can provide a rigorous definition, but I thought these examples would be easier to understand.

The sets of colours can include even more than two colours, but should not be pairwise disjoint (otherwise it is â€śjustâ€ť normal multiplayer go).

Scoring

This is up for debate, although I have a neat idea in mind: How about using area scoring separately for every colour? So for example player (Red | Yellow) gets points for every red stone on board (including red stones from other players), and every intersection that is surrounded by exclusively red stones. And the same for the colour yellow. Hereâ€™s an example:

Yellow: 54 pt
Blue: 58 pt
Red: 48 pt

Note that the intersections H2 and J1 were counted for Yellow but not for Red or Blue, because they are adjacent to only stones with the colour yellow. This is not true for the colours Blue or Red, hence these colours did not receive points for H2 or J1.

With this we get the player scores:

(Red | Yellow): 48 + 54 = 102 points
(Red | Blue): 48 + 58 = 106 points
(Blue | Yellow): 58 + 54 = 112 points

Lets play

This modification to the rules can be combined with other variants. For example we could play with SAS Go, on an Escherian Board or with Pyramid Scoring. But letâ€™s keep it simple for a first game

I would like to use this thread to discuss the rules and hopefully set up games if there is interest.

Thanks to @Vsotvep for providing an awesome tool which I used to generate these pictures.

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I see we have a Go Variants category now, nice.

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Lots of new tactical considerations! Am I seeing correctly that (Red | Blue) could play H2 here, and then capture the yellow chains with J1 on their next move?

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Well spotted, I did not see that
But yes it works that way. Guess the example game is not finished then and (Red | Blue) should play that to claim the territory.

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Awesome idea! I volunteer as lab rat!

Another idea, would be that each player controls their own colour, but has to choose a second colour for each of their stones. So the Blue player has the choice of playing Blue | Red or Blue | Yellow stones. This obviously makes the game even more diplomatic than it already is in the current form.

Another way of considering life would not be that both colours of a stone need liberties, but either colour of a stone needs liberties. With three players this would effectively make every stone immortal, but with 4 or more players it could become interesting, with lots of possibilities to live.

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Fantastic, I look forward to the first game

Interesting idea, and if a player plays stones of varying second color, they might even end up capturing their own stones

I agree that this variant is similar to diplomatic go (like every multiplayer go variant), but I see subtle differences. For example this ruleset clearly incentivises players who share a color to cooperate (especially if we play with the scoring I suggested).

I considered this before, but thought that it would change the game too much to my liking. For example imagine a player surrounds territory, but eventually another player who shares one color simply starts playing stones inside, and thereâ€™s no way to stop them.
In fact I believe this might make it impossible to create a group that is permanently alive, independent of other players, because opponents that share a color could always close the eyes. Maybe this is not as much of a problem as it seems, as those players may not want to capture the group, provided that they profit from your points. But the possibility to create an independently living group seems appealing to me.

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Iâ€™m interested in playing.

Would the players be allowed to discuss, plot, and negotiate in one-on-one, private channels? Or is all game discussion limited to public discussion in the game thread? Or are we required to play silently? Or something else (e.g., only smoke signals and emojis)?

What about alternating vs simultaneous turns? What do people prefer for that aspect?

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Awesome, you are welcome to play!

There are several aspects of the rules that still need to be fixed, and I would like to discuss those and perhaps make polls to decide.

Regarding negotiations, I think communication in one channel shared by all players should (at least) be allowed. Itâ€™s a forum game afterall, and the diplomatic nature canâ€™t be denied. Whether we allow private communication between two players is up for debate.

Both can work with the fractional rules. In case of alternating turns, chains with no liberties associated with the most recently placed stone are taken off the board only after all other chains with no liberties are removed.

If we want to play with simultaneous turns, then the order in which chains get removed could be determined by your concept of old vs. new chains from the diplomatic go game.

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I would like it more without private communication. The scheming is a bit too time- and energy-consuming for me at the moment

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I am up for a game.

I would prefer some private communication though, it negates the point of sharing a colour with someone if you canâ€™t coordinate imo.

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You can coordinate, just not privately.

Haha, fair point.

Itâ€™s not a deal breaker for me, I just think it would be better.

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In case we decide to play with sequential move order, it remains to decide how the shared colours are positioned with respect to the move order. For a first game I would suggest we play with two colors each, and each color has exactly two players. I have prepared two possible set-ups:

P1 â€¦ PN stand for the different players. In the first set-up players next to each other share a color. This works for any number of players.

In the second set-up players share colors with players on the opposite side in the move order. Here it looks a bit different depending on whether N is even or odd. Hopefully the picture is (for the most part) self-explanatory.

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Great, welcome to the game

Iâ€™d like to wait a bit, see if somebody else wants to join, and then make a poll to decide. I personally agree with @Vsotvep that the private scheming can be exhausting. Unfortunately Iâ€™m sometimes pretty stubborn, which easily results in discussions without end In case we allow private communication, I may make it a point for myself to keep it to a manageable amount.

So far we have @Vsotvep @yebellz @Here_We_Go and me participating in the first game (unless there is the need for a game master, in which case I could take that role).

Anybody else interested in playing? Donâ€™t be shy, weâ€™re all just trying out something new.

What about @bugcat @le_4TC @Groin @shinuito @Samraku ?

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Thanks for invitation but I am out. Not in any mood for go variants or other games these days.

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Itâ€™s a little complicated for me

Maybe the second game

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If we use alternating turns, I think we could manage without having a host, so that @martin3141 could play as well.

Also, Iâ€™m fine with public chat only (no private channels), since that makes the game less complex and time-consuming from the communication perspective.

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I think thisâ€™d be a bit too much for a simple countryside bugcat like meâ€¦

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Iâ€™m all for the fractional coloring part, but Iâ€™ve learned that multi-player variants just arenâ€™t my cup of tea (since itâ€™s so hard to define incentives).

Maybe for the second game, we could try making it â€śteam-basedâ€ť: for instance 4 players, 2 teams of 2, each person sharing one color with their team member and one color with one of the opponents. I would probably join a game like that, if there still is interest after the first game

In any case Iâ€™ll enjoy spectating the first game!

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