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:

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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.