Multi-color go

    Keywords: Variant, Theory

Three color go
Three color go allows three players on one board

This page explores how go might be played with more than two colors.

There is an important distinction between number of players and number of colors. Traditionally, go is played with two players and two colors. Some simple variations of go change the number of players but not the number of colors; pair go is played with four players and two colors, and a person playing a game against himself is playing with one player and two colors. This page is concerned with the number of different colors of stones on the board.


Go with three colors

[Diagram]
Three-color go  

Here the third color will be red, marked by red squares in the diagrams. The order in which the players move is important. In these examples we will use the order black, white, red.


Observations on three-color go

With introduction of a third and more colors multi-color Go does resemble multi-player strategy games where off-board interaction is a decisive part of game play (like e.g. Diplomacy) more than actual Go.

The possibility of several moves by opponents before your next move alters even basic features of the game.

An altogether different game

Most of the time, a group left with two liberties at the end of a player's turn can be captured before he has a chance to play again. One can think of a group with two liberties as being in something like atari.

[Diagram]
Safe bamboo joint (White to play)  

With the same color on both ends of a bamboo joint, Black can always defend against the cut, as in two-color go.

[Diagram]
Vulnerable bamboo joint (White to play)  

Black's bamboo joint can be cut by White and Red working together, if it's White's turn. On Red's turn, the cut fails. Also remember that if White attempts to cut, she has no guarantee that Red will cooperate.

[Diagram]
Capturing different colours with one move  

In a three-color game, it's possible to capture stones of two different colour with one move. The stones can also be enclosed by two colours, because capturing happens when the group's liberties have been exhausted.

For an example of three-color go, see Three Colour Ongoing Game.


Scoring

[Diagram]
Who gets credit for the capture?  

Territory scoring becomes problematic with more than two colors, because it is not always clear who should get the points for the capture of prisoners. In this example, who gets the points? Is it White, because she took the final liberty, or is it Black, because he occupies more liberties? Should the points be split somehow?

For this reason, it is much easier to use area scoring when playing with three or more colors.

Anonymous1?: I can't see a problem with Territory scoring here, because the prisoners are simply put into the territory of the red player when scoring takes place. So the capture of some stones is simply a minus for the player of the stones which were captured.

Anonymous2?: The problem with that form of territory scoring is that the capturing player(s) see no direct benefit from the capture. For area scoring, each capturing player gets some credit as they will likely be able to fill in some of the vacated territory with their stones.

Anonymous3?: I think most of all the one whose stones were captured made a kind of mistake, which should be taken into account. Hence it makes sense for me to have both "capturing parties" benefit from it, rather than taking into account who the final liberty filled.

Cuc? I don't agree with Anonymous2, and perhaps Anonymous3 is addressing this as well. So, to clarify, I believe that the idea of Anonymous1 works just fine, because if Red's stones are captured by either other player, those stones will end up taking points from Red; this will be of *equal* (!) advantage to both other players. Note that after removing the red stones Black can play a2 and gain another point, or even a3 to threaten to take 2 points. Alternatively, if White plays a2, and Black tries to capture White, White can prevent it and both players end up with no "extra" points, because all the points have been turned to dame. So, I don't think that Territory Scoring is faulty (looking only at this example for now), even it can't be decided from the capturing move alone "who benefits more". As shown, this depends on the follow-up. Of course, in the time that Black and White struggle over 1 or 2 points, Red will perhaps be able to compensate for his loss with better moves! If there are better arguments against Territory Scoring, I would like to know.

pokemonsta433?: problems originate with the proposed scoring by anonymous1 when only one party captures a group. While he does get potential territory, (provided the other two parties aren't able to take it down together) the lack of a guaranteed advantage for the capturing player just gives the third player reason to expand and fix shape while the capturing player wastes 5-10 moves capturing. This is also a problem that arises in variants with more than three people, as it's a common occurrence for only two players to capture, and one player gets to solidify a corner. Area scoring seems like a cleaner solution to these problems while also keeping the game more compact (which seems to be an advantage, when trying to fit 3+ people on one single go board)


[Diagram]
Which stones get captured?  


Coiffe?: In this case it makes sense to allow suicide and SimultaneousCapture because otherwise there's no incentive for red to play there and maybe no way for red to capture either. DelayedSuicide should work too though it would be more complicated; one would have to find out how to define the order of capture.

Ko

The basic ko rule doesn't apply well to three or more colors. Capturing a single stone that has itself just captured a single stone doesn't necessary lead to repetition. Superko works with any number of colors. Colorblind superko allows ko fights that feel familiar.

Miscellaneous

infraredux: I've never been a fan of adding more players to a two player game because often the game degenerates into politics; players A and B decide to gang up on C because C is winning. Is it interesting to have two players use multiple colors between them?

wms: I agree with infraredux. Interestingly, though, there is a game that has go's "surround area for points" rule that plays excellently with more than two players - see [ext] http://www.boardgamegeek.com/game/503 for a description of Through the Desert. One thing that is done in TTD is to severely restrict where you can move your pieces; you start with five stones on the board, each a different color (so in an n player game, there will be nx5 stone colors in use). You can only place a stone where it is adjacent to a current stone of the same color. This solves the "everybody gangs up on the winner" problem because with clever play you can control which opponents are able to attack your positions. Perhaps it would be possible to construct a multiplayer game more like go, but that also uses a similar mechanism, letting players control which opponents may attack them?

Asd: In sociology, they say that [ext] triads are inherently unstable. I think this applies to multi-player go aswell. In my opinion, games with 4 or more players are more interesting and generally work better than 3-player games. Two players will still gang up on a third occasionally but it's not as much of a problem as with 3 players; while A and B might attack C, D might take his chance to invade A or B when they're busy fighting elsewhere. Of course, that's just an example, but the dynamics between the players get more and more complex (but not really chaotic) the more players you add.

Prone: On usual go capture rules, you check if enemy pieces are possible to be captured and then capture then, after it you check if capturing your pieces are possible and then "capture it", if a move would capture your own pieces this move is not allowed. How this capture rule works on multi-color go? Do you check possibility of enemies captures in order one after another (and then check for the capture of your own) or check simultaneously for the capture of all enemies at the same time (and then of your own capture)?

Onionbro: Regarding strategy, a strong live base is more useful than scattered territory stones or moyos, especially if the base is not entirely surrounded. Anyone who claims territory with one point jumps, knight's moves, etc is very likely to lose it if simultaneously invaded by two players. This from a game between two 14-kyus and a 20 kyu.


An interactive implementation of multi-color go can be found in [ext] 3D Tashoku Go


See also:


Multi-color go last edited by PJTraill on May 10, 2018 - 00:04
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