Tri-color Balancing Go

Tri-Color Balancing Go

Here’s a variant for three players I thought might be interesting. If it works as intended (and what ever does on the first attempt?), then kingmaking and one player being left out in the cold will be minimized or (if I may be unreasonably optimistic for a moment) eliminated. It’s probably been done before, but I’m not sure what it was called.

I would love to try this if I can find two other players. I’d recommend making a ternary pm thread for the game where we write our moves, as I don’t see any way to use OGS for it.

Rules

  1. NZD rules with 0.0 komi apply unless specified otherwise. First exception: suicide is not allowed. Any board size (or shape) may be used, though I think 13x13 may be a good size to begin play-testing on.
  2. There are three players hereafter called Alpha, Beta, and Gamma. Alpha plays first, followed by Beta, followed by Gamma. Turns continue in this sequence until all three players pass consecutively. (As a variant of the variant, players could play according to the Thue-Morse Sequence)
  3. Liberties are not shared between different colors, and a group’s liberties may be removed by a combination of colors of opposing stones.
  4. Area scoring is used. The player with lowest score loses. The player with the highest score also loses. The player with the middle score, wins. If two (or three) players tie, then one of them is the middle score, and so they all share in the win/it’s a draw amongst them. If the tie is two or more players with 0 points, all players with 0 points lose and the remaining player (if any) wins.
  5. A single player may not unilaterally resign, but if two out of the three players agree that neither of them can win, they can both decide to resign together, and the remaining player wins.

Strategic Implications

For the following examples, Alpha will be assumed to currently have the lowest score on board, Beta the middle score, and Gamma the highest score (thus Beta is winning for the moment).

Alpha must work to increase their own score, while decreasing Beta's score, and not letting Gamma decrease their score.

Beta must work to keep Alpha's score low and Gamma's score high, while being pulled in opposite directions by Alpha and Gamma.

Gamma must work to decrease their score while increasing Beta's score, while not letting Alpha increase their score.

Gamma wants to reduce their own score, but as suicide is disallowed, they cannot get their groups captured without the cooperation of one of their opponents, both of whom want them to maintain a high score and thus stay ahead!

Gamma might try filling in all of the eyes in one of their groups, but Beta will attempt to gain a border with this group so that they can create a seki with one shared liberty: Gamma will be disallowed from playing there, and Beta would no longer have the middle score if they played there, so seki! On the other hand, Alpha may try to prevent the seki if it would be a large enough loss to give Gamma the lowest score, thus putting Alpha into the winning position.

Since Area Scoring is used, captures are not used in determining the final score. If using them while counting the game, remember to subtract them from the player who lost them; it doesn’t matter who made the capture.

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Chances are one play will reveal breaking flaws, but until we know for sure, anyone want a game?

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Doesn’t NZ rules allow suicide?

Well I am in. Add me to the game :slight_smile:

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Yes, hence why I explicitly forbid it, as otherwise it would be too easy for the player with the highest score to shed points, leading to a very silly endgame.

I’ll send you and the 3rd player a pm for the game once we get said 3rd player. :smiley:

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Do you want an expendable 3rd player so you can get the serious players after this 1st trial-and-error attempt? (No is fine, no is always fine.)

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Are you interested in playing? If so I’d be happy to have you play.

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And you think I’m much better?

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I would like to give it a try, but keep in mind it might get too complicated for me. If you prefer someone who will follow easier, I won’t mind.

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How do you intend to play it with only two colours?

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It is a variant which requires 3 colors, so, we don’t. :smiley:

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I mean, how do you intend to play it, considering OGS only supports two colours?

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We’re using triangles, circles, and squares on a demo board, with red, green, and blue highlighting.

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Here’s the first Game (it’s ongoing):

Haze with a Z is Triangles (red), Gia is Circles (green), and I am Squares (blue).

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Converting a two-player (or team) game into a match between three factions can already have a strong balancing effect (as long as one player/team is not so dominant that they can overcome a 2v1 situation), since the two trailing teams would be incentivized to work together to beat down the leading team, until all three teams are roughly balanced in position/advantage.

Thus, I think this rule is unnecessary and drastically changes the nature of the game, i.e., it’s no longer about controlling the most territory. I think the game should just be the usual, highest score wins, with life/death disputes settled by “playing it out”.

With the goal being to have the second highest score, it’s not even clear how you would define life/death, since one player might want to have their own group declared dead, while their opponents could refuse to capture it and insist it was alive.

Similarly, people have experimented with three-sided football.

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I’d be interested in playing this as well. It would definitely feel more go-like.

I have actually defined this in the rules. After all players pass, they must agree on dead and alive stones. If they can’t then the game resumes (see NZD rules), and when all players pass again, all stones remaining on the board are considered alive. The prohibition against suicide may result in a living group which has only one eye, that noone wants to (or can) play on.

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I guess I should instead say that it hard to sensibly define life and death in this game.

Life and death would be completely changed in a game like this (as you originally defined with a “second-place goal”). I think that’s an even bigger strategic implication than you’ve mentioned about the 3-player dynamics.

Consider if Alpha had a unsettled group, and that Alpha would be leading in points if it were to “live”, while Beta would be leading in points if it were “captured”. Hence, Beta would not want to capture that group, however, I think Gamma might, since by dropping Alpha down to second place, that could also make it easier for Gamma to overtake second place. The odd thing is that Alpha would not want to play any more defensive moves to protect that group, and maybe Beta would want to play moves that protects the group from capture by Gamma (not always possible, and maybe impossible in general, but maybe some shapes exist where this could happen.).

Further, although Alpha cannot commit suicide to drop to second place, they can still ruin some of their “safe” groups by filling in eyes, in order to let Gamma capture them, which Gamma might want to do, since it also makes it potentially easier for Gamma to catch up to a closer Alpha that has now dropped below Beta in points.

I think this would all lead to a very weird and lengthy end game that is almost as pathological as if suicide was not forbidden.

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Yep. I’m interested to see how it plays out. I’d prefer to have as few rules as possible which result in varied and interesting strategic implications. It has occurred to me that forbidding suicide may not be sufficient to counteract endgame silliness, but I want to actually try it before adding in another rule.

If it does prove to be a problem, I think it would be possible to forbid the filling of the penultimate eye of one’s own group, but that’s getting dangerously close to Japanese-rules-level edge case breakages. I think it should be possible to define sufficiently well to use as a rule, and if the edge cases come up, that’s that, play it according to the rules despite some silliness, but I’d like not to have to resort to that, as the current formulation is more elegant in my opinion.

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I think the cleanest way to avoid all of these problems is to just make the goal to have the highest area score possible. It would more closely resemble Go, while still having the balancing effect of a three-way struggle, and whether or not suicide is allowed is a far less consequential option.

Why have a “second place” goal? What was the motivation behind that design choice?

That sounds like a nightmare to adjudicate or even formulate a rule to prevent such cases. What if someone has a group with a “living eye shape” that is just one single eye (e.g., five or more empty points in a straight line)? I guess it should be against the rules to start filling that in, but it would be incredibly difficult to codify “don’t play pathological moves” into clear and well-defined rules.

Edit: I guess it’s not surprising that there is already significant discussion about three/multi-color go.

https://senseis.xmp.net/?MultiColorGo

From that page

Group dynamics

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.

It must be specified how players are allowed to bargain: privately, publicly or not at all; this would be part of the rules of a tournament, and should be agreed before starting a casual game.

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A while back I read the rules to an 3-player abstract that had an interesting mechanism similar to this. Unfortunately, I remember neither the game nor the mechanism.

I was thinking today about the ternary TM sequence, and how it could apply to 3 player go, and it occurred to me to posit a rule that the winner was the player with the highest score, unless their score was more than n points greater than the player with the second greatest score, in which case the player with the fewest points would win. I was thinking through the implications of this, and wondering how one would decide on the size of n, when a smaller n would obviously make more sense for stronger players, when I realized that just giving the win to the middle player could have all the effects I wanted. Elegance at its best: minimum of complexity combined with maximum of strategy.

And that was basically the game, minus ternary TM, which, while it would probably make for a slightly better game, I don’t think it would be by as much as it is in orthogo. So this sort of balancing mechanism really was intrinsic to the formulation of this variant, which explains why I see the strategic implications as interesting consequences of the rules, and not as flaws (unless of course those implications have problems from a game-design perspective).

One other thing which has something to do with why I want some sort of rule-based reason to encourage certain behavior, is that I’m not that big on games with alliances and the like. So I’d like a 3-player game which codifies the inevitable alliances in a natural way where the board state dictates what is in one’s best interests to cooperate on, if anything.

It has occurred to me that players filling in all but the last two points of territories (or a good part of the way towards doing that) could become a tedious undertaking tantamount to going back to stone scoring instead of counting in orthogo. I’m hoping that there is enough strategic consequence to this sort of thing that it does not end up feeling like that, but we’ll see.

The bigger potential issue you hit upon is what made me consider a ban on filling in the penultimate eye. Here is a way it might be defined:

Any group (string) which, if all stones not belonging to said group were removed from the board, could not be killed by any arbitrarily large number of consecutive moves by a single other color, is considered unconditionally alive. A player may not play a move which would cause such a group to no longer be unconditionally alive, regardless of its life and death status.

This rule does not cover all cases, most notable cases where two strings of like-color stones share two separate liberties, and are thus alive, but are not “unconditionally alive” by this definition. I would hope that such cases are sufficiently edge so as to be an acceptable loss. There might also be some strategic implications if a player finds it in their interest to prevent someone from forming such a flexible group.

I decided to table this rule as I was writing it, when it occurred to me that a suicide prohibition might actually do what I wanted. And if a simple solution suffices, I don’t want the complex one.

PS: I’d love to play a game with the highest score winning as well; I just see them both as interesting variants until proven otherwise: too different to supplant the other’s niche.

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