Tri-color Balancing Go

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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There are many “living” or “safe” groups that are not “uncondtionally alive” as you’ve defined it (which I guess is similar to the concept of “pass alive”). For example, a group that has just one eye that consists of 5 points in a line. Or, another example, a group with two eyes: one is a single point and the other eye is a square of 4 points in the corner of the board. Both of these examples are “living” (in typical Go), but are not “unconditionally alive”, since if one were to only pass, the opponent could still capture it. Typically, a group that even surround large areas of territory, but is not divided into multiple eyes, would not be unconditionally alive.

Hence your proposed rule would not prevent the pathologies similar to suicide.

I don’t quite understand what you wanted now. I thought it was established that only banning suicide would not be enough to prevent all sorts of pathological end game, which you wanted to avoid?

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Sorry if this has been answered before, but I cannot see what prevents the leading player with more territory to keep filling his own territory at the end, while the two other players must pass. Since suicide is prohibited, each player ends up with one point per group, but can also capture groups from the other players and fill the territory to try to become the middle player. This looks like a strange endgame.

Hmm, those are some good exceptions I hadn’t thought of. I’ll try and think of a more robust potential rule (if it’s needed) at work today.

It’s area scoring, so filling in one’s own territory won’t do anything once dame have been filled. It will be a strange endgame, the question is how strange, and if that strangeness detracts from enjoyment, or adds to it.

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Suicide

Okay, here’s another proposal. It loses some elegance, but I think the trade-off will be worth it if the current ruleset proves to have insufficient power to stymie the silliness.

Suicide is Forbidden.

It is forbidden to make a move such that a group which was pass-alive becomes no longer pass-alive after the move is played.

On any turn, instead of playing a stone of their own color, a player may (but is never forced to) choose instead to place a stone of either opposing color, provided that it would fulfill the following two conditions:

  1. It would be a legal move if played by the owner of that color.
  2. It causes a group that was previously not pass-alive to become pass-alive.

A looser (in most cases) restriction #2 would be “It forms an orthogonal connection with a stone of like color”, but I’m not sure if there’s much to recommend this restriction over the one I put above.

Balance

The more I think about the pressures in Tricolor Balancing Go and Tricolor Go, the more I think I may have dismissed the basic variant too early. I was probably biased by all the bad press most three player games get, without considering that Go, by it’s nature, may not share those flaws.

A common problem with 3-player chess is that if red and blue start fighting and exchange a few pieces, they are both weakened with respect to green, and thus players are discouraged from engaging the enemy. I think, in Tricolor Go, that if red and blue get into a fight and green stays out of it, the best case scenario for green is that the fight ends evenly and it’s still an even game overall. But if either red or blue win the fight, then yes, green will be in a good position relative to the loser, but may well have taken a severe blow to their winning chances now that another player has had a good result in a fight. Thus, when a fight breaks out between two players, it will make sense for the third player to join in, and fun will be had by all.

One problem which I think Tricolor Go and Tricolor Balancing Go both have in unique ways, is being able to get ahead/becoming completely lost.

In Tricolor Balancing Go, it is in both the low-score and high-score player to maneuver their scores closer together, so that they can get a chance on overtaking the mid-score player. This will result, between strong players, with the score being very close throughout the game, which may make for an unsatisfying end that may feel as if it’s almost up to chance. I think this may be a fatal flaw in the core concept.

In Tricolor Go, on the other hand, the players may be able to develop a meaningful point spread amongst themselves, as everyone will be trying to gain points while reducing everyone else’s. More specifically, the low-score and mid-score players will both be trying to reduce the high-score player’s score, as well as eachother’s score, while the high-score player need only focus on reducing the mid-score player’s score. I expect there would be some pressure for scores to converge, but it would probably be much weaker than in Tricolor Balancing Go. The downside is that the low-score player might reach a stage in the game where it’s just not feasible for them to win, which may result in a king-maker scenario. This may not be as much of a problem considering that the low-score player only has half the attention of the mid-score player (and none of the attention of the high-score player) focused on keeping them down, which may be an incredibly elegant and balanced catch-up mechanism.

All in all, I’d still like to play a few games of Tricolor Balancing Go at the very least, but the simple solution may be best here.

I’d love to play as it sounds fascinating. I’m not sure I could in practice as it would need to be correspondence pace.
Are there rules about colluding/discussion during the game? I guess the resigning rule means that discussion is permitted between players but I wonder how that might affect things.

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I’d be interested in starting a second game with the rule proposal I listed above to see the difference it makes. In my, Haze with a Z’s, and Gia’s game we are playing correspondence style, so that’s all good. :smiley:

I have not reached a conclusion on this. The closest I’ve come is considering putting a recommendation in the rules to agree prior to play on the level of discussion permitted in the game. The major options I see are:

  1. No discussion or collusion allowed. (Contract Bridge style)
  2. Table-talk allowed, but no collusion.
  3. All table-talk including but not limited to alliances and discussions regarding the game state are allowed as long as all 3 players are privy to all messages.
  4. As with 3, but private conference between 2 of the 3 players is also allowed.

Players could then agree on which of the four they were playing with. I’d personally prefer 1 or 2, maybe 3 depending on the group, but I think there are people who would like each of them.

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My personal inhibition with a 3+ person game is that, with a square-tiled grid, if two players decide that one player is too much of a threat from the beginning of the game, they can always kill that person’s stones. In 3 player it takes a few moves, looking like this in the end:
Screenshot 2020-06-01 at 3.20.18 PM

which is an uncommon problem for most political games… Usually it takes a lot more to take someone out, and in all that time they can try to talk one of the players out of it. This just feels terrible. And the thing is if the player as b is good enough at the game to be considered as a threat, the triangle and square players might feel compelled to do this multiple times. And to further salt that wound, it is likely that no talking is required to get something like this to happen.

Of course, the problem of “who gets the capture” is probably going to be a point of contention between triangles and squares, but even the first 3 triples of moves is enough to put b in a sour mood.

This is a common problem in political games, and it’s called “effective elimination”, and generally the solution there is to either get the eliminated player(s) to resign, or to actually eliminate them, which is why I’m a tad skeptical for the “resignation is only possible if two players agree” ruling. I’d be far more tempted to do the typical “pieces remain on the board but makes no moves” which can lead to some potential seki-like situations where neither player will move to atari because it gives the other player the stones.

It’s an idea that I think could be really nice if it works, but very, very frustrating if not

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I’m not sure if these changes work, but my suggestion is that your proposed variant is trying to do two things:

  1. Play Go with 3 players, which I think is already well understood and explored
  2. Introduce a “second place” objective, which can create some pathological strategy that bear less resemblance to Go.

I think it should be possible to separate these two. One way to consider your rules for a second place objective work would be to imagine them applied to a two-player game, which I guess you could think of as anti-Go.

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Yeah, I’m growing increasingly doubtful that this idea is salvageable. Still, it was a productive learning experience as to the dynamics of 3-player games and unintended consequences in game design.

I’m still up for a vanilla 3-player game if we get someone else.

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