Some musings on a "reverse" ko rule

This post is long and takes a while to get to the point, but I hope some readers find the journey interesting!

The convention in combinatorial game theory is that a game ends when one player has no legal moves (and that player loses). Thus when formulating the rules of go in this setting, passing can obviously not be allowed. No Pass Go is quite similar to regular go, but has some peculiarities (in particular a much longer endgame). This is “fixed” by introducing Prisoner Return, which yields regular go with Group Tax.

Now, suppose we are making a ruleset with prisoner return, legal suicide and positional superko. We could use the CGT convention and end the game when one player has no legal moves (for this case, that would typically be when every move is a one-stone-suicide, violating PSK).

But suppose we don’t care about combinatorial game theory, we just want to make the rules as “simple” as possible. Rather than say

  1. Repeating a board position is illegal
  2. The first player without a legal move loses

we could simply say “The first player that repeats a board position loses”. This works especially nicely here since ko is the only type of forbidden move, but the same idea works if we also want to “forbid” suicide, just make suiciding a losing move.

Obviously this distinction between making a move illegal or losing doesn’t affect the game at all, except at a very superficial level. I think it’s aesthetically pleasing to allow every intersection on the board to be played as a legal move, but for a good user experience on a go server it also makes sense to just not let a player make a ko move. So I’m not here to argue that this formulation is “better”, but I think it is an interesting different perspective on the rules: The players take turns making moves until one of them violates superko.

While pondering these things last night as I went to sleep (as you do), I wondered what would happen if we made this one small change: what if the first player to “violate” the ko rule won instead of lost? This means that you can never take a simple ko-shape, because the opponent takes back and wins. Also, some fun stuff happens with Sending two, returning one:


Black just played 1. If white captures at A1, black will recapture at A2, repeating the position before 1 and winning the game (note that the distinction between positional and situational superko matters here). If white had had a ko threat elsewhere on the board, white could play that first and then capture at A1, but in this case there is no ko threat. So white will have to pass/return a prisoner/play a random move inside black’s territory, depending on the specifics of the rule set. Next black captures two stones, white recaptures one stone, and black plays atari:

Is white dead? No! Black can never ever capture at B4 (white would recapture and win). White is therefore alive with two eyes. In fact, even something like this would be alive:

So far I’ve glossed over the other details of this variant ruleset, because I’m not sure what they should be yet… if we allow suicide and use positional superko, then making a one-point eye is an automatic loss (the opponent suicides one stone, repeating the board position). Let’s save that crazyness for the future, and make a more familiar ruleset by disallowing suicide, and if you have no legal move you lose. Or, to incorporate the idea from earlier in this post:

  1. If you repeat a board position, you win.
  2. If you suicide, you lose.

This should lead to a pretty standard go endgame, where the player with more territory wins (especially if we add in prisoner return). To make it even more “practical” we can reintroduce passing and use regular old boring scoring. This variant can easily be played on OGS by using any ruleset with PSK (for instance Chinese): if you manage to get the “illegal ko move” or “illegal board repetition” error message you have automatically won. Else the game continues normally to scoring after both players pass. Would someone like to try a game?

For the more theoretically inclined, can you find a way to make this ruleset more “pure”? No disallowing suicide, no “player without a move loses”. Basically, I would like to always end the game with a repetition. Clearly if we continue playing long enough, eventually one player will manage to repeat. But I’m not sure such an endgame actually favors the player with more “territory”, so the game could become unrecognizable (and probably not very interesting). Is it possible to fix this with some tweaks to the rules?

6 Likes

I feel these are more rigid (or maybe more “primitive”) rules which might have been used in the precursor of Go. We see a watered-down version of it in Tibetan Go ko rule, where it doesn’t allow a stone to be placed immediately inside a captured area for one more turn (and not just one stone, but a whole area). This essentially means the captured ko stone spot is effectively “colored” as a territory for good (in Tibetan go it only lasts for one turn temporarily, but in your case, for the rest of the game).

I read in The Evolution of rules in Go, the author hypothesis there was a primitive “one captured eye/area” count as alive shape Go rule existed before. Where whenever one side captures stones by killing them, then the area within would become “settled”, and neither side can play inside that area anymore. The end of the game will be reached when both players run out of place to put their stones, and the winner will be determined by who captured more stones.

It is a very simple rule set and can reach the end of the game very easy with no ambiguity. However, it might be less fun in comparison, since it forbids any form of ko, or tesuji, and such. And what we considered ko or super ko, no suicide etc, might just be “expansion packs” added to the original rules to spice things up.

4 Likes

Without passing and allowing suicide.

Let’s say Black has at least two eyes, the smallest of which has size N and White has no eyes, then White has a winning strategy.

  • If N = 1, White can suicide in the eye to repeat the board position
  • Assume the statement is true for all n < K, and let Black’s smallest eye be of size N = K. White plays any move inside this smallest eye, making sure not to create any White eyes. If Black also plays inside the eye, we see that this creates an eye for Black of size smaller than K, thus White has a winning strategy by assumption. Otherwise, Black plays a move outside the eye. There are finitely many moves outside the eye for Black to play, thus eventually Black will have to reduce the size of the other eye, until this has become an eye of size smaller than K, thus White has a winning strategy by assumption.

Thus, the first player to separate the board into at least two eyes loses. I’m not sure which player would be able to force this, capturing makes this quite difficult…

3 Likes

It can last for the rest of the game, but not always! Take for instance this position:


Black can not capture D3 right now. But black can play atari from the other direction, threatening to capture without ko:

If white connects, black captures everything:

So instead, white should give up the two stones and live small:

Obviously the idea of playing atari from another direction, to threaten capture without ko, works in the center of the board as well. So it’s not some super rare edge case, it will probably come up pretty regularly in a full game. But it was more fun to demonstrate along the edge, since black’s E4 move also exploits the special rules, and we got to see “in practice” a group living with two “false” eyes.

3 Likes

I think because exactly due to this, the best strategy would be a reverse tiger’s mouth along both sides’ boarder backward facing each other, in order to prevent this type of “loose surround” possible. And try to get sente to be the first to create a bogle along the “zig zag boarder” where your opponent couldn’t take it. And backfill until your opponent is forced to take the ko. (if allowing pass, this could end in draw). Another strategy would be creating a jumping wall boundary 1 space away first, and then be the first to break the no-man’s land.

Some variations form of this types of forcing move games might actually existed in the past, because it is essentially a kind of shape arranging game, like Gomoku. And instead of achieving stones in a row, it is achieve a outward facing tiger’s mouth to your opponent’s tiger’s mouth, each player tried to play like a checker board pattern, and preventing the other side to do it first.

2 Likes

Indeed, this is the crux of the problem. More territory is essentially punished instead of rewarded. Rules like that don’t lead to a very deep game. Maybe every game goes like this: The players build huge dumplings without any eyes. Eventually one of them gets captured, when there is only one liberty left for both (this has nothing to do with skill, but is predetermined based on the parity of the board and who plays first). Let’s say that it was an odd board, so black captured white.

Without prisoner return, white is probably easily winning from there. With prisoner return, the situation is slightly more interesting, since black now has lots of passes. Thus they can wait while white fills out all the empty space again, until black is captured. This may continue back and forth many times, with the edges of the dumpling moving slightly back and forth. Even if this game turned out to be interesting to analyze (I doubt it), it has lost all the flavor of go.

So the “fix” I was looking for was some small tweak (analagous to the prisoner return added to no-pass-go) which would allow the player who has more territory to force a repetition. This might very well not exist, and it doesn’t matter much anyways; the variant can still be played with more traditional scoring as outlined in the original post. But it then necessarily takes the position of a less natural variant compared to regular go. I was a little excited by the prospect of a sort of “Bizarro go” with just as simple rules (just changing one word), similar strategy, but very different tactics (there are other natural ways to modify the game, Delayed Suicide is one example, but that has much less effect on the game).

From one perspective, it’s a nice thing if it doesn’t exist. The idea that go is so simple and universal that it could be independently discovered relies on the fact that there are many different ways to formulate the rules which lead to essentially the same game (i. e. no pass go still rewards territory, despite the lack of a scoring phase, so the opening and midgame look very close to normal go, even though the endgame is different).

If there were adjacent games with completely different strategy (even more so than in the diagrams here, which still resemble go), with just as simple rules, and just as deep strategy, then maybe aliens would play those instead. So if the go rules “fight back” when we try to change them too much, that is some extra evidence for their universality :slightly_smiling_face:

4 Likes

Another example of a small change leading to quite similar weirdness:

Many rules formulate capture like this:

  1. Remove opponent strings without liberties
  2. Remove own strings without liberties

If we switch the order of those two, we get a super different game, which still has the flavor of go. Territory is good, capturing things is good, etc. However, living is much much easier. One eye, even a false one, suffices. Thus this game is much less interesting. If aliens came up with this one first, I expect that after a while some of them would experiment with switching it up, and discover how much more interesting the other order of capture is.

3 Likes

The reconstruction of Ludus latrunculorum, has an even stranger liberty shortage rule, when a piece been clamped (has 2 liberties left), it will be immobile (since pieces can move in latrones), and after one turn of immobile and still been clamped, it will be dead.

It’s easy to imagine other rules of “atari” existed in the past been experimented upon. And some of the strange ones survived today. Ming Mang (game) - Wikipedia, and this is just one of them.

1 Like

the game resembles Jul-Gonu, Hasami shogi, Dai hasami shogi, Mak-yek, Apit-sodok, Rek (Game), Seega, Ludus latrunculorum, and Petteia.

That’s a nice linklist for OGS lazycats~

I’ve never heard of most of these, only ludus latrunculorum and hasami shogi.

The “clamp-capture” rule is called custodian capture, as I’m sure you know. The etymology of that term isn’t clear.

2 Likes

Come to think of it Reversi is an extension of this clamp-capture rule, but it applies to none moving pieces using “long clamp”.

1 Like

The Reversi clamp is also a “group custodian capture” – just like in Go, it “captures” an entire group of tiles, which can be considered connected in the same way.

Ah, I guess that’s what you meant by “long clamp”.

I was just thinking this could quickly turned into a very different type of game, say if the “capture stones” don’t turn into the captor’s color, but turn into neutral inactive obstacle - like a grey color. And expand the legal move to all intersections of the board. And the game is till be determined by who would have more pieces on the board at the end of the game.

1 Like

I found this on the mak-yek article – note the interesting “intervention capture”.

1 Like

This type of capture rule, normally has two steps, and a player needs to choose to either capture the opponent’s piece, or forgo the opportunity and move a piece. So by willingly “sacrifice” a piece that is currently not doing anything (like a weak group), you can delay two of the opponent’s pieces. Most time, it’s not the best idea to waste movement “sente” to just capture one piece. A small local victory, doesn’t win the war, when the victory gains too little, and the investment is too high.

And the delay tactic is common across many strategy games, using a weak group to hold a stronger part of the opponent’s, and eliminate the weaker one.

1 Like