A couple of years ago, while I was reading about cycles on Sensei's Library, I noticed that, in all of them, there was a sequence of at least two consecutive captures. This gave me the idea for Stoical Go, a Go variant where ko and superko rules are replaced with the simple prohibition to make a capture immediately after a capture by your opponent. While this is much more practical than superko, it does change tactics to some extent.

I've kept looking for common features in all known forced cycles in order to create new human-friendly alternatives to superko that keep the game as unaffected as possible. I've posted my findings in a revision of my Stoical Go article on Sensei's Library. Everything after the example diagram is new content.

The section "Variants with the ko rule" lists some rules that result in finite games practically indistinguishable from Go. They only restrict moves following sequences of two captures. My favorite is the 2-2-2 rule, which reads as follows:

If the latest two board plays (one by each player) have been captures, your placement must be part of a group with more than two stones or more than two liberties after removals (or both).

You've clearly put a lot of thought into it, but I'll be blunt. I think you're trying to solve something that is barely a problem to begin with, and your solution is a Frankenstein's monster.

I play go using what you might call "naive super ko" as my mental model. I have never, in ten years, encountered a position where I did not know if my move was legal, or where I perceived that the life of a group depended on whether the game was played under Positional Super Ko, Natural Positional Superko or what have you. I know that there are incredibly complex cases out there where it matters, but I'd rather take my chances than internalize rules about disturbing captures.

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Occupy Babel!

I realize that the rule about disturbing captures is tricky to internalize and I'll admit that I created it mostly as a theoretical exercise. As such, it would still be nice if some talented mathematician managed to show which features included in the definition of disturbing capture are actually shared by all possible forced cycles, known and unknown.

However, I think the variants with the ko rule are much more practical than both the former and superko, and they don't seem terribly inelegant to me. Does your judgment apply to all of those as well?

I can second this, and I have been playing 43 years. I have had 3 NR games but the rules under which I was playing were clear so there was no dispute. I think all these obsessions with obscure possibilities should be left to the pros and RJ and the rest of us should just enyoy playing.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

I don't know why I gravitated to the variant I did in spite of you saying you prefer the 2-2-2 variant. Maybe because the other one was labeled "optimal" or because I spent more time trying to understand it.

Anyway, I have a weaker gut reaction to the 2-2-2 rule, but that's because while it's conceptually simple, I have a harder time thinking of how it will change play. However, it seems like the following is a bad case: I play a capture as a ko threat, putting my opponent's group in atari. He responds by capturing a different stone of mine to rescue his group. Now I cannot take the ko. Am I understanding this correctly?

Click Here To Show Diagram Code

[go]$$c Is 3 at a forbidden?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . X O a O . . . , . . . . . , . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X X X . |
$$ | . . . . . . . . . . O O X X X X W X . |
$$ | . . . . . . . . . . O X O O O O 1 X . |
$$ | . . . . . . . . . . . 2 . X X X X . . |
$$ ---------------------------------------[/go]

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Occupy Babel!

... and to computer programmers and to beginners.
A go-playing program must be aware of possible cycles.
Beginners often play on small boards. The smaller the board the more frequently one encounters questions on the precise rules. Try a 2x2 board.

No one plays 2x2 so that is fatuous. I've never come across a problem on a small board so the beginner case is not a big deal: if it happens then just explain it. As for programmers, okay I will concede that, but I still think it is a lot of fuss over nothing as programs can be written to interpret anything which is given: just program them to declare a game as NR if a position is repeated a certain number of times.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

Nobody says things are difficult. But things are badly defined, and there are no completely satisfactory precise definitions. Maybe Tromp-Taylor comes closest. In actual play the uncertainty seldom plays a role, you are quite right.

Let us generalize go. The players agree on a graph, and play on that graph, as one usually does on a rectangular grid: play on an empty vertex, remove connected components without liberties.

Counting, end-of-game, handling of repetitions is as usual. Now study this game on small graphs. Very quickly it appears that "as usual" is not precise enough.

Stoical ko greatly changes the game. OC you can invent lots of variants greatly changing the game, but for what purpose? If you want practical alternatives to superko, please specify what you consider "practical".

Vier,
For me the issue that I am a mathematician (algebraist) and I have studied graph theory. I understand everything that everyone is say when it comes to this topic. But I play go to get away from mathematics, not to embrace it. To me go is a game of harmony and balance, not of mathematics and analysis beyond that which is necessary to enjoy the game as usually played.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

Yes, 3 is forbidden under the 2-2-2 rule. It's played after two consecutive captures (one by each player) and it neither has more than two liberties after removals nor is part of a group greater than two stones.

(Of course, neither 1 nor 2 are disturbing captures, so this would play out exaclly as in regular Go with the rule that forbids sequences of two consecutive disturbing captures.)

Stoical Go greatly changes the game, but these other variants don't. However, even "greatly changing the game" is fine to me as long as the game isn't arguably worse than Go, since, if it isn't worse, the absence of superko makes it actually better to my eyes. In Stoical Go, there are actually more ko fights than in regular Go, which might even be an advantage. A minor drawback is that sente is a bit more powerful as captures restrict the opponent's next move (so Black's winning ratio might be slightly higher), but, at the same time, this same restriction might actually create some additional tactical interest.

For me, a practical alternative to superko is one that prevents all known forced cycles without requiring players to keep track of all previous board states while keeping the game close to Go (Tibetan Go is close to Go; Redstone and Atari Go aren't) and without making it arguably worse than Go. Having to remember a few bits of information that any average player will remember naturally anyway, as in the variants I present here (coordinates of the previous move and whether the latest two moves have been captures), is fine.

The Basic-Fixed-Ko-Rules eliminate all forced cycles other than basic ko but permit playing useless long cycles so that one must recognise repetition if the opponent plays a useless long cycle.

Yes, I admire those rules myself, even though you still have to recognise repetition in those cases.

(But I think you meant to say Fixed-Ko-Rules there. Basic-Fixed-Ko-Rules are meant to make ko play out as in regular Go, right? Also, if I understand correctly, Fixed-Ko-rules eliminate basic ko in the same sense that they eliminate all other forced cycles as well: it's legal, but not optimal.)

if there are practical alternatives to superko then we would be using it already.
if you think you can invent something that so many great minds didnt think of then you head must be about to burst.

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"The more we think we know about
The greater the unknown"
Words by neil peart, music by geddy lee and alex lifeson

There is a practical alternative to superko and it was in use for hundreds of years until someone came up with the, in my opinion, stupid idea of superko. That idea is No Result.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

DrStraw, I agree 99% with your statement.

but as a math and programmer myself i dont think superko is useless.
as 5 years old boy, I learned that taking one stone and opponent taking same stone that i placed... would be problem so we play somewhere else first and we called it ko threat. <--- very loose definition but worked on me for 20 years.

20 years later i read that it was to avoid duplicate board position (which is one good and logical way to describe the situation).
now they expanded the idea of duplicate board position to all possible problem areas known to go board to avoid tie game.

can people apply that idea to triple+ ko or other situation without getting confused?
i think even professionals will have hard time remembering all prior position.

Chochihun even for that that it was his turn to take ko during championship match.
now what would happen if it is triple or quadruple ko. only alpha-go will be able to trace such sequence.

Current rule of tie game in such rare situation is fine and people still can enjoy game without crazy rule such as super ko.

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"The more we think we know about
The greater the unknown"
Words by neil peart, music by geddy lee and alex lifeson

I don't disagree with your position that superko is pretty decent (and I don't mind NR either), but I really don't think this kind of thinking is very helpful. You can apply this to finding new variations in Go, making science discoveries, or writing new stories. Yes - when you are looking at something that others have looked at, you should be prepared to look at the issue from another perspective or in more depth, but to dismiss such attempts is frankly silly.

In practice, No Result has the same difficulty as superko: one must be able to recognise repetition.

Great mind? Thanks;)

Discovery would already be used? Organisations often need decades to fix even much simpler problems of their rules. Just because something is practical does not mean it would be adopted quickly.

Exactly. With that mindset, nothing would ever be invented.