Weird and wonderful consequences of simple rules

Joining one of the bamboo-joints actually loses the seki for white! It may be easier to see for a smaller version like this one:
image image

The principle is the same in the large version, if white plays any move black will push through all the joints and then eventually capture. So those ko-threats are indeed unremovable, and the example works :smiley:

6 Likes

Oh yes, you are totally right. The fact that those are sente for black creates an asymmetry, since once white plays black can “play sente everywhere else” and we imagine that only two liberties were “actually” remaining, and white just filled one so she loses the fight.

I was horribly misreading once again! :smiley:

1 Like

I feel like this is a good a reason as any to have passing lift the superko restriction no? In that case black would just run out of ko threats?

It seems quite silly (as opposed to wonderful) to have to fill in ones own eyespace in order to avoid repetition.

This is of course a subjective issue, and there are plenty of rulesets which agree with your opinion.

For me, what’s so nice about the superko rule is that it’s the most obvious and natural way to remove all cycles from the game and make it provably finite. If you allow passes to lift ko-bans, cycles are once again possible, and you will need some additional rules to handle these cases. This is less elegant in my eyes.

Also, why is it silly to have to fill in your own eye-space? There are so many strange things in go which we wouldn’t dream of trying to “patch out”. For a total beginner, the idea that stones can be alive without two eyes may seem like a flaw! Or perhaps the fact that an obviously alive group can die as the result of a ko fight? We’ve learned to accept these strange things only because we’ve seen them many times and they have become normal, but I think in some sense they are just as weird as the stuff in this thread.

And even if you find the “23 eyes can die”-example appalling, there is no need to worry, since it will not happen in an actual game within our lifetimes :smiley:

Some of the other “strangeness” might happen a few times in recorded go history, but probably never in your own games (see for instance eternal life). Is it really worth it to make the rules more complicated and harder to understand just to avoid such a rare issue?

To me the much more common confusions that arise from the Japanese rules is a far larger problem. My local tournaments use Japanese rules, but of course nobody present actually knows the rules! And I’m not sure anybody can be expected to - it seems that even experts on these rules can have lengthy debates on how they should be interpreted and applied. (see recent threads on lifein19x19 :roll_eyes:)

Of course Tromp-Taylor and Japanese are not the only two options - there are rulesets where passes lift ko-bans which are still relatively simple. But I think the horrificness of the Japanese rules is a good cautionary tale for what happens when you try to make the rules conform to some preconceived notions of how the game “should” be, rather than adapting simple rules and accepting (or in my case, enjoying :blush:) the rare oddity as a natural consequence.

6 Likes

Another example is (I think) the Ing ko rules. I don’t fully understand the Ing ko rules (so, I qualified my previous sentence with an “I think”, and if someone wants to try to explain them, please go ahead!), but I think the general motivation was to patch out a superko “anomaly” that Ing did not like, so he wound up with ko rules that mostly behave like superko, except that some exceedingly rare life/death situation is resolved as he wished (rather than how they would be resolved under typical superko rules). However, the drawback is that virtually no one understands what the Ing ko rules actually are.

5 Likes

I wonder what would happen to “sending two, returning one” under the rule I suggested here which you might call delayed-capture go or sanitary go.

After 2, the captured black stones stay on the board until Black’s turn:

image

So Black needs to play a ko threat elsewhere (3, 4) and remove his stones before returning to capture:

image

White can play elsewhere or just pass, removing the stone at A1, and we return to the original corner position. White has lost nothing while Black wasted a ko threat, right?

3 Likes

That is a nice idea, it’s reminiscent of Delayed suicide which has some lovely consequences that I’ll probably make a post about at some point.

A sligthly different version of your capture rule would be:
“After you’ve made a move, remove all your own chains without liberties, but never the chain which your last move belongs to.”
(this one “accidentally” introduces delayed suicide as a bonus!)

The rule takes care of basic ko’s, but doesn’t prevent longer cycles, so some superko or equivalent is still needed. Without it, black could for instance infinitely prolong the game in a position like this one:
image

Since we’re not used to having stones without liberties on the board, it’s a little confusing to keep track of which board states may be repeated, but let’s try to analyze this simple triple ko:
image

Under normal superko rules, black could play the sequence 1-5 below, and white would not be allowed to play 6 since it would repeat the initial position. Instead, white makes a ko threat 6-7 elsewhere before playing 8-12 in the ko, forcing black to make the next ko threat 13-14, and so on. Essentially it’s the same as a basic ko, only with a 5-move “taking the ko” sequence.
image

However, under the delayed capture rule, the position after 6 would be:
image
Which is legal, and it’s actually black who is forced to find a ko threat, even though black took the ko first. But if white responds to the threat and black starts the sequence again, the same scenario repeats - white never needs any threats. If black has only finitely many threats, I guess black is just dead here?

The reason for this counterintuitive result is the delay between cause and effect of the moves. White’s move in the last diagram kind of is the source of the repetition - let’s say for instance that black passes next and that we have worded the rule so that this would remove the black stone. Then we’re back to the initial position, but surely the black pass cannot be to blame here?

I had a phase where I thought Delayed suicide was the superior capture rule (it’s easier to state than the normal ones, and I think it’s cool that you get these new situations where you need just one ko threat to live - for instance a group can be unconditionally alive as long as it has one local ko threat), but since there is some confusing results similar to what we saw here I’m not so sure nowadays.

3 Likes

Long cycles of the eternal flavor

There is a huge variety of possible cycles in go. In this post I’d like to share four different ones which are kind of related to one another. I don’t have anything new to add about these - it’s just nice to collect them in one place, and maybe reach some new interested people. Also, the last one is directly connected to the Ing ko rules that @yebellz just mentioned.

Eternal life

This one is famous enough to have an established name!
image
Black must prevent white from making a bulky-five, so he starts at 1. White capturing at 2 and black capturing at 3 are both forced. Finally, white has to throw in at 4 again (note that making the bulky five at that time does not kill).

If white insists on killing, and black insists on living, this cycle will repeat endlessly. Under superko rules, only 3 moves can be played locally before a ko threat is needed. Just like the triple ko in my previous post, it works similarly to a normal ko, and the side with more ko threats will win.

Here is a hard tsumego where black’s best result is eternal life:
image

Solution

image

image

Here is an example of Eternal life occuring naturally in a pro game from 2013:
An Sungjoon vs Choi Cheolhan (2013)

Under Korean rules, the game was voided. According to a comment on go4go, it was reported by GoGameGuru that this was the first occurence of Eternal life in the Korean pro baduk scene.

The sensei’s page on Eternal life links two more pro games which in my opinion do not fit the name “Eternal life”, I will instead call those “Eternal ko” in accordance with this sensei’s page. Another reasonable name would be “Double hot stones”, as we will see later.

Does anyone have some more examples of Eternal life happening in actual games? (pro games, amateur games, AI games?)

Eternal ko / Double hot stones

This is a curious situation where both sides can get infinite ko threats in a sequence similar to Eternal life (the similarity is in sending two returning one, but the context of the moves is quite different). To show the idea, consider this contrived position and use your imagination to pretend that the central ko is game-deciding:
image

When black takes the ko, white’s only threat is to play this atari:
image
(note that connecting on the first line would not threaten to kill the black group)

After black responds to the threat, we’re in this position:
image
This is where we started, but with the colors reversed! Next white can take the ko, black can sacrifice two stones as a threat, and so it continues forever. Under superko rules, if we treat the entire thing as one big ko, there would be 5 local moves between each ko threat elsewhere on the board.

Here are the two games linked on sensei’s where an Eternal ko occured:
Rin Kaiho vs Komatsu Hideki (1993)
Uchida Shuhei vs O Meien (2009)
These games were under the Japanese rules so were also voided. I recommend looking at both of them - although the idea is the same as above, the shapes are very unique and interesting.

Triple hot stones

The next two examples of cycles were brought to my attention by Harry Fearnley, and the below diagram is directly taken from this page which features some translations from a 1958 Japanese book “Igo no suri” (Mathematical Theory of Go). Please visit his page for some more historical background, I’ll just focus on the basics of the position!
image
On the lower half of the board we have a two stage ko. On the upper half we have something similar to earlier, except that both sides will now sacrifice three stones instead of two.

When black takes the ko, there is no threat for white, but she can prepare a threat with 2. Black’s only option is taking again with 3, and then white makes an actual threat with 4:
image
By now the similarity to our previous example should be apparent. Black captures three stones, and then the sequence repeats again from white’s perspective. Treating the whole thing as one big ko, there would be 9 moves (!) between each ko threat elsewhere on the board.

Quadruple hot stones

The obvious question now is, can we extend the same pattern once more? You could simply add more stages to the ko, but unfortunately we then run into the complication that one side may diverge from the sequence partway through and get a better result. It requires some additional insight to make a position where the sequence is forced for both players.

The position below was constructed by Matti Sivola and Bill Spight and published 2002 in the Nordic Go Journal:

I highly recommend reading the full article above (pages 28-30, the article is in English). It gives some background and a thorough analysis of the position which I will not replicate here.

Now apparently, this somehow relates to the Ing ko rules which tries to prevent long cycle by not allowing the capture of hot stones. The hot stones in these examples are the stones along the first line that are repeatedly captured. Since I don’t understand the Ing ko rules myself (even the simpler Ing-Spight ko rules are beyond me), I do not fully understand the context of the above construction.

I believe the existence of Quadruple hot stones was supposed to be something that the Ing rules overlooked - but I don’t know if there was a simple “fix” to this, or if the constructed position above is somehow fundamentally incompatible with Ing’s original intention.

Furthermore, since the position is constructed for (and analyzed under) the Ing rules, I’m not sure what actually happens under Tromp-Taylor. In particular, variation 2 (featuring the “disturbing ko”, one of the two types of ko under Ing rules) might lead to a different result under Tromp-Taylor. Maybe someone else wants to do this analysis for me? :sweat_smile: Otherwise, I’ll return to it with a clearer head sometime in the future.

6 Likes

I feel like this is appropriate to be here, even though it is probably more well known and relevant than most of the other “rule beasts” shown, as it is still a bit surprising when one first learns about it :slight_smile:

The following is an endgame problem that might surprise players only used to (Current!) Japanese rules.

Under either AGA, Tromp Taylor, Lasker-Maas or Chinese Rules (all give the same result as far as I understand), the following problem is “white to move and win”. There is no komi, and there have been no captures in this game.

3 Likes

I just fixed the image in the previous post, the original was wrong sorry :sweat_smile:

The solution:

Spoiler! Try to solve first!

The winning move is first J1 using the kothreat, to reduce the remaining dames, and then play B9 to fight and win that ko finishing it with A9 AFTER all dames have been filled. You can verify that way, white gets 41 intersections instead of only 40. If white plays B9 directly, black must not take A9 (that is a losing move!) but instead just connect J7, reverting to the same score as normal dame-filling.

The intuition is that the endgame in that case will finish with “black pass [or makes useless move inside self territory] , white fills A9, black pass, white pass”, instead of finishing “white pass black pass” as would end for normal dame-filling. So white manages to play one more time after black was forced to pass, getting one more stone on the board without black getting compensation for it!

Reasoning in territory terms (this should always be possible, as area scoring and territory scoring are equivalent, if territory is counted correctly with the same criteria as the area-scoring rule :wink: ), the trick is that we can imagine that white passes after black passes, without playing A9. So white managed to keep it open in the end, and thus scores A9 as an extra territory, giving it a win.

A more detailed explanation of this same principle is in this other thread: https://forums.online-go.com/t/is-an-endgame-ko-worth-more-in-chinese-rules-than-in-japanese-rules

4 Likes

Situation: White has 38 area points, Black has 40 area points, 3 neutral points (at A9, B9, J1) remain to be contested. White needs to win them all.

Question/Spoiler

Is it not also possible for White to play B9 first?

Then,

  1. If Black takes the ko with A9, White plays the threat at J1, forcing Black to connect at J7, White takes back the ko with B9, Black passes (since no threats left), and White connects at A9.
  2. If Black connects at J7, White fills the dame at J1, Black takes the ko with A9, but White plays the threat at E9, which forces Black to respond at F9, allowing White to retake the ko with B9, then Black passes (having no threats), and White connects at A9.
3 Likes

Yes, you are right, that order works too, I missed one line so I though only one move worked :slight_smile:

Spoiler

The interesting thing that, in a ko fight for this extra point, J1 and J7 are miai and work similar to a mutual ko threat, so that is why it makes sense to play it early for both.

Mutual ko threat at Sensei's Library

This is very unintuitive: If your opponent plays right, then you need not only a surplus of extra ko threats big enough to fill all dame: also when counting that ko-threat difference, you can’t count ko-threats such as J1, because if you try to wait to play them, your opponent will defend first and create an extra dame, so you cannot use them effectively as ko-threats now. You can only count your “ko-threats even after all dame are filled” as true ko-threats, and you must have enough surplus of those specifically to keep the ko open until after all dame.

4 Likes

Here are three easy problems to illustrate the basics of kos and dame under area scoring rules. All problems are black to play and win, no komi.

Since these boards have a total area of 25 (and there are no sekis in sight), black needs to secure an area of 13 points to win.

Problem 1

image

Solution

image
Black should throw in at 1 to start a ko. Note that the ko is sligthly unfavorable for black: white takes first, so black must be sure that he has more threats than white, otherwise he would be better off playing E1 instead.

In this case, black has one ko threat at 3, and white does not have any threats, so black can recapture and win the ko for a final score of B+1:
image
(white 6 passes - filling the ko with 7 may be unnecessary depending on the exact rules)

Problem 2

image

Solution

image

Black can claim the last dame and still win the ko. 3 is an interesting type of ko threat since it doesn’t directly threaten anything, but rather prevents white from filling the ko. I sometimes like to think of it as “this move would be atari if the ko was filled, therefore it works as a threat”. I’m not aware of a name for this type of move, I think most people would just call it a local ko threat?

Problem 3

image

Solution

Immediately capturing the ko is a mistake. White has a ko-threat at 2 and black will lose by 1 point.
image
So black starts by removing white’s ko threat, and threatening to play A1. If white responds at A1, black can now win the ko for a score of B+3:
image
White does better by filling the ko and letting black have A1:
image
This sequence is best for both. The result is B+1.

(I originally intended to make these into OGS puzzles as well, but it breaks if you try to add both correct and incorrect variations, since the automatic transposition feature doesn’t take ko bans into account.)

8 Likes

Here is a nice position that Gérard Taille shared recently:

image

Assuming area scoring and superko, what is the best move for white?
(the image links to a demo board if you want to play out some variations)

Solution

image
In general, the value of A is greater than the value of B (we could say that A is a 1.5 point move and B is only a 1 point move). But due to superko shenanigans, B is strictly better in this position!

The idea is that if play continues like this, white could create a frozen life at the bottom:
image
Thus black will be forced to play 4 at G1, conceding the G5 dame to white.

The same sequence does not work if white starts at B5, because then black can play 6 on one of the triangles to unfreeze the game:
image

Original thread on lifein19x19

6 Likes

Unremovable ko for both sides

Consider this position:
image
Black cannot fill the ko at A3 (then white could create a dead eyeshape with C1). So eventually white can capture on A3, but white should not fill the ko afterwards! This is because as long as the threat of a direct ko exists, black needs to keep the ko threat on E8, leaving the two white stones on top alive for now. If white fills the ko, black no longer needs that insurance, and could safely capture 2 stones to gain 5 points.

So this is a case where neither player wants to fill the ko, but of course both sides would prefer to have it captured in their favor when entering scoring. Thus if the opponent just took the ko, you would rather play inside some territory (either your own or the opponents’) instead of passing. The one who runs out of such moves first will be forced to enter scoring without the ko, so if the result hinges on the ko the game has turned into a form of no-pass go, where optimal play can involve playing into the opponents territory to gain extra moves.

In this minimal example there are no territory-filling moves available, but that is what would happen if we embed this on a larger board with territories for both sides: the winner would be determined not only by the sizes of territories, but also by the shapes of those territories. (No-pass go deserves its own post in this thread in the future)

The position is taken from the Sensei’s article Unremovable ko for both sides, which states that it was discovered by user 序列號 in 2008. The idea of a ko that neither side can “finish” is fascinating, and it’s an interesting beast to consider under various rulesets. However, the above example is quite complicated and comes in multiple parts: the ko itself, and then two types of unremovable ko threats elsewhere on the board. The sizes of all the groups involved must be precisely balanced to make the ko truly unremovable.

Recently, a new example was discovered by Francisco Criado and René Martínez:
image
Go read the lifein19x19 post from Criado for a very nice explanation of how this one works! In my opinion it is much simpler than the earlier one, and has some desirable properties such as not relying on unremovable ko threats.

This one we can easily put in a global context where we can see the no-pass go play out:
image
Assume it is black to play. I believe correct play is as follows:

  1. Black pass.
  2. White takes ko.
  3. Black fills an eye.
  4. White pass.
  5. Black takes ko.
  6. White fills an eye.
    …etc

In this case, black has 5 eye-filling moves available while white has only 4. Thus black will get to take the ko last, and claim B1+C1 as points.

If we took away one of black’s eyes in the starting position, it would instead be white that gets to capture last and claim B1+C1. In other words, simply adding a black stone on A7 changes the area score 4 points in white’s favor!

I made sure to fill the territories with 1-point eyes to remove the possibility of playing inside the opponent’s territory instead of your own. This lets us easily analyze the situation by just counting who has more eye-filling moves available. With bigger eyes, it becomes non-trivial to find the correct endgame sequence. Let’s look at examples of that in a future post - for now I just wanted to share this unremovable ko discovery.

7 Likes

It may worth noting that this is only the case for rules that enforce a strict superko rule (without exceptions and without passes lifting bans), namely AGA/NZ. Under rules that allow PassAsKoThreat and resumptions (Japanese, and presumably Chinese as well), you get a unique kind of perpetual repetition instead which includes periodic two passes.

2 Likes

Indeed, I assume positional superko without passes lifting ko-bans throughout this thread (as stated in the top post), but thank you for clarifying and adding the info about other rulesets :slight_smile:

2 Likes

Japanese rules have further complications with how kos are handled differently in the life and death determination phase, so it seems tricky to resolve these and they might behave very differently in that rules set. I’m not sure, since I haven’t tried to work through them yet.

I got stuck on the five points part

And the

I think I’d need to look at it again another day, presumably the OP as well given the ruleset discussion :slight_smile:

1 Like

Indeed, but L/D determination (with its special ko rule) will not come into play here since a finished end position (and scoring) is never reached. For Japanese rules the interesting question is possible limits on resumptions (though it seems likely that no resumption can be denied while a player has a desirable score-improving move left).