Weird and wonderful consequences of simple rules

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:
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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:
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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.
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However, under the delayed capture rule, the position after 6 would be:
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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.

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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!
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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:
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Solution

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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:
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When black takes the ko, white’s only threat is to play this atari:
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(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:
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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!
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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:
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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.

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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.

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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

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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.
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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.

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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

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Solution

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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:
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(white 6 passes - filling the ko with 7 may be unnecessary depending on the exact rules)

Problem 2

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Solution

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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

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Solution

Immediately capturing the ko is a mistake. White has a ko-threat at 2 and black will lose by 1 point.
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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:
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White does better by filling the ko and letting black have A1:
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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.)

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Here is a nice position that Gérard Taille shared recently:

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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

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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:
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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:
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Original thread on lifein19x19

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Unremovable ko for both sides

Consider this position:
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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:
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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:
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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.

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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.

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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:

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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:

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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).

Very interesting position!

This position sort of combines features from two previous special positions shown before:

  1. In a strict “dispute? Now play until two consecutive passes, then everything on the board is alive” ruleset (like AGA rules), a “dead ko” can live simply because the opponent has run out of moves (if enough “resumptions” were allowed, they would manage to capture the dead ko eventually)

  2. With a mannen-ko (thousand year ko) on the board, under “must actually capture to show stones are dead” rulesets, sometimes “dead groups” can live, because capturing them necessarily creates ko threats in the process, and those ko threats make the capturing player lose the mannen-ko, thus making them prefer to actually allow the “dead group” to live.

In the first position shown by antonTobi, 2) happens to the white stones on the top (D9 and D8). Actually we have a variant of 2): instead of capturing them creating a ko threat for white, rather, the process of capturing them destroys one ko threat for black. But it is functionally the same, as the net effect is a difference of one ko threat.

Due to that peculiarity then, those white stones “live” and are not captured. But the ko on the corner then is settled, as in 1), just by “who runs out of moves”, which would change if resumptions were allowed.

Amazingly, Superko is not essentially involved in this position at all, as the potential for a long cycle (on the board, without passes/resumptions) never arises: the key features are a) To capture dead stones, you must actually be able to remove them during play (that is, the actualy definition of life is simply “it is still on the board after the final two passes in a disputed game”) and b) The game immediately ends after the first two consecutive passes (no resumptions, no pass-just-to-lift-ko-ban).

My understanding is that the no-pass-go fight at the end should be the correct play under AGA rules.

I wouldn’t dare to bet on how a Chinese referee would rule such a position. On the one hand, locally, the A2 black stone behaves as a “moonshine life” stone: once we assume that the large ko for the whole corner is not played, only the single-stone ko remains, and by local shape this is a ko that white can fill anytime, and black cannot threaten anything, just prolonging the ko, exactly as moonshine life. So, by the precedent that moonshine life is normally ruled dead under Chinese rules, the black A2 stone might be considered dead and thus white allowed to simply win the ko, and even with the D9 and D8 also alive as those are not captured during the game.

However, the reason why “moonshine life dies” as explained in the Chinese Rules is because of the “no repetition allowed” clause, not because of a shape consideration: Under a normal game, when black tried to prolong this ko, they would run out of moves even with infinite ko threats, because repetitions are not allowed. But repetitions do not occur here, so that ruling moonshine dead just by precedent seems wrong. If a referee did not rule it just dead according to moonshine life, and relied on actual play, then whether it goes to no-pass-go or becomes no-result (as in triple ko) depends on whether “b) The game immediately ends after the first two consecutive passes (no resumptions, no pass-just-to-lift-ko-ban).” holds in actual Chinese rules. The texts I have seen so far are not clear and unambiguous enough about it (in fact, the Chinese tournament rules that I have seen stipulate that in case of dispute, the OPPONENT of the player claiming that “the group is alive” goes first when resuming, which is of course very problematic and obviously implicitly assumes that there is only ONE group under dispute).

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If the two white stones are alive, that’s 2 points for white (and the liberty next to them is dame, not counted for either side). If they are killed, those two intersections + the intersection that was previously dame becomes 3 black points. In total, this is a swing of 5 points in blacks favor.

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I think it is fairer to speak of trying to codify tradition in the rules: the consequences are much the same, but it is easier to sympathise with, for me, at least.

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I agree, but would be more careful. Go rules have evolved for centuries, gradually changing or dropping things that didn’t stand the test of time. In today’s Japanese rules, almost everything have important logical purpose, even seemingly arbitrary things like “no suicide” or “no territory in seki”. This is more than codifying random traditions - logical territory scoring is not easy, unfortunately. OC, nothing wrong with prefering area scoring instead.

From a heretic and exaggerated view :slight_smile:, the thread’s underlying theme may also be seen like this: with rules that lack fully functional passes, you get these weird and wonderful consequences whenever correct play with regular rules would be a pass (often as a ko threat). BTW, one particular example still seem to be missing from the collection is molasses ko under positional superko.

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My quote about the Japanese rules being a “cautionary tale” comes off as very harsh and I probably could have phrased that better. Of course trying to formalize the rules while also adhering to tradition as much as possible is a very different challenge from just making up your own rules from scratch.

I don’t mind playing with Japanese rules (I would prefer Lasker-Maas personally, but the cases where they differ are rare enough that it’s not worth losing sleep over). However, when it comes to discussion of artificial beasts (that will never or almost never happen in real games) I find it not very interesting to try to apply Japanese rules, since this is not what those rules were made for.

Indeed! I will make my next post about molasses ko, and then probably a longer one about no-pass go.

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Molasses ko

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It is black to play in this position. We note that:

  • If black passes/plays elsewhere, white can take on E1 and then capture the whole group with F2 after that.
  • Black E1 and F2 are both self-atari.

Therefore the only promising local move is E5 (or equivalently E4), to which white’s only response is taking the ko:
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3 and 4 are also forced:
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Now there is no local move for black. If there is a large enough ko threat on the board, black could use that threat and then take back at E2 - but let’s assume there is no such threat.

Luckily for black, black can simply play away (say, F8), and white does not have a way to “win the ko”. Instead, white can only exchange a similar sequence of four moves as black just did:
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And so it continues:
imageimage
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With the moves 5, 10, 15, 20 and 25, we saw a normal sequence play out on top. But the players had to exchange a 4-move sequence between each move, or else lose their big group. Thus we see a normal game continue, at 20% speed. Sounds kind of tedious right? This 5-move sequence took 25 moves, imagine playing out the whole latter half of a game in this way…

But wait, it gets worse! Let’s go back to the last diagram above. Black has played the final move at 29. There are no normal endgame plays left on the board, so can white finally pass now? Nope! If white 30 passes, black plays 31-33…
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…and white cannot capture on F2, because this would repeat the exact position we had after move 25, just with black to move instead of white to move.

This is one of the rare cases where the difference between positional and situational superko matters.

Positional superko says that the board position may never be repeated under any circumstance.

Situational superko only says that the position may not be repeated with the same player to move.

So under situational superko, 34. F2 would be legal: it would be a repetition of the position, but not of the situation.

Since there’s no way for black to make headway after white passes, we can assume that the game could end with (30. Pass 31. Pass), with both big groups involved in the ko left alive for scoring.

But in this thread we are always assuming positional superko, so let’s get back on track…

What we now realize is that playing away from the molasses ko is safe, but passing is not! The moves you make elsewhere don’t have to be ko threats, but they do have to change the board position (and of course all non-passing moves meet this requirement).

For move 30, white may play inside her own territory, or even better, inside black’s!
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We will now enter a long phase where both players throw in obviously dead stones into each other’s territory, to be able to make as many moves as possible. And remember, the game is still going at 20% speed! Some time after move 200 we’ll reach a situation looking like this:
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Now it is again white to play, but every empty intersection on the board is either illegal or self-atari (note that even if suicide is legal, single-stone suicide is illegal under positional superko). It has finally become clear that white lost: she could resign here, or pass to end the game, in which case black will take the E3 group off the board before going to scoring.

Going back to the previous diagram, you can see that black had more territory before the territory-filling started. It is generally the case that the player with more territory will be able to make more legal moves, but because playing into the opponent’s territory can gain you extra moves, it is not easy to play this phase of the game correctly, or to predict which side is going to win.


In conclusion: The molasses ko can slow play down to 20% and turn the game into no-pass go, introducing a territory filling stage after the normal endgame. Weird and wonderful indeed, but probably not something you thought you signed up for when starting a game of go! Luckily they are exceedingly rare (Sensei’s only mentions one known example in a casual club game, is anyone aware of other examples?), so even if you’re playing with positional superko your whole life, you will most likely never have this happen to you.

(See Molasses Ko at Sensei's Library for some discussion on the status of the molasses ko under other rulesets)

We have now seen two different types of beasts which effectively turn the game into no-pass go: the unremovable ko for both sides, and the molasses ko. Next up we’ll take a closer look at no-pass go in isolation, to get a better idea of how these endgames would play out in practice.

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