Fantastic stuff, I love it. I had no idea you have to capture stones in seki in Japanese rules.
Repeating Positions Can End the Game with “No Result”
It is possible for the game to wind up in a loop, where the same board positions repeat in a cyclical sequence. When this happens, the game might (but does not always have to) end with “No Result”. Here is the relevant rule.
Article 12. No result
When the same whole-board position is repeated during a game, if the players agree, the game ends without result.
A game that ends in “no result” is viewed as an inconclusive outcome that is different than the game ending with a tied score (jigo), which would only be possible if using an integer komi. The latter can be considered a draw, but the former should not. Traditionally, if a decisive result is needed (e.g., in a tournament), the players would have to replay an entire new game to make up for a game that ends with no result.
Further, a key provision of the rule is the phrase “if the players agree”. In this post and several of the following ones, we will explore the nuances of that provision.
The classic triple lo example for no result
A Triple Ko is perhaps the most commonly given example of a cycle that can lead to a no result. Broadly speaking, any position where there are three active kos could perhaps be called a triple ko, however the exact specifics can wildly affect what happens. Hence, let’s start with a basic “self-contained” triple ko, where all of the kos are part of the same local position:
Starting with Black’s turn to play, Black can give reprieve to their stones in atari by capturing one of the kos (move 1 in the diagram below). Now, White’s stones are in atari, and since White cannot recapture the ko, they must take another ko with move 2, which in turn forces Black to take the third ko with move 3.
Note that after 3 moves, the parity of the kos have flipped:
However, it’s White’s turn to play, and White must similarly continue by recapturing the first ko with move 4, which further compels moves 5 and 6, if both players wish to save their stones.
After move 6, the entire position has returned to where we had started. If neither player wishes to give up their stones, they could continue this loop indefinitely, and hence trigger the rules to end the game with “no result”.
Side note: a helpful way to visualize triple ko is to imagine each ko in the diagrams above as a light switch. Black is trying to flip all of the switches down, while White is trying to flip all of them up. They take turns flipping one switch at a time, but they cannot flip the switch that their opponent last touched.
Triple ko does not have to end with no result
The no result outcome for the basic triple ko discussed above requires this loop to occur and for both players to agree. If one of the players was so far ahead in score that it did not matter whether their stones were captured, then their best play would be to abandon this loop (assuming that they would rather win than end the game with no result). However, even if one player was far enough ahead, they could mistakenly persist with the cycle and have a winning game turned into a no result.
In general, three active kos does not necessary mean that the players are locked into playing the cycle indefinitely either. Moonshine Life is an interesting example, which I will talk more about in another post, where there are three active kos, but should not end in no result (unless one player makes the blunder of insisting on the cycle rather than winning).
Just a few more notes for now
- Triple ko involves a six-move cycle, but a four-move cycle (that could force a no result) is also possible with a position called Eternal Life.
- The are “three-move” and “five-move” cycles the do not cause a “no result” since they have an unbalanced number of captures.
- The possibility of abusing double ko seki is perhaps another reason for requiring both players to agree to a no result.
- The exact timing/procedures for compelling players to break a cycle (if they do not agree to a no result) is somewhat unclear, and it could have strategic implications.
- Comparing the preference between jigo vs no result would perhaps depend on external factors, such as specific tournament procedures, rating systems, prestige, etc.
- Moonshine Life is also very interesting, as mentioned above.
- I plan to write more about most of these topics on this list. If you thought my earlier posts revealed some really weird quirks about the Japanese rules, then buckle-up, since kos are where things really get crazy.
- There are many more examples of longer and more complex cycles, but I can’t hope to cover or even understand them all.
Is a “No Result” Better than a Tie?
Consider games that are played with integer komi, which makes the possibility of a tie by jigo (equal scores) a possibility. Suppose that a cyclic position arises (like triple ko or eternal life) and the following becomes apparent to one of the players:
- Their opponent is committed to continuing the cycle is willing to agree to ending the game as “no result”.
- They can abandon the cycle (by playing elsewhere), but that would lead to the game ending as a tie (jigo).
- They can continue the cycle and accept the game ending with “no result”.
What should the player do? It is not clear from just the rules whether a tie or “no result” is preferable. While one could assume that both are preferable to losing and that winning is better than both, these two are not directly comparable.
In fact, I think that depending on other external factors, either could be preferable, or it could remain indeterminable.
From a ratings system perspective, a tie should be treated as a data point that suggests that the two players are evenly match and close in strength. Hence, although different systems will vary in the exact formulas and implementation, the general expectation would be that a tie would bring the two players’ ratings closer together (by decreasing the higher-rated player’s rating and increasing lower-rated player’s rating).
On the other hand, a “no result” should be treated a game that did not produce an outcome, and hence most rating systems would ignore such games, until they have been replayed to produce a settled result.
Hence, the higher-rated player might prefer the “no result”, while the lower-rated player might prefer the tie".
Likelihood of Winning a Rematch (and Risk Tolerance)
Suppose the agreed contingency is to play a rematch in the case of a “no result”. If a player believes that they have a very high chance of winning a rematch, then they would likely prefer the “no result” rather than accepting a tie. On the other hand, if they feel that they have a high chance of losing the rematch, they would probably prefer the tie instead.
If a player believes that they have a roughly 50-50 chance of winning vs losing the rematch game, then whether they prefer to take a certain tie versus forcing another game by taking a “no result” would depend on their risk tolerance, and how strongly they might prefer a tie over a loss, or a win over a tie. This risk tolerance and outcome preference could also depend on further additional factors, such as tournament considerations.
Tournament Procedures and Position
Suppose the choice to accept a tie versus a “no result” occurred in a tournament setting. Consider a tournament structure that involves accumulating points in order to move onto the next round, and that they give a full point for a win, half a point for a tie, and no points for a loss, while “no result” games are replayed.
A player might find themselves in a situation where they must win their next game (i.e., the tie is as bad as a loss since the full point is needed in order to advance). In such a case, they would prefer the “no result” over a tie, since that still gives them a chance to advance. Alternatively, a player might find themselves in a situation where either a win or tie is sufficient to advance, but a loss would lead to elimination before the next round. In this case, the player would prefer the certain tie versus the uncertainty of replaying the game after a “no result”.
Alternatively, a tournament might decide not to replay any “no result” games, and simply treat them as ties for scoring purposes. Then a player might not care whether they finish the game with a tie or a “no result”, unless they are also concerned about potential rating implications.
Subjective Concerns about Image and Prestige
Even in a one off game, where the players understand that they will not play a rematch in the case of a “no result”, but instead let that stand as the outcome, the players might still have different preferences regarding the possibility of the tie versus “no result” endings. One of them might subjectively view reaching a jigo with their opponent as more or less prestigious/desirable than reaching a “no result”.
Do you know of any rating system that does something different from the obvious solution of:taking, for each player; the average of the points he would have gotten for a victory and the (negative) points we would have gotten for a loss?
Since many rating systems aren’t about “this game is worth X points”, but use your performance in multiple games at once to estimate your rating, the answer is yes. (Simply because they don’t assign a point value to the game, they cannot average them)
(I accidentally bumped with a stupid question )
eyes of groups in seki [in Japanese rules] do not count as territory
I really should have known this, huh?
In another post, I linked to and briefly discuss a study of a the history of the rules. There’s speculation that the peculiar “eyes in seki don’t count” aspect of Japanese rules may be a historical remnant of the group tax effect from the stone scoring rules.
There is a fascinating side-effect of this version of the “written Seki rule” (which I think, nobody actually applies in practice, even professionals). I’ve seen it called “pseudo-seki”, so it is the name I use for the lack of a better name. I found it on the internet here: https://lifein19x19.com/viewtopic.php?f=45&t=3666&start=60.
The position is the following:
No prisoners, 5.5 Komi.
The black group in the upper right corner is involved in the possiblity of step ko: When completely surrounded, White could capture the corner stone, then if black cannot retake the ko, white can add the J7 stone to start a direct ko for the life of the black group. In the game however, white has one and only one ko threat at A5, and black also has one and only one ko threat at b (which is large enough: this will change later!), and thus white has no hope of winning the step ko during the game (since in the resulting direct ko, black will take first).
Furthermore, the black group is deemed alive by endgame hypothetical-play, with no need to add an extra defense move (capturing the white stone). This is because the existing ko is a step ko, so in hypothetical analysis, there are no ko threats, so white will take first, black will pass for the right to take the ko, white can only make the J7 move and then when black takes the ko, white can do nothing, so black wins the hypothetical play.
This is crucial because the game is very close: if black makes an additional defensive move like capturing the white stone so that there is no ko and his group is clearly alive, he loses by 0.5 points.
So, it looks like black should win by 0.5 points. However, white will argue that the top groups touch dame, and so are in seki! If they are counted as seki, white only loses 4 points of territory, but black losses 5 points (4 territory + the stone inside), and thus, white wins. So, to avoid this, black’s only hope is to fill dame, playing both triangle-marked intersections.
Note that, if white fills those, our analysis so far has been correct, the groups would not be in seki anymore, and black rightfully wins by 0.5 according to Japanese rules.
However, when black fills those dames, the situation changes, because filling them has made the black group larger. This means that, if white captures it, he will gain more points than before (2 more territories + 2 more prisoners). This makes black’s ko threat at b) no longer large enough: that means that if black fills the triangle-marked dames, then he loses because white will now start the ko, and will not answer black threat at b), effectively exchanging both corners, but now the difference is winning.
Thus, the seki rule makes this possition winning for white, if followed as written.
To the best of my knowledge, such a situation has never been actually claimed in a real professional game. My understanding is that in a real game, even professionals would deem the black group to be alive and not claim a seki instead, considering the written rule just “flawed”. Unfortunately I have no evidence for this, other than the lack of a counterexample (that would be: an actual pro game where a pseudoseki situation occurred and in which white won by claiming seki).
I’m convinced that Go Seigen would be the kind of pro player that claims seki. The whole argument reminds me of his rule disputes.
What a position!
Interestingly, (without having explicitly checked) I think KataGo’s computer-suitable formalization of Japanese-like rules actually does agree with your guess of what pros would think, rather than the literal interpretation of the written rules. White can neither win the ko during normal play nor during post-game cleanup, and during cleanup black can safely fill the dame and capture the white stone without cost, so will win by 0.5.
Wow!! Thanks for sharing that “KataGo” rules formalization, I had not seen them before. Indeed, the two-phase idea is genius, the amount of “theoretical match” with actual Japanese rules is incredible for such a well-defined ruleset that solves disputes based on actual board play (and not some “hypothetical best play as defined by competent authority / exhaustive analysis”).
All territory-style rules based on actual play that I had seen before “suffer” from such non-Japanese features mentioned, such as one-sided dame or “fight for the point of territory within the last ko” (which is called a “pass fight” in the KataGo page, and is directly linked to the Go Seigen disputes, as that point of territory is awarded by Chinese rules).
Indeed, in KataGo formalization the situation would not end as seki, as black fills dame as soon as the first phase starts and the ko rules turn into “local mode”, since by then filling the dames becomes completely safe and ko-threats irrelevant.
This is quite amusing because the concept of “enabling a new permanent stone in the locality of the group”, which is a key new feature of the Japanese 1989 rules that is necessary to explain various rulings (snapback, a common corner seki not being instead an alive-group-with-prisoners, some positions where playing a new stone exactly on top of the single live-stone is no possible, but it is possible to do so “near” that), is a concept that is not present at all in KataGo formalization, yet the theoretical best play result is identical for these positions.
Hehe, thanks, that was basically the goal when designing them :).
“Find rules that won’t break even with completely stupid automated self-play that still reproduce the spirit of Japanese rules.” It took a while, a few months of on and off just having it in the back of my mind, and iterating on it over time.
As I played with it, it started to make sense a little what the Japanese pros were/are going for. You blindly feel enough different parts of the elephant that it starts to come together as a semi-coherent picture, and if you get it right at least all the common cases magically all fall out the right way, even if the rules beasts don’t. I find it amusing that you also get three-points-without-capturing too (and it naturally falls out of lots of other territory-rules-via-cleanup-phase formalizations too), suggesting that the traditional Japanese pros very much “knew what they were doing” when they made that ruling, and that the J89 rejection of it is in some sense a “mistake” resulting only from not being able to figure out the right way to word the rules to justify that ruling.
Of course, KataGo’s version of the rules also has a few known bugs so it’s definitely not perfect. Some of which were discovered when hammering out the fine points in the L19 forums. But they should be rare enough that I’m okay for now to just live with it. Even superhuman bots still blunder in much larger ways in vastly more than the <0.1% of games that will have such an anomaly.
Resulting trained nets seem to work okay for Japanese rules games on KGS. Eager to see if over time more engine GUIs and sites like OGS will eventually have APIs for varying the rules, as inbae mentioned in this other thread (Rules support for bots)
Do you have any link to such discussion? I would love to see examples where KataGo rules with perfect play differ from japanese judgement (other than torazu sanmoku, which up to 1989 was actually judged by Japanese in the same natural way that KataGo does).
I believe @hexahedron was referring to this discussion on the LifeIn19x19 forums:
The “non-Japanese-result” positions that I was able to extract from that discussion were only:
- Torazu sanmoku (KataGo gets the pre-1989 result though, so it is quite Japanese too )
- Molasses Ko (I think that in Japanese rules an antiseki (0 points locally) should be the final result, while in KataGo a no-result should occur because both players want to be the first to pass, in order to win when the game resumes).
So far, the mismatch seems to be remarkably small!
You may also be interested in positions A,B,C here:
However I have looked at position A and I think that Japanese rules would consider that white does not need to add an extra move there. This is because all white groups should be alive, the corner group in particular because in hypothetical play it enables placing new permanent stones (at F19, G19).
This is the very same justification of why the two black corner stones in https://senseis.xmp.net/?SekiInAreaAndTerritoryScoring are considered alive and not dead, and why this is seki and not “white lives with prisoners and territory” under japanese rules: White can capture those two stones, but capturing them enables the placing of new stones “in the locality”.
This also matches the Jasiek 2003 formalization, as far as I have been able to analyze, because the new permanent stones are within the group’s local-2.
So position A would be a difference because if my understanding is correct, KataGo rules imply that you must add an extra move to defend or you lose the corner group.
I have not looked at the other positions yet but they all seem very interesting.
I have seen all three positions. My understanding is that in all three cases, actual Japanese rules in use say that no extra defense is necessary (because new stones in the locality are enabled by the capture, which deems the corner group alive).
It seems that in KataGo rules, positions A and B require an extra defense in order not to lose the group during the extra phase. In position C, no extra defense is needed in KataGo rules.
So it would seem to me that only A and B generate a slight 1-point difference, and C is a “non-difference”.
Fun discussion of anomalous positions here for KGS’s attempt to detect seki in order to implement Japanese scoring (taking advantage of human players marking life/death appropriately but still having lots of fun corners to consider):