That’s why white won’t play at D9 before black connects at F9. I think the only exception is when it’s white’s turn and there are no more dame points left except D9. But in that case, black also wouldn’t have anything to play but connect in response?
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At first I thought white should start with 3, but I now think you’re order of moves is right, because it ensures white gets to play the last valuable move.
If instead white starts with 3 and then black plays 1 instead of 4, white can play 5 (sente) and 4, but then black gets the last valuable move 7 (move 2 doesn’t get played, so this sequence is only 6 moves until only dame are left). I think that result is 1 point worse for white than your move order.
Edit: Now I’m wondering if after white 1 and 3, black should play 5 to ensure getting 7.
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You can also ensure getting 7 by just playing 7 instead of 5 
I analysed a bit more (assuming territory scoring with no previous captures), and this changed my view again.
If it’s black turn (which seems to be the case in this puzzle?), I think black has an assured win by 11 points, but there is more than one possibility for the complete move order:
(^^ @shinuito’s solution)
When it’s white’s turn, I think black has an assured win by 7 points, but again there is more than one solution:
(^^ @Groin’s solution)
I think a proper puzzle should have only one solution.
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Well I think it’s a game, not a puzzle but OP could confirm?
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It’s an endgame puzzle. I think I. Have tried every variation of B plays D1 and they all lose. I really don’ think this is a k8 or9 puzzle at all. IN wonder how you would label it level wise, just out of interest?
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Perhaps this puzzle has a mistake in it, causing the app to reject correct solutions?
Already the puzzle doesn’t seem to be a particulary good one, because AFAICT there is no unique solution and that already triggers my suspicion that this puzzle might have issues.
If the puzzle assignment was to just find black’s first move (instead of the whole move order of the remaining endgame), then there is only one solution (D1) and I think the puzzle would be good. In that case ranking its difficulty at 8-9k is probably fine.
Which app it this BTW?
It’s from HJJ GO
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I’d never heard of this app before, but Mike Chen 1p AGA made a 2 hour review about it.
He did encounter a puzzle that had the assignment worded incorrectly (what I suspect to be the case for OP puzzle). For example:
But other than that, it seems that the HJJ GO puzzles are very good (he even got some of the hardest level problems wrong due to misreading, perhaps by initially underestimating the difficulty) and his overall conclusion is quite positive (if you can afford it):
BTW I thoroughly enjoyed a lecture that Mike Chen gave during the 2024 European Go Congress. I like his dry humor a lot.
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signed up after watching the Mike Chen video about a month ago. I think it is top quality. In general the puzzles and games are superb and after working through their carefully considered suggestions may playing has improved dramatically. I did however find a flaw in the system as it relates to me personally… although I score highly in the opening puzzles, and average in the middle, I struggle to complete some of their end game puzzles and I honestly feel that they are requiring some kind of level of reading/knowledge which I do not possess although I often find my endgame helps me to beat players on OGS (mostly because I always consider sente and gote) which my level often ignores.). AS a result I am, for example completely stuck on this puzzle, have tried so many variations my accuracy score has gone to rock bottom so my overall evaluation may be getting skewed. I have explained to the makers that some players require a feedback system such as a hint after ten fails that drops their score slightly but allows them to continue with the rest of the program which I can no longer do because of this one problem. In my field as an educator I am always concerned about the need for scaffolding and feedback pitched at the right level. I think the one flaw of this superb site is that it is based on the premise that continual failure will lead to continual reflection and therefore improvement. In fact it can also lead to annoyance, depression and disillusionment as well.
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Thank you everyone for your kind suggestions in this matter. D1 was obvious. The point I couldn’t grasp was the key point of G4 to prevent white threatening to cut at H5.
Still highly recommend HJJ GO to all and sundry….
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This is a nice example of a position where Chinese rules are sharper than Japanese rules, in the sense that you can have two options that are equal in Japanese rules, but one is a mistake in Chinese rules. (It’s more common to find positions where the reverse happens.) Notice that some of your sequences end with two dame, and some with three. Fill the dame, count the final position with area scoring (I mean Chinese style, no AGA pass stones), and spot which black moves are mistakes (-:
The rules only seem random before you’ve understood them. They can all be justified. Yes, you do need to spend many hours studying (not actually random) examples, trying out different move orders, counting the score carefully, figuring out why the rules make sense. Books can help by offering explanations (and I wish there were more good endgame books in English), but there’s no substitute for treading the ground yourself. This thread is a good example, although it’s better to start with simpler positions (such as the endgame section of Graded Go Problems for Beginners volume 3).
(And no, I’m not saying I’m an expert here. I’ve managed to get beyond the beginner level and convince myself it’s not hopeless. There’s a coherent body of knowledge there which is within reach of determined amateurs.)
I can think of four good English language sources for learning the theory. (No, Mathematical Go is not one of them! That book was written for a different purpose.)
- The Endgame from the Elementary Go Series has informal, approximate explanations and some well chosen examples. It’s not as precise as more modern books, but good enough to get started with.
- Rational Endgame is beautifully clear and precise, but unfortunately is rather short and doesn’t go much beyond the basics.
- Robert Jasiek’s books can be challenging to read because of the large amount of detail, but they do include complete and correct logical explanations of each principle and lots of relevant examples, and they cover both the foundations and some rather advanced topics.
- If you read everything that Bill Spight wrote on SL and L19, you’ll understand the endgame very deeply, and have a good time along the way (he’s an entertaining and lively writer). Unfortunately it’s a bit of a lucky dip: he never got around to writing up all his thoughts in a structured way. But it’s fun to browse and learn and pick out examples for study.
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Except my point is that from many sources I’ve looked at, most do such explanation in a fairly poor way over all, in that it becomes quite hard to take what you’ve supposedly learned and then go on to apply it correctly to your own examples.
Hence the rules are seemingly random, from how they’re presented or not in some cases.
I think that’s where you’re wrong in some sense. People can pass on their experience in such a way as to make new learners have to spend less time to learn and more time progressing. I don’t see it as a justification for poor content, that you should “just do it yourself” and reinvent the wheel every time, and each and every person too.
Basically I’ve no problem with endgame Tesuji in books, but when they try to teach counting it tends to be a hard to follow mess.
I appreciate that the books exist, but it feels like there has to be a better way to explain it overall, and enough professional players must know how to count decently precisely that some amount of knowledge should be transferable in a clean/clear way.
If you want my opinions on your recommendations:
Anything bar the section that “explains” move values is ok, but generally it’s about as good as just a table that shows you a position and tells you the answer - this move is 6 points, and then you struggle to be able to apply it in novel situations.
I think in the first section sure, but then it starts to move on much more rapidly and feels like it quickly becomes less precise in order to make progress quicker. I think it could’ve done with a lot more explanation and examples on gote moves, sente moves and what sente is etc before trying to move quickly onto ko and other examples.
Something I’ve been looking through recently, the endgame books 2,3 and 5 on values, local analysis and mathematics. While I appreciate the purpose of the books, I think it might go too far in the opposite direction, where it can spend a very long time, several pages explaining n! move orders and which one is the best, or doing out an entire identical example again but with the colors swapped. I’m still in the process of reading them anyway, so not a good overall opinion of them yet.
It feels like there should be some in between of not telling you anything but the answer and a vague justification, and going into several pages of detail on examples that arguably don’t require it.
Let’s be honest, this can’t be a realistic suggestion. It sounds like it’ll be quicker to reinvent endgame theory yourself than read every random post thread and comment by someone on the internet.
Anyway there’s plenty of books (including the ones you’ve mentioned), which I happen to have
- Ogawa Davies Endgame
- Rational Endgame Antti Tormanen
- Robert Jasiek Endgame series (many books but I just have the ones I mentioned)
- Get Strong at Endgame by Richard Bozulich
- Kano Yoshinori (technically has endgame puzzles in the graded go problems)
- Vital Endgame - Janice Kim
- Lee Changho’s Endgame Techniques
- The Monkey Jump by Richard Hunter
- All about Ko by Rob Van Zeijst and Richard Bozulich (bits on the values of ko)
- Yose by Motoki Noguchi (in French)
- 実戦のヨセ120 some kind of fundamental yose problems
- ヨセを得意に: 仕上げは快調 yose calculations
- 基礎からのヨセと計算 Ishida Yoshio’s book on calculations
- ヨセ・絶対計算 calculations
- ヨセ200 endgame puzzles
I guess we can mention as you did
- Chilling gets the last point by Berlekamp and Wolfe
There’s also
- Endgame for nerds Stanislaw Frejlak has a mini endgame course on Go Magic
and a YouTube channel that does endgame problems
Essentially if you have any suggestions other than “try harder” I would be interested in hearing it.
Equally if you would like to settle the question of this thread, on the endgame in the given position or
if you can explain how to calculate the value of E9, whether or not the possible ko affects the value etc, that would be useful.
Otherwise we’re just stuck with two potential answers, and one would have to start trying to set up positions to verify the values of the moves (which again requires more knowledge, not usually mentioned in books).
Yeah there’s no possible ko at E9 for the purpose of counting. After black captures, the position has no further moves worth anything.
If white plays first next and plays D9, worst case black just connects at F9. Black has lost nothing despite white playing first.
If black plays first next and plays F9, white could ignore, but worst case white could at least play D9 (to avoid black eventually getting bot D9 and D6 and forcing white to fill in a point). White has lost nothing despite black playing first.
If the result is the same when either player plays first, then it’s a zero position, it’s done. At best there are ko threats for kos elsewhere on the board, but locally there is no more endgame.
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If you want a more general rule, given any local position P, here is a thing that is always true about the value of any local position (as evaluated by this kind of CGT theory or by just miai-counting if you disregard the infinitesimals, and so long as you are willing to disregard the potential ko threats that the position may offer for kos elsewhere, which this kind of theory already generally disregards).
Rule: The value of P from black’s perspective is always >= the final local value if white plays there first and black precommits to answer each white play there. (allowing for the possibility that one or more of either player’s “local plays” or “answers” could be to pass, if they would actually prefer not to play because all local moves are suicide or otherwise point-losing).
Proof outline: Call that value V. Given any board position, black is never worse off we penalize black by V points in exchange for adding another copy of P on the board. Black’s strategy is simple - they follow exactly the strategy they would have followed on the rest of the board, and whenever white interposes a move in P, black answers it. No matter what white does, the rest of the board will play out the way it would have without P (because we are disregarding ko threats from P, white’s interposing moves in P can never enable white to do anything they couldn’t have done without P), and black will score at least V points from P.
By a similar argument, the value of P from black’s perspective is always <= the value if black plays first and white precommits to answer every black play there.
And so as a special case, if we play any position out with black having the option to move first (and white always responding), and we play it out with white first (with black always responding), and we find both give the same value, then the value of the position is both >= that value and <= that value, so it must be exactly equal to that value, and be effectively finished.
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Lots of questions:
Are we assuming V here to always be an integer? If not, assigning a non integral values doesn’t really seem to make much sense. If it’s an integer, which integer would it correspond to? One of the stops (left/right stops L(P), R(P) )?
Equally, I’m not sure the relevance of this copy? Is P part of a whole board position, and we’re giving black a copy plus a penalty for the copy? Are they only answering every white move on P in the copy or also in P in the whole board position?
I can’t tell how exactly this ties to miai counting etc or how you apply it to the position at hand, for instance E9.
Are you saying that if white plays it’s worth 1 point, if black plays and is prepared to answer white no matter what, even if the timing is wrong, then it also looks like one point, and hence it’s worth 1 point?
There’s no follow up to white playing first in this instance.
My take on this is: D9 is local sente. In any full-board position where D9 is a good move for white, it’ll be correct for black to answer it. Therefore black’s capture at E9 is a 2 point swing, or 1 point by miai counting, and the ko shouldn’t ever be played out.
Slightly more formally: if white plays D9 and black doesn’t answer, and if white goes ahead and takes and connects the ko, then white has spent 3 moves to gain one point. On the other hand, if white postpones playing D9, black doesn’t have any threat in that area. So white shouldn’t be playing D9 until the biggest move elsewhere is no more than 1/3 of a point by miai counting. So black will answer locally, because there isn’t a bigger move elsewhere.
Hypothetically, if there were no stones at C9 or C8, so that a black followup move at D9 would gain something, then white would have an incentive to play D9 earlier, and in that case you’d treat D9 as gote and count the fractions for the ko.
Robert Jasiek goes through the principles in the “Endgame Problems 1” book, in some painfully detailed discussions of the definition of “sente” and “gote”. Yes, I agree with you about his writing style.
I do actually agree with you this far. The key phrase is “less time to learn”. Not zero time. Even the ideal book isn’t going to download the knowledge and skills into your brain with no effort on your part. And I agree that the currently available books in English are very far from ideal. But they’re not a complete waste of time either.
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I suspect you might be allowing yourself to get lost in the details. Keep hold of your common sense as a Go player too as you try to learn the theory!
As a Go player, would you ever count a position like this to be worth anything other than 0 points for both players in the A17-A19 area? (all outer stones assumed alive).
Black obviously has no moves to gain any points. And white has no way to gain any points because if white ataris, black can just connect. The “potential ko” is worth nothing to white except as a ko threat for another ko, but we’ve already assumed we’re ignoring that. So then this position is worth 0.
This is the same as the shape left behind in your example after black captures at E9. So what we’re saying is that you shouldn’t be counting any value for the “potential ko”. If black captures at E9, black got 1 point from the capture and the position remaining on the board is that shape, which is worth precisely 0. If white connects, white gets 1 of territory. So the swing is 2 points, and the average per move value is 1 point per move. There is no extra 1/3 or 2/3 point from any “potential ko”, because the on-the-board position after black E9 is worth 0, rather than -1/3 or 1/3 or 2/3 or any such value like that.
Are we assuming V here to always be an integer? If not, assigning a non integral values doesn’t really seem to make much sense. If it’s an integer, which integer would it correspond to? One of the stops (left/right stops L(P), R(P) )?
Yes it’s an integer, and I stated what it is, right above, sorry if the grammar was unclear:
The value of P from black’s perspective is always >= the final local value if white plays there first and black precommits to answer each white play there. (allowing for the possibility that one or more of either player’s “local plays” or “answers” could be to pass, if they would actually prefer not to play because all local moves are suicide or otherwise point-losing).
Proof outline: Call that value V…
Equally, I’m not sure the relevance of this copy? Is P part of a whole board position, and we’re giving black a copy plus a penalty for the copy? Are they only answering every white move on P in the copy or also in P in the whole board position?
Yes we are justifying the claim that P has value >= V for black by taking any board position at all, and adding one copy of P to it and charging black V points, and then observing that black is never unhappy about this trade.
Don’t forget the big picture of what even the meaning of assigning values to positions is. Conceptually, what does it mean to say “Local endgame position X has an average value of 2.5 points for black”? It means that on average that if I compare whole-board optimal play between a whole-board position that contains X and the same whole-board position but with X replaced with all dame, so long as I average over a “wide variety” of board positions with diverse and varied kinds of endgame moves on the rest of the board, on average black will do about 2.5 points worse.
(With the one caveat that we are assuming that the specific position X whose value is in question is not itself providing any value via extra ko threats for a ko or potential ko somewhere else).
That is what it means when we say this shape is 0.5 points on average for black:
And indeed, if you add 20 copies of this on a board (assuming outer stones are alive and everything), black will indeed do about 10 points (20 * 0.5) points better.
And that is what it means we say this shape is a third of a point for black:
Adding an extra copy of this to a board, across a wide variety of positions, will on average add 1/3 to black’s score. And you can see this physically manifest if you add 30 copies of this to a board, no matter how you play it out black will win 10 of the kos for a total 10 points (= 30 * 1/3).
And we can sanity-check our understanding of the A19-A17 shape at the top of this post as being worth 0, in that we expect that no matter how many copies of this we add to a board, it won’t affect the resulting score (again, so long as the ko threat it gives white is not relevant). And that matches up with common sense as a Go player - these will generally just remain unplayed until basically the end of the game, and then black will connect. Even if white ataris first, black will still just connect.
So, getting back to the Rule (the theorem) whose proof I outlined, we’re claiming that in general, if in some local position P play Black can locally guarantee a score of at least V when white plays first, then P must be worth >= V in the above “average value” meaning. That is, on average if you add a copy of P to a board, it results in Black under optimal play doing better by V points or more. (Equivalently, if you add a copy of P but subtract V from Black’s score, Black is at least no worse off, that’s how I originally phrased it).
How do we show that this results in Black doing better by V points? All we have to do is show that Black has at least one strategy that guarantees them at least V points from P. That strategy is the one I explained. Whatever black would have played on the rest of the board before we added P, black still plays exactly the same on the rest of the board, so black earns the same score on the rest of the board. And when white plays in P, black responds in P, and by assumption black still earns at least V points even when white plays first in P, so overall black earns the score that they would have originally, plus V. It’s possible of course that black can do even better, for example perhaps by deviating to play first in P at an opportune moment if P ever becomes the biggest move on the board, instead just following white around. But we know black can achieve at least their original score, plus V.
And since adding P to any position increases blacks score under optimal play by at least V, certainly on average it increases it by at least V, so the average value of P is >= V.
The result of this is that if you ever do some complex calculation in some position and get something like “such and such local position is worth 4.16667 points for black, and the average gain per move is such and such many points” and so on and then you discover that even when white moves first black can achieve 5 points as long as they just answer each move, you know you made a calculation mistake. The value of the position cannot be less than 5 points for black, so it can’t be 4.16667.
And similarly, if there’s a position where either player can let the other move first and still manage to keep the score to 0 points (or any other fixed number of points), then that’s the value of the position. Like the A19-A17 position, or like the shape after black’s E9 in the endgame puzzle. If white plays first, such as atari at A19, black can connect and white gets nothing. If black plays first, then black can’t make any points either. Either player playing first gets the same result of 0, so the value of the position must be >= 0, and <= 0, and therefore it must be = 0.
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