Basic endgame problem -- feedback requested

Violence · **#41**

Well, I'm a 10 kyu.

I don't think I solved this correctly, but then again, I'm bad at endgame. To make this like a real endgame situation, I like to try and solve them in under 10 minutes.

I don't really count the value of moves very precisely, when things get close, I just... read out the endgame board states.

So here's my unrefined, "blunt club to the face" answer to this Gordian knot.

To hell with fractional endgame values. We're doing this simple and dumb.

Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . x . . | $$ | X . X O O O O . O . X X . | $$ | . X O x . x . O O O X O . | $$ | x X X X X . X x X O x X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X x X . X O X X X . | $$ | . O O . O X . X O x O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . x . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O x O O X O O . O x . | $$ ---------------------------[/go]

First all, let's look at all the endgame plays. I will mark them with x's.

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Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . c . . | $$ | X . X O O O O . O . X X . | $$ | . X O b . c . O O O X O . | $$ | c X X X X . X c X O c X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X a X . X O X X X . | $$ | . O O . O X . X O b O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . b . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O b O O X O O . O b . | $$ ---------------------------[/go]

Knowing just the basics of counting, I put all the endgame plays that are roughly the same value together. A is worth a whopping 4 points, b's are worth around 2-3, and c's are worth around 1. I doubt I've lost anyone at this point. Let's play A because it's the biggest, and move on.

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Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . c . . | $$ | X . X O O O O . O . X X . | $$ | . X O b . c . O O O X O . | $$ | c X X X X . X c X O c X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O a O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . b . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O a O O X O O . O b . | $$ ---------------------------[/go]

And then we come here, and the first decision has to be made.

I've remarked the diagram. the b's are exactly 2 points, no tricksies. The A's are where things get weird, right? If black captures two stones at the bottom, it creates another 2 point gote play.

What an odd situation! Gee, I sure wish we could see the end of the game at the end of each branch. Oh wait, we can read.

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Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . x . . | $$ | X . X O O O O . O . X X . | $$ | . X O x . x . O O O X O . | $$ | x X X X X . X x X O x X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X x X . X O X X X . | $$ | . O O . O X . X O x O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . x . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O x O O X O O . O x . | $$ ---------------------------[/go]

I don't know what the hesitation with reading is here. I know for a fact that people can read sequences deeper than than number of moves left in this game, so if you aren't comfortable with memorizing value calculation, "When in doubt, read it out!"

Here's we'll see if black takes the 3 points raw, or the 2 points that generate another 2 point gote. First, we have him take 3 points raw. Naturally, white takes the other one. The final three 2 pointers are bigger than the rest, so we take them in turn.

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Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . b . . | $$ | X . X O O O O . O . X X . | $$ | . X O 6 . a . O O O X O . | $$ | b X X X X . X b X O a X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 2 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . 4 . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O 3 O O X O O . O 5 . | $$ ---------------------------[/go]

Now we come to the 1 pointers, and we see we have 3 b's and 2 a's. The 2 a's are miai, right? both are 1 pointers that have 1 points after you play them. The b's are just straight up 1 pointers. We play a's first.

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Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . a . . | $$ | X . X O O O O . O . X X . | $$ | . X O 6 . 8 . O O O X O . | $$ | a X X X X a X a X O 7 X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 2 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . 5 . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O 3 O O X O O . O 4 . | $$ ---------------------------[/go]

4 1 pt plays, they become miai. Finish the game!

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Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . 9 . . | $$ | X . X O O O O . O . X X . | $$ | . X O 6 . 8 . O O O X O . | $$ | B X X X X 0 X W X O 7 X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 2 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . 5 . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O 3 O O X O O . O 4 . | $$ ---------------------------[/go]

Now count the score! Wait, is that too hard? Not a problem, let's just do a comparison! Let's go back and see what the other board looks like if black moves the other way.

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Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . x . . | $$ | X . X O O O O . O . X X . | $$ | . X O a . x . O O O X O . | $$ | x X X X X . X x X O x X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 3 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . a . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O 2 a . X O O . O a . | $$ ---------------------------[/go]

Same value, 2 points a piece. Let's make it look as much like the other one as possible.

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Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . 0 . . | $$ | X . X O O O O . O . X X . | $$ | . X O 7 . 9 . O O O X O . | $$ | B X X X X W X W X O 8 X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 3 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . 5 . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O 2 4 . X O O . O 6 . | $$ ---------------------------[/go]

What's the difference between these two diagrams? In the previous one, Black just captured 1 stone and made 3 points on the right, and in this one, he captured two stones and made 3 points on the bottom. Looks pretty equivalent to me! Maybe our choice didn't make a difference after all.

Let's count, finally.

Black, 28 points.

White, 29.5 points.

White wins by 1.5.

And yes. Your reading will be wrong sometimes. Mine probably is right now. I might be off by... a whole point!

But the way I see it, while I respect the mathematics behind the counting methods, when you apply it to other aspects of the game, the ability to calculate fractional endgame becomes rather useless.

But the ability to visualize and analyze the board state 7-8 moves from now?
That's pretty useful.

This is how I usually recommend kyu players do endgame. I feel like too many people stop reading and start counting. Ideally, you should do both, but if given the choice between one or the other, I'll stick with my reading.

daniel_the_smith · **#42**

Heh, that's what I try to do to solve a problem like this. For me it's different from normal reading because everything is scattered all over the board. (In a game I just play whatever looks biggest unless it's really close, then I try this and fail).

Maybe if I ever gain another couple stones I'll be able to do full-board reading at that level of detail... (actually the arrow of causality probably goes the other way.) As it is, comparing points from more than two variations rapidly becomes extremely difficult for me...

Bill Spight · **#43**

Wow! The responses have been terrific! Many thanks!

(I have tried to thank everyone at least once.

)

John Fairbairn calls for a new approach to writing about yose. I am afraid that he might call my approach just another way of justifying the numerical approach. <sigh> But I do want to satisfy two audiences, regular go players and mathematically inclined players. (I do write papers for mathematicians and computer scientists, as well, but that's another matter.

)

Your feedback has been very helpful.

Now for breakfast and a write-up on the problem.

P. S. About aiming at 10 kyus: This is close to minimum complexity (I thought) for a full board problem. So it is definitely in the beginner range. ALso, it seems to me that there is a low correlation between yose skill (aside from tesuji) and go strength. I once made a problem that I thought was elementary, but to my dismay it stumped a dan player. Fortunately, a DDK solved it.

daniel_the_smith · **#44**

I'm still curious, for those who can do these problems: Do you all have a table of values memorized, do you calculate them out each time, or do you just read everything out and compare results?

Dusk Eagle · **#45**

I imagine that with experience, the value of certain moves would just be memorized naturally over time. If you constantly refer back to something (like, to take a mathematical example, the value of sin (0)), it eventually just gets ingrained in your memory.

There was something confusing me about calculating the value of one of the positions on the board, but as I typed it out to ask I figured it out. I'll just leave it here in case I forget or if anyone's curious to see my thought process.

mw42 · **#46**

Dusk Eagle wrote:

I imagine that with experience, the value of certain moves would just be memorized naturally over time. If you constantly refer back to something (like, to take a mathematical example, the value of sin (0)), it eventually just gets ingrained in your memory.

There was something confusing me about calculating the value of one of the positions on the board, but as I typed it out to ask I figured it out. I'll just leave it here in case I forget or if anyone's curious to see my thought process.

Magicwand · **#47**

daniel_the_smith wrote:

I'm still curious, for those who can do these problems: Do you all have a table of values memorized, do you calculate them out each time, or do you just read everything out and compare results?

basic endgame values given in the example is in the head and it only takes few sec to verify if not sure.
i think i am speaking for all dan level players. correct me if i am wrong.

Magicwand · **#48**

Violence · **#49**

All I can do is be able to do the most basic of calculations. Recognize a 1 pt gote, a 2 pt gote, a 3 pt gote, and so on and so forth.

The rest is reading.

John Fairbairn · **#50**

Quote:

I'm still curious, for those who can do these problems: Do you all have a table of values memorized, do you calculate them out each time, or do you just read everything out and compare results?

Someone told me that Rob van Zeijst (insei level) had memorised the counts of about 1,000 endgame positions. I have no idea if either the story or figure is true, but the fact that the story is out there suggests there's at least a grain of truth in it.

At the other extreme, I do know one strong pro who claimed not to know how to count a yose ko.

Dusk Eagle · **#51**

mw42 wrote:

Dusk Eagle wrote:

I imagine that with experience, the value of certain moves would just be memorized naturally over time. If you constantly refer back to something (like, to take a mathematical example, the value of sin (0)), it eventually just gets ingrained in your memory.

There was something confusing me about calculating the value of one of the positions on the board, but as I typed it out to ask I figured it out. I'll just leave it here in case I forget or if anyone's curious to see my thought process.

Click Here To Show Diagram Code: [go]$$B $$ ------------- $$ . O X . . X . $$ . O O X X X . $$ . . . . . . .[/go]

If white plays he gains a point, if black plays he gains a point. From the perspective of white, we consider a black gain as a "negative" gain for white. So, from white's perspective it is a 1p-(-1p)=2p play.

Yes, but it is a gote play for both white and black, and thus the local tally is 2. So a play in the area is worth:
Count / Tally
= 2 points / 2
= 1 point.

This is using the Miai Counting method, which I believe I am using correctly (let me know if I'm doing something wrong).

Magicwand · **#52**

Bill Spight · **#53**

John Fairbairn wrote:

At the other extreme, I do know one strong pro who claimed not to know how to count a yose ko.

Only a few people in the world know how to count a yose ko.

Perception · **#54**

My endgame is terrible so I'm not going to attempt this right now. I did however get The Endgame from the Elementary Go Series a couple days ago so when I've read that I'll give it a shot (probably in a week or two).

Also if anyone knows of a Japanese book about the endgame, I remember seeing it mentioned on godiscussions, that had full board 11x11 problems I'd like to get a copy of it. If you know the title or ISBN or even better where I could find a copy (I think it's out of print) that would be great. I'm going to go try to find the original post about it in the godiscussions archive.

edit: I found the post, the book is a Yose Dictionary (新編ヨセ辞典) by Kano Yoshinori (加納嘉徳). I don't know where to find it since it's out of print.

mw42 · **#55**

Dusk Eagle wrote:

Yes, but it is a gote play for both white and black, and thus the local tally is 2. So a play in the area is worth:
Count / Tally
= 2 points / 2
= 1 point.

This is using the Miai Counting method, which I believe I am using correctly (let me know if I'm doing something wrong).

Yes, you are using it correctly, but I'd prefer to say 2p gote play then a 1p play as you did. I thought you were counting wrong, sorry. :-)

Bill Spight · **#56**

Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O . . . . | $$ | X . X O O O O . O . X X . | $$ | . X O . . . . O O O X O . | $$ | . X X X X . X . X O . X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X . X . X O X X X . | $$ | . O O . O X . X O . O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . . . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O . O O X O O . O . . | $$ ---------------------------[/go]

First thing we do, we kill all the miai.

(We can do that because there are no kos. The same player might get both miai when the opponent takes and wins the ko.)

Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. $$ --------------------------- $$ | . . X O . . . O O 5 3 4 . | $$ | X . X O O O O . O . X X . | $$ | . X O 1 . a . O O O X O . | $$ | 6 X X X X . X . X O b X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X . X . X O X X X . | $$ | . O O . O X . X O . O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . . . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O . O O X O O . O 2 . | $$ ---------------------------[/go]

and

are miai. The result is 2 points (we take Black's point of view), whichever player gets which. :w3:

-

and

are also miai. The result is 1 point, whichever player gets which.

So we can assume that one player gets one while the other player gets the other, and go ahead and make the exchange.

"a" and "b" are also miai, but to know that you have to know that they are not sente. I know that, but I will assume that the solver does not know that yet.

Click Here To Show Diagram Code: [go]$$W White to play. Japanese rules. 6.5 komi. {Miai removed.} $$ --------------------------- $$ | . . X O . . . O O O O X . | $$ | X . X O O O O . O . X X . | $$ | . X O O . . . O O O X O . | $$ | X X X X X . X . X O . X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O a O X . X O 2 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . . . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O b O O X O O . O X . | $$ ---------------------------[/go]

As has been pointed out, our eyeballs tell us that :w1:

and

are the largest and next largest plays on the board. (If we want to count, :w1:

gains 2 points and :b2:

gains 1.5 points.) Now, Wa also gains 2 points and would also lead to a White win, but, with no kos it is never better than :w1:

. Again, our eyeballs tell us that, because it leaves the possibility of :b1:

. (In a ko position, Wa might be right, to leave :w1:

as a ko threat.)

Our solver might briefly consider "b" as an alternative to :b2:

, because it also has a potential swing of 3 points. However, that swing takes 3 moves instead of 2 moves for :b2:

, so it must be a smaller play.

Note to numsgil: It is possible to prove that :w1:

is correct, and then :b2:

, by direct comparison of plays.

Click Here To Show Diagram Code: [go]$$W White 3? $$ --------------------------- $$ | . . X O . . . O O O O X . | $$ | X . X O O O O . O . X X . | $$ | . X O O . c . O O O X O . | $$ | X X X X X d X . X O . X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 2 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . a . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O b O O X O O . O X . | $$ ---------------------------[/go]

The comparison of "a" and "b" is not so obvious. Their game trees look like this:

Code:

"a" is a gote, and each play gains 1 point. "b" looks kind of like a 1 point sente, but each play gains only 1 point. (It is ambiguous.)

Unless the solver has read the relevant material, such as that on SL, this is not particularly helpful.

What about "c"? Could it be a 1 point sente? No, because after Wc, "d" is worth only 0.5 point.

It's a guess, so let's try the one that sort of looks bigger, "b".

Click Here To Show Diagram Code: [go]$$W Variation 1 $$ --------------------------- $$ | . . X O . . . O O O O X . | $$ | X . X O O O O . O . X X . | $$ | . X O O . 5 . O O O X O . | $$ | X X X X X 7 X 8 X O 6 X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 2 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . 4 C X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O 3 O O X O O . O X . | $$ ---------------------------[/go]

When we play the rest of the variation, we discover something interesting. :w5:

and

are miai, as are :w7:

and

. We can assume that they are played the same way in the other variation.

(BTW, we can tell that :w5:

is bigger than :b8:

by eyeballing.

)

Click Here To Show Diagram Code: [go]$$W Variation 2 $$ --------------------------- $$ | . . X O . . . O O O O X . | $$ | X . X O O O O . O . X X . | $$ | . X O O . O . O O O X O . | $$ | X X X X X O X X X O X X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 2 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O C 3 . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O 4 W O X O O . O X . | $$ ---------------------------[/go]

at

The score differences between the two variations lie around :w3:

and

. In variation 1 Black gets 1 point (marked). In variation 2 Black gets 2 points for the White prisoners, while White gets 1 point (marked) plus a Black prisoner, for a net local score of 0. Plainly, variation 2 is better for White.

Click Here To Show Diagram Code: [go]$$W Solution $$ --------------------------- $$ | . . X O . . . O O . . . . | $$ | X . X O O O O . O . X X . | $$ | . X O 7 . 9 . O O O X O . | $$ | . X X X X . X . X O 8 X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X 1 X . X O X X X . | $$ | . O O . O X . X O 2 O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . 3 . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O 4 W O X O O . O 6 . | $$ ---------------------------[/go]

at

Click Here To Show Diagram Code: [go]$$Bm10 Solution {continued} $$ --------------------------- $$ | . . X O . . . O O 6 4 5 . | $$ | X . X O O O O . O . X X . | $$ | . X O O . O . O O O X O . | $$ | 3 X X X X 2 X 1 X O X X . | $$ | O O O O X . X . X X . X . | $$ | . . O X . X . X O X . X . | $$ | . . O X O X . X O X X X . | $$ | . O O . O X . X O X O X . | $$ | . X O O X X X O O X . X . | $$ | . O . O O X X . O X X X O | $$ | . . O . O . X O O O O X X | $$ | . . O O X X X O . O O X . | $$ | . . O . O . X O O . O X . | $$ ---------------------------[/go]

A count reveals that White does indeed win.

Bill Spight · **#57**

A couple of notes on the problem:

First, most of the plays are miai.

That is no surprise, because. . . .

This is a last play problem. Namely, :w5:

. (We call :w5:

the last play, even though there are more to come, because the rest of the plays are miai.

)

Third, eyeballing can help.

and

are obvious.

Fourth, this is a reading problem. Whether to play 3 or 4 cannot be told just by comparing the two plays.

unkx80 · **#58**

A bit late into the game... but here are my opinions anyway.

The original problem is not likely to be solvable by a 10k on the first try. The simplified problem may be solvable by a 10k, if given sufficient time. In a 19x19 game where each player has 30 minutes to 1 hour, I suspect there may be insufficient time even for dans to read an endgame problem of the size of the original problem.

I never attempted either problem. It is very likely I get something wrong.

Bill Spight · **#59**

unkx80 wrote:

In a 19x19 game where each player has 30 minutes to 1 hour, I suspect there may be insufficient time even for dans to read an endgame problem of the size of the original problem.

Reading a typical endgame with 10 different small positions while in 30 sec. byoyomi might be daunting.

Still, with a little knowledge, even a 10 kyu would find this endgame trivial to play correctly.

lightvector · **#60**

Bill Spight wrote:

unkx80 wrote:

In a 19x19 game where each player has 30 minutes to 1 hour, I suspect there may be insufficient time even for dans to read an endgame problem of the size of the original problem.

Reading a typical endgame with 10 different small positions while in 30 sec. byoyomi might be daunting.

Still, with a little knowledge, even a 10 kyu would find this endgame trivial to play correctly.

I'm a weak dan player, and reading and exactly counting the result in 30 sec byoyomi is not possible for me. Mainly the counting part, while holding in my head the result of the best play. But I can find the sequence of best play very easily.

I bet I could teach a 10k to easily do this sort of thing too. For me, it was enough just to know the endgame values of some of the common moves by sight. I saw the center move had a 4 vs 0 swing, so 2 points, and saving the white stone was 3 vs 0, so 1.5 points, and the rest was a bunch of 1 pt moves, two 0.75 pt pushes, and some 0.5 pt pushes, which I simply knew the values of. It takes me only a few more seconds to convince myself that nothing tricky will happen, like white cutting at K10 doesn't force black to eventually have to capture the stone.

Basic endgame problem -- feedback requested

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