Here is another problem that some people would find easy. It is smaller than the previous one, but trickier.

Click Here To Show Diagram Code

[go]$$W White to play and win.
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O . . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O . X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . . X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]

White to play and win.

Enjoy!

Feedback still appreciated.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

edit:

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"The more we think we know about
The greater the unknown"
Words by neil peart, music by geddy lee and alex lifeson

_________________
We don't know who we are; we don't know where we are.
Each of us woke up one moment and here we were in the darkness.
We're nameless things with no memory; no knowledge of what went before,
No understanding of what is now, no knowledge of what will be.

@ Magicwand and Dusk Eagle

Thanks, guys!

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

_________________
"The more we think we know about
The greater the unknown"
Words by neil peart, music by geddy lee and alex lifeson

I've looked at the problem for about 3-4 min and this is my first thought. I will look at it later some more to see if I missed something. (I felt this problem was easier than the last, but Bill said it was tricky

Solution:

_________________
While I was teaching the game to a friend of mine, my mother from the other room:
"Cutting? Killing? Poking out eyes? What the hell are you playing?"

Stab at a solution:


My thoughts on the difficulty:

_________________
We don't know who we are; we don't know where we are.
Each of us woke up one moment and here we were in the darkness.
We're nameless things with no memory; no knowledge of what went before,
No understanding of what is now, no knowledge of what will be.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

My thoughts are not 100% clear on this but I figured I'd write down what I have so far:




Calculations of some of the miai values:

I think the difficulty level of this problem depends on how much time you allow the solver. Anyone who can solve it in a minute or so is probably dan level. I guess a mid-kyu player could also solve it given considerably more time.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Wow, I think I got it. I hope. Doing this problem has taught me a few things I didn't realize before. I think I understand much better how tedomari works.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Again, many thanks to the solvers.

It has been enlightening to me to find out how people think about these problems, Also, it is gratifying that so many feel that they are learning something about getting the last play. I am going to pass that along to Berlekamp and Wolfe, the authors of Mathematcal Go, which is where I learned this stuff.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

These deliberations are very interesting of course. But I'm wondering if this is the best way to improve one's endgame.

In a game, most of the time it's not necessary to compute exact values of moves. It's usually enough to find the largest place and play there, taking sente and miai into account of course. Only relative size of various plays matters.

Take a look at this elementary problem. How quickly can you decide which place is bigger, top or bottom?

Click Here To Show Diagram Code

[go]$$c Black to play
$$ --------------
$$ | . . . . . |
$$ | X X O O . |
$$ | . . X O . |
$$ | X X X O O |
$$ | . . . O . |
$$ --------------[/go]

I don't really want to compute the size of plays there. What I want is something like an intuitive feel for the relative size of the two places. And a good way to develop this skill is to solve hundreds or even thousands of simple yose problems where there are only two or three unsettled boundaries left and you just have to pick the largest place.

ひと目のヨセ (http://senseis.xmp.net/?YoseAtAGlance) by Cho Chikun attempts to do something like this, but it only has about a hundred problems. I need more.

For common endgame moves, you don't need to compute. You can just know the values in advance, which isn't hard.
The top move is 1 point because it's a gote hane+connect, the bottom is just shy of 1 because it's a corridor push. So black plays the top, solved on sight (there's also a tedomari issue, but...). I don't ever actually compute the value of a complicated move during a game, unless it's a big trade or something (and then only approximately).

For me, having a few values gives a useful anchor. The following scale is roughly what I have off the top of my head, and is really useful for me in games.

1/3:
Final endgame ko

1/2:
Gote push to destroy 1 point

1/2 to 1:
Push down corridor ending in dead end (closer to 1 if longer)

1:
Sente push or push that is "eventually" sente (the corridor leads to a sente move at the end)
Gote 1st line hane-connect
Capture 1 stone and make 1 territory
Destroy 2 points
Capture2-recapture1 (this one's useful to know)

3:
1st line hane-connect sente for one side
2nd line hane-connect with gote followups
Capturing 2nd line stone with gote followups

4-5:
1st line hane-connect that can't be directly blocked by one side
Playing/blocking "typical" gote monkey jump

~4-10:
Capturing 2nd line stone with varying senteness/severity of followups
2nd line hane connect with varying senteness/severity of followups

8
Playing/blocking "typical" sente monkey jump

~11-14+
Medium to large opening moves

~14
Opening move, taking empty corner

~N/2:
Make a move that turns N potential points into dame

~N:
Save N stones
Resolve a small capturing race with N stones involved (owned by either player)

Basically, I play a lot by feel too, but having this rough scale in mind makes it a lot easier to keep everything coherent, and helps compare things like capturing stones with first line and second line moves. It's nice to instantly know that your second line hane and connect is better than saving 4 stones from capture.

I'm afraid to say that I've not really attempted most of these endgame problems that Bill (and others) has posted lately. And this despite me being about the 10k "target audience" - the first problem was just a bit too fiddly for me to solve at any speed, and didn't seem enough fun to want to spend time working it out I guess I need to learn from the experts here how to evaluate the size of these plays quickly. Right now I have to read out 3 or 4 moves, then compare the two positions, before I can say "OK, so A is a 2 point gote" (or whatever).

Because walleye's problem is so small, it was easy enough for me to figure out that the top was bigger than the bottom, but only because I was able to read all the way to the end of the game in both cases, to see that starting on top led to a win by one whereas starting on the bottom was jigo. But it wasn't intuitively obvious to me what the answer would be from simply looking at the position.

I'm not sure what this proves, other than that my endgame sucks

(Although, at my club I quite often get to take white in high handicap games on small board against near-beginners; and against those who don't gratuitously let their groups die, most of my wins in these situations come from bossing them about in the endgame, so I guess my endgame isn't that terrible compared to my rank. I feel I'm OK on the general principle that you shouldn't just follow your opponent around, but make sente plays of your own if they threaten something bigger than your opponent's last "sente" play does. I'm just not very good at choosing the biggest move - particularly online when I'm always in byoyomi by the endgame, and 30 seconds just doesn't seem long enough for me to decide which the biggest areas are.)

Considering I answered the last one correctly simply by my first pass being lucky, I will be interested in if and how I've made mistakes. I did intentionally take the last move (successfully, I believe) this time. Thanks for the fun, Bill.

My Solution and slight variations:

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Revisiting Go - Study Journal
My Programming Blog - About the evolution of my go bot.