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One of my old problems

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One of my old problems

Posted: Thu Feb 03, 2011 9:09 am
by Bill Spight
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. :)

Re: One of my old problems

Posted: Thu Feb 03, 2011 10:00 am
by Magicwand
Click Here To Show Diagram Code
[go]$$W White to play and win.
$$ -----------------------
$$ | . . . . . 9 7 8 . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 6 . X , . |
$$ | . . O a O X X . X . . |
$$ | . . O 4 X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 0 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]

11 @ a
i dont know about winning..but this seems ideal.
it took me 10 sec to comeup with above seq.
i hope i am right :)


edit:
ok ..i did another sequence..which appears to have same result.
Click Here To Show Diagram Code
[go]$$W White to play and win.
$$ -----------------------
$$ | . . . . 7 6 8 . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 X X . X . X . |
$$ | . . O . 0 O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 9 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]

Re: One of my old problems

Posted: Thu Feb 03, 2011 10:00 am
by Dusk Eagle
Click Here To Show Diagram Code
[go]$$W White to play and win.
$$ -----------------------
$$ | . . . . . 9 7 8 . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 6 . X , . |
$$ | . . O 0 O X X a X . . |
$$ | . . O 4 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]


Click Here To Show Diagram Code
[go]$$Wm11 White to play and win.
$$ -----------------------
$$ | . . . . . O O X . . . |
$$ | . . . . O O X . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O O X . X , . |
$$ | . . O X O X X . X . . |
$$ | . . O X X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 1 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]

:w1: is the biggest move. After that, I believe :b4: and :w7: are worth the same amount (1.0 points). However, before :w7:, white should play :w5:, which is sente for him (the followup is bigger than the move itself). The reason it is sente is because 'a' will not be worth a point if white can play on :b6:. With :w9:, white has obtained tedomari, and only miai plays remain.

This took me a little while to get, but I think I have it right now. I'm quite enjoying these problems: I feel like I'm really learning with each one.

Re: One of my old problems

Posted: Thu Feb 03, 2011 10:17 am
by Bill Spight
@ Magicwand and Dusk Eagle

Thanks, guys!

Click Here To Show Diagram Code
[go]$$W Jigo
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . 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]

Re: One of my old problems

Posted: Thu Feb 03, 2011 10:33 am
by HermanHiddema
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 7 6 . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 X X . X . X . |
$$ | . . O . 8 O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 9 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]


White wins by 1 point.

:w3: is vital to get the last move. If :w3: simply connects, black can later play the first line hane-connect and it will be jigo:


Click Here To Show Diagram Code
[go]$$W White to play and win.
$$ -----------------------
$$ | . . . . 7 6 8 . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 X X . X . X . |
$$ | . . O . 9 O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 0 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]



I solved it by having seen it before, I don't think I would find this tedomari in a real game :)

Re: One of my old problems

Posted: Thu Feb 03, 2011 10:41 am
by Magicwand
Bill Spight wrote:@ Magicwand and Dusk Eagle

Thanks, guys!

Click Here To Show Diagram Code
[go]$$W Black wins.
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . 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]

i felt something was missing..and was looking into top :w3: and realized what i missed just before you post.
thank you for intresting problem.

Re: One of my old problems

Posted: Thu Feb 03, 2011 11:37 am
by Mnemonic
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 :sad:

Solution:
Click Here To Show Diagram Code
[go]$$W White protects at a
$$ -----------------------
$$ | . . . . . a 9 0 . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 6 . X , . |
$$ | . . O 7 O X X . X . . |
$$ | . . O 4 X X . X . X . |
$$ | . . O C . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 8 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]

:w1: is a 5 point gote move and the biggest on the board.
:b4: should be a 2,5 gote move ,because it destroys the possibility of a white point at :ec: and White needs to protect at :w7: at some point.
:w5: and :b6: are 1,5 gote moves and the rest are 1 point gote moves

Re: One of my old problems

Posted: Thu Feb 03, 2011 11:59 am
by jts
Stab at a solution:
Click Here To Show Diagram Code
[go]$$W White to play and win.
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . a . . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O c . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O b X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . d X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]


"a" is 6 pts in gote (with a 1 pt gote follow-up), "b" is 2 pts in gote (with a 1 pt gote follow-up), "c" is 1.75 pts in gote (with a 1.5 pt follow-up if white plays) 2 pts with a 2 pt follow up, "d" is 1 pt in gote.

I looked at the descent one point to the left of "a" and it wasn't as good for white.

Click Here To Show Diagram Code
[go]$$W White to play and win.
$$ -----------------------
$$ | . . . . . . 9 0 . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 6 . X , . |
$$ | . . O 7 O X X . X . . |
$$ | . . O 4 X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 8 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]


Which gives a final score of -1.


My thoughts on the difficulty:
This strikes me as doable by a 10k. It took me 6 minutes to score the main line, 3 minutes or so to double-check all the variations on the top edge, plus a bit to count. I didn't find any tricks, though, so perhaps I missed the point of the problem. Edit: yes, I missed it.

Re: One of my old problems

Posted: Thu Feb 03, 2011 2:07 pm
by Dusk Eagle
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O a 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]

It's actually a tie, isn't it? I just didn't think about black playing :b4: at that spot - I thought he had to play at 'a'.

So, more to learn :) .

Re: One of my old problems

Posted: Thu Feb 03, 2011 4:08 pm
by Bill Spight
Dusk Eagle wrote:
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . 3 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O a 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]

It's actually a tie, isn't it? I just didn't think about black playing :b4: at that spot - I thought he had to play at 'a'.

So, more to learn :) .


Yes, it's jigo.

Oops! ;)

Re: One of my old problems

Posted: Thu Feb 03, 2011 4:25 pm
by yoyoma
My thoughts are not 100% clear on this but I figured I'd write down what I have so far:

Ok well I know how to calculate Miai values, and this understanding is already more than enough to satisfy me as far as practical game play is concerned. But I am interested in trying to get a proper 10,000 foot level of understanding of what those things are. So here is what my current 10,000 foot explaination would be, please correct any mistakes:

Some plays involve creating an even/odd number of smaller followup moves to ensure you get the last move of a certain size (Tedomari), or at least prevent the opponent from getting Tedomari. Some of them involve the order of equal sized moves and deal with 'should I play this 2 point gote or this 1 point sente/reverse-sente'.




Click Here To Show Diagram Code
[go]$$W White to play and win.
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . a . . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O c . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O b X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . d X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]



Miai values:
a = 3
b = 1
c = 1
d = 0.5

White plays the A sequence, and then (here's a part where I'm not sure) analyzes the entire rest of the board to completion and determines hanging connection is better than solid connection in this case?? And this is an example of.... Creating an even/odd number of smaller followup moves??

Miai values:
a' = 1 (new play created after a)
b = 1
c = 1
d = 0.5

Black.... Well how does black pick among the 1 point plays? Does it matter? Let's say for now black plays C, because that's what Bill's solution has! :)

Miai values:
a' = 1 (new play created after a)
b = 1
d = 0.5

White.... Well again here I'm not sure but as before I randomly pick the one Bill picked. :D
White plays b

Miai values:
a' = 1 (new play created after a)
b' = 0.5 (new play created after b)
d = 0.5

Black plays a' (easy!)

Miai values:
a'' = 1 (new play created after a')
b' = 0.5 (new play created after b)
d = 0.5

White plays a''
Black plays b'
White plays d



Calculations of some of the miai values:
a - 3
6 point double gote, leaving behind a 1 point reverse sente for white

b - 1
white to play makes 2 points + 50% of 1 more point
black to play prevents white's move, but white still has 50% to make 1 point
(2.5 - 0.5)/2 = 1

c - 1
White to play here will be sente, since followup is worth 2 points, which is more than Black's reverse sente (worth 1 point)

d - 0.5
1 point double gote

Re: One of my old problems

Posted: Thu Feb 03, 2011 7:38 pm
by mitsun
This problem has two fairly separable parts -- the top and the middle.

A play at the top is clearly biggest, and the hane is better than the straight descent (since the follow-up in either case is gote). Then the question is how W should connect:

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . b c . . . . . |
$$ | . . . . a 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . 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]

(a) can be ruled out, as it is never better than (b), no matter who gets the next move
(c) seems equivalent to (b), since a B response looks like sente in either case
(b) might be a better choice if W could conceivably let B get the next two moves

Continuing, plays at (a) and (b) in the middle are now miai

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . O O X . . . . |
$$ | . . . . . O X . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O b . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O a 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]

W at (a) leaves a local position worth 2.5 points for W by the OM count
B at (a) leaves a local position worth 0.5 points for W by the OM count
W at (b) leaves a local position worth 1+ points for B by the OM count
B at (b) leaves a local position worth 3 points for B by the OM count
The OM count does not help us here; the end of the game is so close that we need more accuracy.

If B plays (b) and W plays (a), two points remain and will be split. This is the correct play for B, although he still loses the game. This B move can be considered reverse-sente, if that helps.

If B plays (a) and W plays (b), B needs to block. Two points still remain and will be split. This continuation is one point worse for B.

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.

Re: One of my old problems

Posted: Thu Feb 03, 2011 8:05 pm
by Bill Spight
mitsun wrote:
This problem has two fairly separable parts -- the top and the middle.

A play at the top is clearly biggest, and the hane is better than the straight descent (since the follow-up in either case is gote). Then the question is how W should connect:

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . b c . . . . . |
$$ | . . . . a 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . 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]

(a) can be ruled out, as it is never better than (b), no matter who gets the next move
(c) seems equivalent to (b), since a B response looks like sente in either case
(b) might be a better choice if W could conceivably let B get the next two moves

Continuing, plays at (a) and (b) in the middle are now miai

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . O O X . . . . |
$$ | . . . . . O X . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O b . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O a 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]

W at (a) leaves a local position worth 2.5 points for W by the OM count
B at (a) leaves a local position worth 0.5 points for W by the OM count
W at (b) leaves a local position worth 1+ points for B by the OM count
B at (b) leaves a local position worth 3 points for B by the OM count
The OM count does not help us here; the end of the game is so close that we need more accuracy.

If B plays (b) and W plays (a), two points remain and will be split. This is the correct play for B, although he still loses the game. This B move can be considered reverse-sente, if that helps.

If B plays (a) and W plays (b), B needs to block. Two points still remain and will be split. This continuation is one point worse for B.

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.


I think that this is your line of play.

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 5 4 . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 6 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 7 X X . X . X . |
$$ | . . O . 8 O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 9 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]


:b8: and :w9: are miai, and could go the other way.

If so, :b6: is a mistake.

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 5 4 . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 7 8 . X , . |
$$ | . . O 0 O X X . X . . |
$$ | . . O 6 X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 9 X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]


:w9: and :b10: are miai.

The result is jigo.

Re: One of my old problems

Posted: Thu Feb 03, 2011 11:23 pm
by lightvector
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.
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 . a . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O b . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O c X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . d X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]


White begins by playing the biggest move. Now, abc are all worth 1 point miai counting. But they behave slightly differently (I bet CGT would give them all some different weird infinitesimals).

If black plays a, then there's a 1 point reverse sente left for white there.
If white plays b, then there's a 1 point gote left for white there.
C is just a straight-up 1 point gote with nothing special. Regardless of who plays first, there's an 0.5 point gote left, but it's always going to be miai with d, which is also 0.5 points, so we can ignore that and ignore d.

White's goal is to be the last to play a 1 point move.

Variations:

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 6 4 . . . . |
$$ | . . . . 7 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 b . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O a 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]


If :b4: descends, then white pushes at 5. Black takes his sente with :b6: , but sente gains nothing (it already was factored in when we declared :b4: to be a 1 point move in the first place). Now, a and b are miai, so white will get the last 1 point play. If we finish up the miai pairs from here, white wins by 1 point.

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 7 6 . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 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]


If :b4: blocks, white takes the other 1 point play with :w5:, then when black descends, white gets the last 1 pt play with the reverse sente at :w7:. White wins by 1 point.

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 c a . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 b . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 4 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]


If :b4: pushes here, then :w5: pushes. Next, if :b6: descends at a, white pushes at b and gets the last 1 point play (black can take his sente at c, but under miai counting, sente gains nothing). If on the other hand :b6: blocks at b, white hanes at a which is the last 1 pt play again. In either variation, after the miai pairs are finished off, white wins by 1 point.


I hope this is right. Fun problem.

Re: One of my old problems

Posted: Fri Feb 04, 2011 12:36 am
by Bill Spight
lightvector wrote: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.
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 . a . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O b . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O c X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . d X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ ------------------------[/go]


White begins by playing the biggest move. Now, abc are all worth 1 point miai counting. But they behave slightly differently (I bet CGT would give them all some different weird infinitesimals).

If black plays a, then there's a 1 point reverse sente left for white there.
If white plays b, then there's a 1 point gote left for white there.
C is just a straight-up 1 point gote with nothing special. Regardless of who plays first, there's an 0.5 point gote left, but it's always going to be miai with d, which is also 0.5 points, so we can ignore that and ignore d.

White's goal is to be the last to play a 1 point move.

Variations:

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 6 4 . . . . |
$$ | . . . . 7 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 b . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O a 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]


If :b4: descends, then white pushes at 5. Black takes his sente with :b6: , but sente gains nothing (it already was factored in when we declared :b4: to be a 1 point move in the first place). Now, a and b are miai, so white will get the last 1 point play. If we finish up the miai pairs from here, white wins by 1 point.

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 7 6 . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 4 . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 5 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]


If :b4: blocks, white takes the other 1 point play with :w5:, then when black descends, white gets the last 1 pt play with the reverse sente at :w7:. White wins by 1 point.

Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | . . . . 3 c a . . . . |
$$ | . . . . . 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 b . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O 4 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]


If :b4: pushes here, then :w5: pushes. Next, if :b6: descends at a, white pushes at b and gets the last 1 point play (black can take his sente at c, but under miai counting, sente gains nothing). If on the other hand :b6: blocks at b, white hanes at a which is the last 1 pt play again. In either variation, after the miai pairs are finished off, white wins by 1 point.


I hope this is right. Fun problem.


Well done! :)


Click Here To Show Diagram Code
[go]$$W Canonical play
$$ -----------------------
$$ | . . . . 3 6 4 . . . . |
$$ | . . . . 7 1 2 . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O 5 b . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O a 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]


Your first variation shows technically correct play by both players. :)
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