Easy endgame problem, Dec. 2014

Bill Spight · #1

A. White to play

B. Black to play

Show failure diagrams, too.

Enjoy!

oca · #2

Hi Bill, what is the komi ?

Bill Spight · #3

No komi. Territory scoring.

oca · #4

Kirby · #5

My attempt:

Edit:

mitsun · #6

Nice problem. At the start B has 13 points of secure territory and W has 11 points of secure territory. If I understand the way you like to like to count, the unsettled position on top has an expected value of 0 by symmetry, the unsettled position in the center has an expected value of -1 for B (two plays make two points), and the unsettled position in the lower left also has an expected value of -1 for B (with a more complicated evaluation tree). So the expected value of the whole board is 0, without considering whose turn it is to play.

If the task is to find optimum play, it is not a simple problem. For the more limited problem of B to play and win, I think I have an simple answer. It may be the best sequence for B (largest win), but no guarantee. I have not looked at W to play yet.

Bill Spight · #7

Note: White to play can win.

DrStraw · #8

Bill Spight · #9

@ Kirby

You found winning plays for each player. But there is a payoff in the failure diagrams. A few questions in the variations.

Kirby · **#10**

A few additional sequences.

Bill Spight wrote:

But there is a payoff in the failure diagrams.

Do you mean that there is value in providing failure diagrams?

Bill Spight · **#11**

Kirby wrote:

A few additional sequences.

Bill Spight wrote:

But there is a payoff in the failure diagrams.

Do you mean that there is value in providing failure diagrams?

Oh, there is.

But I have something specific in mind.

mitsun · **#12**

For W to play, it looks like a win is possible.

Bill Spight · **#13**

@ mitsun

mitsun · **#14**

Oops, I was so sure the hane would be correct in some variation, I fooled myself and counted wrong. The right answer is simpler.

lightvector · **#15**

I love Bill's simple endgame puzzles :study:

. Every time I learn something about how to conceptualize the fight for the last point. Maybe some day eventually knowing how to fight for the last point will win me a game :rambo:

(hasn't happened yet in any memorable way, sadly).

Here's my analysis.

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | O O a b X X O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X | $$ | X . X X O . O X X | $$ | . . X O , O X . . | $$ | . X X O O . X X X | $$ | X X O . O d O X O | $$ | X O O . O . O X O | $$ | c X X O . O X X . | $$ +-------------------+[/go]

Firstly, on the bottom, C and D are easy. They are both the same size of play, but are different in followups.

C is a 1 point ambiguous that leaves behind a 1 point gote if white plays.
D is a 1 point gote directly.

Both players want to come out with sente from the top to play the bottom because doing so wins tedomari and an extra (half-)point.

If black gets the first play on the bottom, black takes D and gets tedomari by recapturing when white takes C.
If white gets the first play on the bottom, white plays C and gets tedomari because the recapture is miai with D.

Now, about A/B. This is a strange beast. Black has the choice between the following sequences:

Black shuts the position down in sente with a local score of 0.

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | O O 1 2 X X O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X |[/go]

Black shuts the position down in gote with a local score of +1 for black.

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | O O 2 1 X X O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X |[/go]

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | . . 5 3 4 . O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X |[/go]

White has the choice of these two options in reverse as well. So whoever has sente can spend it to gain 1 point here, so the miai value of A/B is *also* 1 point! But it's weird. It's as if whoever's next to play can choose for there to be an extra 1 point move on the board but then must immediately take that move, or else can shut the position down in sente and choose for nobody to be able to get a 1-point move here.

Given that both players want tedomari, whoever's first to play in this problem here should obviously shut the position down in sente so that they can get tedomari on C and D as discussed before, thereby winning by 1 point.

To answer Bill's question about mistake variations, if white to play in this problem takes C first, then recapturing C becomes miai with D, so in order to gain tedomari, black *does* want there be an extra 1-point move that he can take for tedomari, so he spends sente by playing B, achieving a draw. Like so:

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | O O 2 1 X X O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X | $$ | X . X X O . O X X | $$ | . . X O , O X . . | $$ | . X X O O . X X X | $$ | X X O . O d O X O | $$ | X O O . O . O X O | $$ | W . . O . O X X . | $$ +-------------------+[/go]

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

Question to Bill:

Bill Spight · **#16**

lightvector wrote:

I love Bill's simple endgame puzzles :study:

. Every time I learn something about how to conceptualize the fight for the last point. Maybe some day eventually knowing how to fight for the last point will win me a game :rambo:

(hasn't happened yet in any memorable way, sadly).

Well, such opportunities do arise. These ideas do generalize to hotter positions, as well.

Quote:

Here's my analysis.

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | O O a b X X O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X | $$ | X . X X O . O X X | $$ | . . X O , O X . . | $$ | . X X O O . X X X | $$ | X X O . O d O X O | $$ | X O O . O . O X O | $$ | c X X O . O X X . | $$ +-------------------+[/go]

Firstly, on the bottom, C and D are easy. They are both the same size of play, but are different in followups.

C is a 1 point ambiguous that leaves behind a 1 point gote if white plays.
D is a 1 point gote directly.

Both players want to come out with sente from the top to play the bottom because doing so wins tedomari and an extra (half-)point.

If black gets the first play on the bottom, black takes D and gets tedomari by recapturing when white takes C.
If white gets the first play on the bottom, white plays C and gets tedomari because the recapture is miai with D.

Now, about A/B. This is a strange beast. Black has the choice between the following sequences:

Black shuts the position down in sente with a local score of 0.

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | O O 1 2 X X O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X |[/go]

Black shuts the position down in gote with a local score of +1 for black.

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | O O 2 1 X X O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X |[/go]

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | . . 5 3 4 . O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X |[/go]

White has the choice of these two options in reverse as well. So whoever has sente can spend it to gain 1 point here, so the miai value of A/B is *also* 1 point! But it's weird. It's as if whoever's next to play can choose for there to be an extra 1 point move on the board but then must immediately take that move, or else can shut the position down in sente and choose for nobody to be able to get a 1-point move here.

Given that both players want tedomari, whoever's first to play in this problem here should obviously shut the position down in sente so that they can get tedomari on C and D as discussed before, thereby winning by 1 point.

To answer Bill's question about mistake variations, if white to play in this problem takes C first, then recapturing C becomes miai with D, so in order to gain tedomari, black *does* want there be an extra 1-point move that he can take for tedomari, so he spends sente by playing B, achieving a draw. Like so:

Click Here To Show Diagram Code: [go]$$Bc $$ +-------------------+ $$ | O O 2 1 X X O . . | $$ | X X X O O O . O O | $$ | . . X O X . O O X | $$ | X . X X O . O X X | $$ | . . X O , O X . . | $$ | . X X O O . X X X | $$ | X X O . O d O X O | $$ | X O O . O . O X O | $$ | W . . O . O X X . | $$ +-------------------+[/go]

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

Bravo!

Quote:

Question to Bill:

In general I think that is right. I have made that kind of argument for similar, hotter positions. OTOH, I do not recall seeing a pro game where the players played that way.

And there is the possibility of a counterexample. Which means that one almost surely can be constructed. Some day.

Easy endgame problem, Dec. 2014

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