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 Post subject: Re: 3-move tsumego rule
Post #21 Posted: Thu Sep 13, 2018 5:14 pm 
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Here is another problem, nicely solvable by this method.
Both marked W moves seem to make two eyes immediately ....
How can B play to make this not true?

Click Here To Show Diagram Code
[go]$$ B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O . o . . X
$$ | . X O . O . . . X
$$ | . X O . O . X . X
$$ | . X O O . o . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]

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 Post subject: Re: 3-move tsumego rule
Post #22 Posted: Thu Sep 13, 2018 5:37 pm 
Judan

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Hidden out of courtesy.

Click Here To Show Diagram Code
[go]$$Wc B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O 4 a . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . 1 . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


Assuming that Black can kill, after :w1:, :b2: and :b4: are necessary. Yes, Wa looks good for :w1:, too, but again the heuristic of making a one point eye helps to make things clear.

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 Post subject: Re: 3-move tsumego rule
Post #23 Posted: Thu Sep 13, 2018 10:42 pm 
Honinbo

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@dfan: Thanks for explaining to me. It's easier to understand now, even at 2 in the morning :-p

@Bill: In your last diagram, how did you select :w1: as 'A' and not the other (lowercase 'a')? Or does selection of 'A' not matter much? By capital 'A', I'm referring to the original rule.

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 Post subject: Re: 3-move tsumego rule
Post #24 Posted: Thu Sep 13, 2018 11:00 pm 
Judan

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Kirby wrote:
@Bill: In your last diagram, how did you select :w1: as 'A' and not the other (lowercase 'a')? Or does selection of 'A' not matter much? By capital 'A', I'm referring to the original rule.


Well, you want to select a White move such that Black has two necessary moves to kill. I picked the one I did because it formed a one space eye. As it turned out, that fit the bill. :)

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 Post subject: Re: 3-move tsumego rule
Post #25 Posted: Fri Sep 14, 2018 1:03 am 
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Click Here To Show Diagram Code
[go]$$W B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O 4 . . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . 1 . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


Click Here To Show Diagram Code
[go]$$W B to play
$$ ------------------
$$ | . . . 4 . . . . .
$$ | . X X O . 1 . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


There are two such moves. The triplets have 1 move in common. So, ....

Click Here To Show Diagram Code
[go]$$ B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O . . . . X
$$ | . X O 1 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


Impressive!


This post by Knotwilg was liked by: mitsun
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 Post subject: Re: 3-move tsumego rule
Post #26 Posted: Fri Sep 14, 2018 1:34 am 
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John Fairbairn wrote:
I do look forward to discussion of this excellent post.

Matthew Macfadyen (ex-European Champion) used to mention this principle a lot and he used it in his seminars (?around 1975~1980). As I recall, he said he got it from someone else, and some others claimed to know about it, but I never understood why it was not more widely known. My brain baulks at thing like that, so I've never tried to use it - frankly, didn't even understand it. Maybe others had the same disinclination. Or perhaps people then were not doing tsumego much. That may sound far-fetched but the only collection available was the small Maeda series.

I think Matthew referred to it as a 2-move rule but I can't remember his exact wording.



Is this the idea that the first step to solving the problem of how to kill is working out how to live?

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 Post subject: Re: 3-move tsumego rule
Post #27 Posted: Fri Sep 14, 2018 3:09 am 
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Knotwilg wrote:
Click Here To Show Diagram Code
[go]$$W B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O 4 . . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . 1 . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


Click Here To Show Diagram Code
[go]$$W B to play
$$ ------------------
$$ | . . . 4 . . . . .
$$ | . X X O . 1 . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


There are two such moves. The triplets have 1 move in common. So, ....

Click Here To Show Diagram Code
[go]$$ B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O . . . . X
$$ | . X O 1 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


Impressive!


The second triplet is a ko :

Click Here To Show Diagram Code
[go]$$W B to play
$$ ------------------
$$ | . . . 4 5 . . . .
$$ | . X X O . 1 . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


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 Post subject: Re: 3-move tsumego rule
Post #28 Posted: Fri Sep 14, 2018 4:18 am 
Honinbo

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Knotwilg wrote:
Click Here To Show Diagram Code
[go]$$W B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O 4 . . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . 1 . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


Click Here To Show Diagram Code
[go]$$W B to play
$$ ------------------
$$ | . . . 4 . . . . .
$$ | . X X O . 1 . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


There are two such moves. The triplets have 1 move in common. So, ....

Click Here To Show Diagram Code
[go]$$ B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O . . . . X
$$ | . X O 1 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


Impressive!


Neat. I can see these specific examples working. I'm trying to convince that this always works for different selections of 'A' - or the boundaries of when it works. I'm a little tired to think accurately now, though.

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 Post subject: Re: 3-move tsumego rule
Post #29 Posted: Fri Sep 14, 2018 4:43 am 
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@zermelo: One thing that interests me a lot is how other people think. Would you be willing to explain how you came up with this insight? It may be a re-discovery but it's still a discovery! And also, your view of it as a 3-move principle rather than the 2-move principle I first heard makes it easier for me to comprehend.


I cannot really remember that well. I imagine I was looking at some difficult problem and thinking "playing at A does not work for black, but then if white gets A, black cannot kill even getting more than 1 move in a row ... no, wait a minute...".

Also, thanks for nice words, John, Bill, Knotwilg. I'm sure many have come up with this, and probably many have used it without formulating it as a 'rule'. And Bill answered the technical comments and explained when the rule works already so well that I have nothing to add to that.

As said, this definitely works only for some problems, and even they could of course be solved just by going through variations sequentially. Myself, I find it really comforting with some difficult problems to at least decisively limit the starting moves to e.g. three moves, and so I really like this approach when it works. As opposed to not finding a solution and thinking that now I need to again go through all the possible starting moves and variations and see where I made a mistake. So different methods could suit different personalities or psychologies too.

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 Post subject: Re: 3-move tsumego rule
Post #30 Posted: Fri Sep 14, 2018 4:50 am 
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Click Here To Show Diagram Code
[go]$$ B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O c . . . X
$$ | . X O b O . . . X
$$ | . X O . O . X . X
$$ | . X O O . a . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


This is a really nice illustration.

Indeed, it looks to me that the actual answer is the ko that Tryss found:
Click Here To Show Diagram Code
[go]$$ B to play
$$ ------------------
$$ | . . . 3 4 . . . .
$$ | . X X O . 2 . . X
$$ | . X O 1 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


Anyway, if the ko is the best result starting from moves a, b, or c, then we know that ko is the best result. Because if black could kill, the solution would start by one of those moves.

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 Post subject: Re: 3-move tsumego rule
Post #31 Posted: Fri Sep 14, 2018 6:14 am 
Judan

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I did not include the ko diagram originally, even though I suspected that the best Black can do is ko, because the logic of the rule relies upon the assumption that Black to play can kill. We have all seen positions where the play to kill is different from the play to make ko.

However, upon reflection I think that the logic should also work with the disjunctive assumption that Black to play can kill or make ko. You just need to check for both ko and the kill for each choice of White play.

Click Here To Show Diagram Code
[go]$$W B to play
$$ ------------------
$$ | . . . 4 5 . . . .
$$ | . X X O . 1 . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . a . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]


:b2: and :b4: appear to be necessary to make ko after :w1:, which means, in conjunction with the position starting with Wa, :b2: is the first move, with Black to kill or make ko.

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


After :b1: we cannot assume that Black can only make ko, so we try :w2:.

Click Here To Show Diagram Code
[go]$$Bm5 (continued)
$$ ------------------
$$ | . . . 7 . 6 3 5 8
$$ | . X X O O 2 O 4 X
$$ | . X O X O 1 . . X
$$ | . X O . O . X . X
$$ | . X O O . X . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]

:w13: at 9

If :w7: at 11, :b8: at 9. (White still dies.)

By convention the rest of the board is empty and White dies.

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


White dies this way, too.

Click Here To Show Diagram Code
[go]$$B Ko
$$ ------------------
$$ | . . . 3 4 . . . .
$$ | . X X O 5 2 . . X
$$ | . X O 1 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .[/go]

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 Post subject: Re: 3-move tsumego rule
Post #32 Posted: Fri Sep 14, 2018 7:22 am 
Judan

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Kirby wrote:
I'm trying to convince that this always works for different selections of 'A' - or the boundaries of when it works.


By the logic of the rule, the necessity of B and C to achieve the goal, given A, is equivalent to the assumption that the goal is achievable. The derivation of A as a possible first play depends upon the observation that if the first play is none of A, B, or C, then the defender can play at A and make miai of B and C. A has to be a good play.

Click Here To Show Diagram Code
[go]$$Wc Black to kill.
$$ ------------------
$$ | . O C . . . X . .
$$ | . C 1 C O O X . .
$$ | . O O O X X X . .
$$ | X X X X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]


In this position :w1: looks like a vital point, threatening to make 3 one point eyes (marked).

Click Here To Show Diagram Code
[go]$$Wc Black to kill (1)
$$ ------------------
$$ | . O . 5 7 6 X . .
$$ | 2 8 1 . O O X . .
$$ | 4 O O O X X X . .
$$ | X X X X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]


Then :b2: and :b4: suffice to kill. But are they necessary?

Click Here To Show Diagram Code
[go]$$Wc Black to kill (2)
$$ ------------------
$$ | . O . 4 . 6 X . .
$$ | 2 . 1 . O O X . .
$$ | 5 O O O X X X . .
$$ | X X X X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]


No, they are not. This :b2: and :b4: also kill.

Click Here To Show Diagram Code
[go]$$Wc Black to kill (3)
$$ ------------------
$$ | . O . 5 . 4 X . .
$$ | 2 . 1 . O O X . .
$$ | 6 O O O X X X . .
$$ | X X X X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

If :w5: at 6, :b6: at 5

We have seen this position before. White is dead.

But it looks like :b2: is necessary, as it occurs in all variations. :) Besides, after :w1:, a White play at 2 would make 2 one point eyes.

Now the fact that :b2: is necessary after :w1: suggests that it is a good first move. The relation to the All Moves As First heuristic is no accident.

Edit: Now, to see that only :b2: is necessary after :w1: in all the variations took either logic, which I did not use, or going through a number of variations. As knotwilg points out, proving necessity may entail just as much search and effort as simply proceeding directly to reading. However, if you can see or show necessity without reading, you may be able to save time and effort. :)

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