Life In 19x19

dfan wrote:This principle isn't a general system of solving tsumego, it's just a nice thing that can narrow your search tree when it comes up.

It narrows the conscious search tree for humans. The requirement that the two moves are necessary means that we have to know that all other combinations of two moves do not kill. Humans either have that knowledge already, deduce it, or perform the necessary search unconsciously.

OK, so the heuristic is "I spot a move A for White, so that Black's only way to kill with 2 moves is B & C"
That sounds like a heavy calculation in itself.
I thought it was about finding one such triplet but then from the answers understood it must be unique (B & C)

I applied both this heuristic and the systematic method on the mentioned problem. The systematic approach gave the first move faster than the heuristic. The real trouble in the problem is finding move 3, which neither the systematic approach nor the heuristic find easily, if at all.

Knotwilg wrote:OK, so the heuristic is "I spot a move A for White, so that Black's only way to kill with 2 moves is B & C"
That sounds like a heavy calculation in itself.

If done consciously, yes. This is probably not a good heuristic for computers.

I applied both this heuristic and the systematic method on the mentioned problem. The systematic approach gave the first move faster than the heuristic. The real trouble in the problem is finding move 3, which neither the systematic approach nor the heuristic find easily, if at all.

Let me illustrate the heuristic by the use of logic.

Click Here To Show Diagram Code

[go]$$W Black to reply and kill with two moves
$$ ---------------------------------------
$$ | . . . . . . . . . . 1 a 2 . O O X . . |
$$ | . . . . . . . X . O B O O 4 O X . X . |
$$ | . . . . . . X . X X O O . . O X . . . |
$$ | . . . , . . . . . , X X X X X , . . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

We find by the heuristic in tsumego of making one point eyes. That is the most efficient eye shape in a cramped space.

Once that is done, we deduce that is necessary to prevent White from making a second one point eye at "a". Then we deduce that, given and , is necessary to prevent White from making a second eye enclosing . To make these deductions we only have to read one move deep for each player. (Edit: At each step, that is. I guess we have read to a depth of 3. )

The best bots today do not use deduction, but humans do. Deduction can save us a lot of conscious effort.

Note that we have not shown that and kill White, only that they are necessary to do so, given . That's all we have to do to find our candidate moves.

Let me try starting with the heuristic of reducing or expanding eye space.

Click Here To Show Diagram Code

[go]$$B Black to kill
$$ ---------------------------------------
$$ | . . . . . . . . 5 3 4 . 6 . O O X . . |
$$ | . . . . . . . X . O X O O 2 O X . X . |
$$ | . . . . . . X . X X O O . 1 O X . . . |
$$ | . . . , . . . . . , X X X X X , . . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Failure 1.

Let's back up to and try 4 or 6.

Click Here To Show Diagram Code

[go]$$B Black to kill, II
$$ ---------------------------------------
$$ | . . . . . . . . . 4 3 . . . O O X . . |
$$ | . . . . . . . X . O X O O 2 O X . X . |
$$ | . . . . . . X . X X O O . 1 O X . . . |
$$ | . . . , . . . . . , X X X X X , . . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

We know already or can see without conscious reading that White is alive. Failure 2.

Click Here To Show Diagram Code

[go]$$B Black to kill, III
$$ ---------------------------------------
$$ | . . . . . . . . . . 4 . 3 . O O X . . |
$$ | . . . . . . . X . O X O O 2 O X . X . |
$$ | . . . . . . X . X X O O . 1 O X . . . |
$$ | . . . , . . . . . , X X X X X , . . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Obvious two eyes. Failure 3.

So we back up to and try 3 or 4 in the last diagram.

Our search has led us to two of the three candidate moves that the two move rule did. And, being humans, we have learned some things along the way which may help us in further search.

Thanks Bill, that's really helpful.

I actually tried zermelo's example with the systematic approach. The first move was easy enough to find that way, but the next was not.

This example is quite good in that the first move is less easy to spot but once you found it, the next move is easy.

So, with some delay, kudos to the OP!

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]

Hidden out of courtesy.

@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 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.

Kirby wrote:@Bill: In your last diagram, how did you select 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.

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?

Knotwilg wrote:

$$W B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . 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 . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .

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]

$$W B to play
$$ ------------------
$$ | . . . 4 . . . . .
$$ | . X X O . 1 . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .

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, ....

$$ B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O . . . . X
$$ | . X O 1 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .

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!

Knotwilg wrote:

$$W B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . 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 . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .

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]

$$W B to play
$$ ------------------
$$ | . . . 4 . . . . .
$$ | . X X O . 1 . . X
$$ | . X O 2 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .

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, ....

$$ B to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . X X O . . . . X
$$ | . X O 1 O . . . X
$$ | . X O . O . X . X
$$ | . X O O . . . X .
$$ | . . X O O O X . .
$$ | . . X X X X X . .
$$ | . . . . . . . . .

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.

@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.