I noticed a simple rule that has helped with some tsumego. It may be close to trivial, and surely others have thought of it, but nevertheless I’ve found it useful for eliminating starting moves that cannot work.
The 3-move tsumego rule: Assume that the problem is black to kill. Now let A, B, C be such intersections that if white would start at A, the only way for black to kill with 2 moves would be playing both B and C. Now the solution to the original problem has to start with black play at A, B, or C.
An example:
If we would let white play at a, black would need to play both b and c to kill. So we know that black has to start either at a, b, or c. Otherwise white would get a, and black would not get both b and c.
I don't think this is quite a theorem as such, because there could be cases where move order matters, if e.g. B would make A illegal, or because of captures.
You can also generalise the rule in different ways. E.g. if after white A, black would need to play either B and C, or B and D, then the correct starting move is one from A-D. It should work in ‘white to connect’ or other problems in the same way.
3-move tsumego rule
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John Fairbairn
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Re: 3-move tsumego rule
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.
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.
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Bill Spight
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Re: 3-move tsumego rule
Edited in toto for clarity.zermelo wrote:You can also generalise the rule in different ways. E.g. if after white A, black would need to play either B and C, or B and D, then the correct starting move is one from A-D. It should work in ‘white to connect’ or other problems in the same way.
The original rule is that if there is a White stone on A, Black to kill must play two stones in a row on B and C. We assume that Black to play can kill, without the White stone on A. Let us indicate this symbolically this way.
WA -> ((BB, BC) <-> kill) ; where the comma indicates "and"
But we are assuming a kill if Black plays first, which would allow her to play two stones while White plays one stone. So that reduces to
WA -> (BB, BC)
which in turn reduces to
¬WA v (BB, BC) ; where ¬ indicates "not" and v indicates "or"
To prevent White from playing on A, Black can play on that point or perhaps make the White play on A illegal, and if he does not do so on his first play he must play on B or C in order to play on both.
The second case is this.
WA -> (BB, (BC v BD))
Unless White to play can prevent Black from playing either C or D, or a play at one of them by White prevents Black from playing the other, then we may regard them as miai. That means that Black does not need to play at C or D first.
Last edited by Bill Spight on Wed Sep 12, 2018 12:40 pm, edited 2 times in total.
The Adkins Principle:
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Visualize whirled peas.
Everything with love. Stay safe.
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Tryss
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Re: 3-move tsumego rule
The problem with this rule is that it can be more complicated to find the moves A, B and C that verify the hypothesis than to solve the problem.
"if white would start at A, the only way for black to kill with 2 moves would be playing both B and C. " is quite specific.
For exemple, these moves A, B, C are not fitting the rule :
Indeed, if white play A, there is two possibilities for black to live :
So, what would be the A, B, C points for this problem?
"if white would start at A, the only way for black to kill with 2 moves would be playing both B and C. " is quite specific.
For exemple, these moves A, B, C are not fitting the rule :
Indeed, if white play A, there is two possibilities for black to live :
So, what would be the A, B, C points for this problem?
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Bill Spight
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Re: 3-move tsumego rule
That's how I heard it. Let White play first, and then give Black 2 moves in a row to kill.John Fairbairn wrote:I think Matthew referred to it as a 2-move rule but I can't remember his exact wording.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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zermelo
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Re: 3-move tsumego rule
Yes, it does not work everywhere. But I noticed I used it already twice while looking through less than 10 Xuanxuan Qijing problems, so I was reminded of it. The above problem is from that collection.Tryss wrote:The problem with this rule is that it can be more complicated to find the moves A, B and C that verify the hypothesis than to solve the problem.
Another was this: It seems to be often useful, when there is some obviously vital-looking point, like point a in this and the previous problem. THen quite often you can find a pair of black moves to go with it.
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Bill Spight
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Re: 3-move tsumego rule
What you have shown is that Black should start at 1 or 2.Tryss wrote:The problem with this rule is that it can be more complicated to find the moves A, B and C that verify the hypothesis than to solve the problem.
"if white would start at A, the only way for black to kill with 2 moves would be playing both B and C. " is quite specific.
For exemple, these moves A, B, C are not fitting the rule :
Indeed, if white play A, there is two possibilities for black to live :
So, what would be the A, B, C points for this problem?
We can regard the different 4 points as miai for capturing the two White stones. OC, that does not mean that Black will actually be able to capture them. The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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Bill Spight
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Re: 3-move tsumego rule
Consider also these three points.zermelo wrote:I noticed I used it already twice while looking through less than 10 Xuanxuan Qijing problems, so I was reminded of it. The above problem is from that collection.
Another was this: It seems to be often useful, when there is some obviously vital-looking point, like point a in this and the previous problem. THen quite often you can find a pair of black moves to go with it.
If White "a", Black "b" and "c" are necessary to kill.
Problem solved. (Assuming that Black to play can kill, OC.
)The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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John Fairbairn
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Re: 3-move tsumego rule
I noticed a simple rule that has helped with some tsumego. It may be close to trivial, and surely others have thought of it, but nevertheless I’ve found it useful for eliminating starting moves that cannot work.
@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.
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Kirby
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Re: 3-move tsumego rule
So let me see if I understand the rule...
1.) You find a move 'A' that white might play if white were going first.
2.) Usually this leaves the state such that black can still kill in 2 moves. These two moves are 'B' and 'C'.
3.) Solve the problem from the beginning in the normal way, but consider 'A', 'B', and 'C' as potentially good starting moves.
Is that it? If so, how is 'A' selected? Just what appears to be the good starting move for white?
1.) You find a move 'A' that white might play if white were going first.
2.) Usually this leaves the state such that black can still kill in 2 moves. These two moves are 'B' and 'C'.
3.) Solve the problem from the beginning in the normal way, but consider 'A', 'B', and 'C' as potentially good starting moves.
Is that it? If so, how is 'A' selected? Just what appears to be the good starting move for white?
be immersed
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dfan
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Re: 3-move tsumego rule
I'll rephrase:
1) You find a move A that would make White live if she played first (e.g., the 1-2 point in zermelo's original diagram; it makes a corner eye and one at the 2-2 point).
2) Often you are now in a state where a) Black cannot kill White if he just plays one move; b) if Black is given two moves in a row, they must be at B and C to kill (not anywhere else).
3) You now know that A, B, and C are the only starting moves that could kill.
(Say you play a different move D. White plays A, and you only have one move to play both B and C, which is the only way to kill. If you could play E to kill now, condition 2b would not have been satisfied.)
1) You find a move A that would make White live if she played first (e.g., the 1-2 point in zermelo's original diagram; it makes a corner eye and one at the 2-2 point).
2) Often you are now in a state where a) Black cannot kill White if he just plays one move; b) if Black is given two moves in a row, they must be at B and C to kill (not anywhere else).
3) You now know that A, B, and C are the only starting moves that could kill.
(Say you play a different move D. White plays A, and you only have one move to play both B and C, which is the only way to kill. If you could play E to kill now, condition 2b would not have been satisfied.)
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Knotwilg
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Re: 3-move tsumego rule
Me too I have a hard time understanding either the rule or its novelty.
My understanding of your rule
0) It's your turn to play
1) Somehow you find A, a move for the opponent, which then requires you to play both B & C to kill
2) You infer that A, B, C are good starting moves (the only starting moves?) to consider for killing
First, a question on symmetries
- If the property of this triplet is fully symmetric, then all of A, B, C are good first moves
Then a question on completeness
- How does finding such a triplet narrow the search tree to something particularly promising?
I have a more structured approach, I think, which is also more fundamental
1) Try solving the L&D problem by narrowing the eyespace (that's for killing, likewise, expand for living)
2) this leads to 1 sequence of consecutively narrowing/expanding; it usually reduces to a well known eyeshape
3) one of the players can play the vital point of that eye shape - this is a candidate vital point for the problem
4) In a second stage, promote this vital point above any of the narrowing/expanding moves
5) cuts are stronger vital points than no-cuts
6) iterate
Killing by narrowing is straightforward and it's also good practice in games because you strengthen the outside position and don't throw away stones if a group is revived (by a ko, or so). Finding the vital point is harder and can be found by narrowing the space.
I think that your A, B, C moves will often have 2 edge points and 1 vital point.
]
My understanding of your rule
0) It's your turn to play
1) Somehow you find A, a move for the opponent, which then requires you to play both B & C to kill
2) You infer that A, B, C are good starting moves (the only starting moves?) to consider for killing
First, a question on symmetries
- If the property of this triplet is fully symmetric, then all of A, B, C are good first moves
Then a question on completeness
- How does finding such a triplet narrow the search tree to something particularly promising?
I have a more structured approach, I think, which is also more fundamental
1) Try solving the L&D problem by narrowing the eyespace (that's for killing, likewise, expand for living)
2) this leads to 1 sequence of consecutively narrowing/expanding; it usually reduces to a well known eyeshape
3) one of the players can play the vital point of that eye shape - this is a candidate vital point for the problem
4) In a second stage, promote this vital point above any of the narrowing/expanding moves
5) cuts are stronger vital points than no-cuts
6) iterate
Killing by narrowing is straightforward and it's also good practice in games because you strengthen the outside position and don't throw away stones if a group is revived (by a ko, or so). Finding the vital point is harder and can be found by narrowing the space.
I think that your A, B, C moves will often have 2 edge points and 1 vital point.
]
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dfan
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Re: 3-move tsumego rule
What I took from the presentation was:
1) Sometimes White has a very clear move (A) to immediately live if it is her turn. If this is the case, it is worth checking whether you could then kill at all given two moves in a row (B and C).
1a) If this is so, you have just narrowed your list of candidate moves down to three (A, B, C).
1b) If you can't even kill given two moves in a row, then you have narrowed the list of candidate moves down to one (A).
2) If there wasn't such a White A, then go back to your regularly scheduled method of solving tsumego (e.g., starting by reducing the eyespace).
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.
1) Sometimes White has a very clear move (A) to immediately live if it is her turn. If this is the case, it is worth checking whether you could then kill at all given two moves in a row (B and C).
1a) If this is so, you have just narrowed your list of candidate moves down to three (A, B, C).
1b) If you can't even kill given two moves in a row, then you have narrowed the list of candidate moves down to one (A).
2) If there wasn't such a White A, then go back to your regularly scheduled method of solving tsumego (e.g., starting by reducing the eyespace).
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.
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Bill Spight
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Re: 3-move tsumego rule
My apologies to zermelo for not congratulating him on his wonderful insight.John Fairbairn wrote:I noticed a simple rule that has helped with some tsumego. It may be close to trivial, and surely others have thought of it, but nevertheless I’ve found it useful for eliminating starting moves that cannot work.
@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 heard it from a Japanese 6 dan back when Japanese amateur 7 dan overlapped with pro strength.
As for the correctness of the rule, it only works if we assume, as with a problem, that Black to play can kill (or connect, or whatever is the goal). If White plays A, Black must play both B and C to kill. B and C are the two necessary moves in that case. B and C have to be such that Black cannot guarantee both with a single play, and White to play cannot with one move prevent Black from playing either.
Given those conditions, Black's first play must be either B or C, or a play that prevents White from playing A. Otherwise White can reply at A, making miai of B and C, and Black cannot then kill.
Last edited by Bill Spight on Thu Sep 13, 2018 11:08 am, edited 1 time in total.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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Bill Spight
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Re: 3-move tsumego rule
2) is incorrect. Moves B and C must be both necessary and sufficient to kill. Otherwise White A might just be a bad move.Kirby wrote:So let me see if I understand the rule...
1.) You find a move 'A' that white might play if white were going first.
2.) Usually this leaves the state such that black can still kill in 2 moves. These two moves are 'B' and 'C'.
3.) Solve the problem from the beginning in the normal way, but consider 'A', 'B', and 'C' as potentially good starting moves.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.