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Maximum Number Of Liberties In A Dead Chain
    Keywords: MiddleGame, EndGame

Maximum number of liberties in a dead chain

[Diagram]
New proverb: 139 liberties live, 138 may be dead.

This should be taken with humour, not as a refutation of the "Five liberties for tactical stability" proverb. It is also a challenge as the MaximumNumberOfLiveGroups page. Can anyone find a higher number of liberties for a dead chain on a 19x19 board?

(If someone doubts black is dead: The only eyes black can do require two miai moves as a + a or b + b. Should black play at any of the a, white must play at the other. The same for b and the same for any other corners. Also, if black plays at c, d is the right answer (or in reverse order). There is nothing black can do to make an eye except z (if in sente) and that single eye is not enough for living.)

Jacques Basaldúa


Rakshasa's suggestion:

[Diagram]
Newer proverb: 153 liberties live, 152 might be dead



unkx80: I can't count, so someone please verify my claim. Note the big eye has 17 - 2 = 15 liberties.

[Diagram]
158 liberties.



unkx80's solution has 148 liberties (still better than mine). Rakshasa's is the best and the simplest. Jacques.

Tom: I think the problem here is the ambiguity described in the Liberty page. I'm going to try an example that may not be entirely original.

[Diagram]
Two more liberties? One eye beats no eyes.

One more at least.



Jacques: I use the word liberty in its first sense, i.e. "an empty point adjacent to a single stone or chain of stones" which can easily be counted with software without any lookahead. This is also the sense used in the rules. This solution has 155 liberties. The best! It may not seem obvious, but black is dead. There is no seki because black can be captured, even if he has sente when this position is reached ..

[Diagram]
.. black is lost, even with sente

How do you count 155 liberties for that?

I don't. I count 155 liberties for Tom's solution. Then, I try to explain why black is dead and white is alive even if she has only one eye. The answer: White can kill black as shown in my diagram (which is Tom's solution after the potential moves white could do to kill black.) Sorry if I didn't explain it ok.



This is a copy of the living page "Maximum Number Of Liberties In A Dead Chain" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.