Re[2]: computer-go: Live or Die

[rbrown@xxxxxxxxxxxxxxx]

Jeff Massung wrote:

> ooooo    ooooo    ooooo    ooooo
> oxxxo    oxxxo    oxxxo    o...o
> ox.xo => oxoxo => ox.xo => o.o.o
> ox.xo    ox.xo    oxxxo    o...o
> 
> If my definition of an "eye" is incorrect, could someone please correct it.  
> But if it is right, I need some examples of multiple space eyes where (b) is 
> true (useless to try).

Jeff has made it very convenient for us to reply, as he has included an
example of what he is looking for in his own message.  Thanks, Jeff!

[I'm assuming that the bottom of the diagram is the edge of the board.]

Take a look at your fourth diagram above, the one with no black stones.
Isn't it usless for Black (x) to play on the points (.) that White (o) has
surrounded?  If so, then don't the empty points comprise an eight-space eye?
I think they do, and I think this is the sort of multiple-space eye that the
other folks are talking about.

It's _legal_ for Black to play in there, but it's certainly useless, isn't it?
At least for the first three or four times he does it.  Fifth one _might_ be
a ko threat.

Of course if White is very, very stupid, he can fill up this eye with eight
white stones.  That's legal, too, if somewhat counterproductive for White.

But even for a group with exactly two one-point eyes for liberties, it's legal
for the owner to fill at least one of them.  (Possibly both, depending on the
rule set.)

Now if White's gonna pass seven times, he could get in some trouble, so he
might have to make a move to ensure that black doesn't capture his group.
Suppose all the external liberties are filled up by Black:

           xxxxx
 ooooo    xooooox
 o...o    xo...ox
 o.o.o => xo.o.ox
 o...o    xo...ox

Now, suppose further that White passes (or plays _tenuki_) after Black adds
each of seven stones:

           xxxxx      xxxxx
 ooooo    xooooox    xooooox
 o...o    xo...ox    xoxxxox
 o.o.o => xo.o.ox => xox.xox
 o...o    xo...ox    xoxx.ox

Now it's "me ari me nashi" -- Black has an eye, but White doesn't!  So, White
can pass six times... er, no... I guess it's only five times..., but must
answer the sixth Black move to preserve his eye.  A seki would also be bad
for White, so some reading might be required after Black throws a few useless
stones away.  Nonetheless, we may consider the original diagram an eight-
space eye.  Mayn't we?  Or is it I who am missing something?

Of course, even a one-point eye may be a legal move, for the opponent, if
it's the unique liberty of the group that has the eye.  Under Ing rules, such
a move may also be permitted for the owner of the eye (multiple stone suicide).
So, I'm not convinced that there is anything special about an eye that consists
of only one point, except under the condition when it's the only liberty, too.

There's gotta be some upper bound, though.  What's the biggest eye (and what is
its shape) within which it is not useless to throw away stones?  I dunno.  The
question is poorly-formed, anyway, because the size and shape of the "eye" is
not sufficient to determine the usefulness of playing inside it.  You also have
to take into account the connectedness or unconnectedness -- not to mention the
liberty count -- of the stones which make up its boundary, when determining
whether it would be useful to throw an enemy stone or two inside it.

Rich

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