Life In 19x19

Thanks for the advice and analysis...when I've studied another month or two I might understand more of it.

I've just thought of another way of thinking about this, which may (or, then again, may not) be of help. (As someone who only started to play almost exactly a year ago, I still welcome the chance to be made to think more deeply about things like this, even though it must be obvious to the experts ). An "eye", often defined loosely in terms of a point (or set of points) completely surrounded by one's own stones (and possibly the edge of the board too), should I think, to be precise, really be defined as follows:



From this definition, of course, it easily follows that a group with 2 (or more) eyes can never be captured, no matter how many consecutive plays your opponent gets. Also (of which the above is a corollary) that the final liberty in an eye must always be the last liberty filled (if you're trying to capture a 1-eyed group), hence all the advantages of having an eye in a capturing race.

But, according to this definition, what you had in the corner there was not an eye! This is because, while one might naturally think of it as a 6-space "eye" (perhaps "pseudo-eye" would be better - note that this is completely different from a false eye), you actually only have 4 liberties there (count them!). This means that your opponent can (given enough plays - as happened here) indeed fill them all without committing suicide along the way, despite the fact you had a genuine eye elsewhere in the group.

So this is why, if the opponent makes an eye inside your "eye", it isn't an eye, because it means that your opponent can fill your liberties without leaving himself with none (as he has the inside of his eye as an unfilled liberty).

This post is, I realise, somewhat in the style of our resident rules authority, which can't be good, so I'll stop here

Incidentally, I think this kind of thing is very easy to miss - at least at my level. I've had games where I've had a group in the corner that I'm sure is alive, and when my opponent played some stones inside still thought was seki, but I later realised (or had it pointed out to me at the end of the game), that my group is in fact dead - because I'd missed that my opponent had (or could easily make) an eye inside

robinz wrote:I've just thought of another way of thinking about this, which may (or, then again, may not) be of help. (As someone who only started to play almost exactly a year ago, I still welcome the chance to be made to think more deeply about things like this, even though it must be obvious to the experts ). An "eye", often defined loosely in terms of a point (or set of points) completely surrounded by one's own stones (and possibly the edge of the board too), should I think, to be precise, really be defined as follows:

Code: Select all

An eye is a set of liberties of your group which, were your opponent to fill all of them, would cause him to leave his own stones with no liberties (unless the last liberty also happens to be the last liberty of your group, thereby killing it).

From this definition, of course, it easily follows that a group with 2 (or more) eyes can never be captured, no matter how many consecutive plays your opponent gets. Also (of which the above is a corollary) that the final liberty in an eye must always be the last liberty filled (if you're trying to capture a 1-eyed group), hence all the advantages of having an eye in a capturing race.

But, according to this definition, what you had in the corner there was not an eye! This is because, while one might naturally think of it as a 6-space "eye" (perhaps "pseudo-eye" would be better - note that this is completely different from a false eye), you actually only have 4 liberties there (count them!). This means that your opponent can (given enough plays - as happened here) indeed fill them all without committing suicide along the way, despite the fact you had a genuine eye elsewhere in the group.

So this is why, if the opponent makes an eye inside your "eye", it isn't an eye, because it means that your opponent can fill your liberties without leaving himself with none (as he has the inside of his eye as an unfilled liberty).

This post is, I realise, somewhat in the style of our resident rules authority, which can't be good, so I'll stop here

Incidentally, I think this kind of thing is very easy to miss - at least at my level. I've had games where I've had a group in the corner that I'm sure is alive, and when my opponent played some stones inside still thought was seki, but I later realised (or had it pointed out to me at the end of the game), that my group is in fact dead - because I'd missed that my opponent had (or could easily make) an eye inside

a complete wrong idea about go rules.
In most rule sets you won't see any reference to eyes at all. rules only talk about capturing, capturable and things like that.

That a live groups have 2 eyes is only a strategic concept, nothing to do with rules. (but that doesn't mean that it is sometimes handy.

for a good definition on eyes see: [sl=BensonsDefinitionOfUnconditionalLife]Bensons Definition Of Unconditional Life[/sl].

and then notice that indeed the "eye" is indeed not a Benson "vital region". because there are empty points that are not liberties of any black chain.

But do remember groups don't need to be benson alive to be alive

No, I agree - I never said my post was anything about rules

willemien wrote:But do remember groups don't need to be benson alive to be alive

You don't even need to be alive to be alive-- just more alive than at least one nearby enemy group...

daniel_the_smith wrote:

willemien wrote:But do remember groups don't need to be benson alive to be alive

You don't even need to be alive to be alive-- just more alive than at least one nearby enemy group...

At least as alive as one nearby enemy group Let's not forget seki.

Just thought I'd say - thanks to your commentaries, when a similar situation came up in a recent game, I was able to create dual life. It's the first time I ever managed to get a seki off the computer!

Thank you guys for clarification on this. However the whole pass-alive thing gets a little confusing. Is there a way to tell if a black enclosed region of X territory is alive regardless of white's attempt to capture from within? I'm familiar with nakade and their vital points.

In general, if you are able to make (or already have) more than two eyes, you're 100% safe. That includes situations where one of your eyes is big enough to make another eye in it.
If you are able to make two eyes, and the opponent can not make an eye inside your eyes, you're safe, too. In general, that is very unlikely. Eyes need to be very big for the opponent to make another eye inside, especially when you react to the moves. And when an eye is that big, it's often easy to make a third eye . But in that regard the corner is special. You only need three or two stones for a eye in the corner. So especially when you're low on outside liberties, that's something to watch out for.

Note that the converse is not true: If your opponent can make an eye inside your eye, you may still be alive. When you have enough outside liberties, you might be able to capture the inside group.

Of course, to decide whether the opponent can make an eye inside, you have to read. For the original situation, that's not so hard:
P12 is an atari, so it's a natural move to consider. The answer is forced. N14 is also natural to consider, because it also forces an answer. After the connection, P14 again forces an answer. And with the next move, white can already atari, and black cannot defend.

The whole sequence just consists of forcing moves, it doesn't really branch. Ok, at N14 it may take some thought to decide that you really have to connect. And it may take some skill to see the other forcing moves after the initial atari. But that comes with practice. For now, it's sufficient to just try to read a few moves ahead. Especially when there is an atari, just try to imagine what will happen after playing the atari and connecting.