I hope someone can tell me where I'm going wrong. This issue is still a mystery to me after reading numerous descriptions of territory scoring.

Click Here To Show Diagram Code

[go]$$
$$ ----------
$$ | . O X . . |
$$ | . O X O . |
$$ | . O X . . |
$$ | . O X . . |
$$ | . O X . . |
$$ -----------[/go]

Everything I've read says that white should not invade blacks territory when there is no hope of forming a living white group in there. BUT, black has to place 3 stones to capture the white invader above. So after the capture black has lost 3 territory and gained 1 capture, and is 2 points worse off. So it is definitely to whites advantage to invade as in the diagram.

Hold on, I know that if the game ended in the diagram position then the invading white stone is supposed to be considered dead and removed, giving black 1 extra captive and 1 more point. Of course this is to whites disadvantage as the scoring descriptions say. BUT it is not actually dead until black captures it. If I am white surely I just say "Go on black, prove it is dead by capturing it" and black has to place those 3 stones and end up 2 points worse off.

Alternatively if black decides not to capture then the white invader still has liberties. So the invading white stone wasn't dead after all!!! It remains sitting there and reduces black territory and score by 1.

To carry on this logic white would go on filling in blacks territory with white invaders, and it's to blacks advantage to capture at some point because otherwise blacks entire territory will be filled in with white, apart from the last illegal suicide move. Nevertheless it is to whites advantage to place at least one invader. Of course black does the same thing to whites territory.



So where is my understanding of territory score counting going wrong?
Why does white agree his invader is dead without further play by black?
Why do both players agree that an alive stone is dead?????

Yes, it's confusing.

Basically, at the end of the game, when both players pass, players set out to agree on the status of groups. If, in this case, Black claims that White's stone is dead, and White disagrees. Then play can "continue" to prove that one side is correct. Once the status of the group has been settled in that way, the board should be returned to the above position to be counted. Any extra stones Black may have placed to demonstrate his argument should be removed and therefore not cost points.

If returning to the position is to prove difficult, disallowing White from passing and making sure both players play exactly the same number of moves in determining the status of the group will have exactly the same result regarding score.

Hi beginsA291,

One source of confusion here is you are 'overloading' the meanings of the terms 'dead' and 'alive', as you did in the above sentences.

The following are two distinct and independent meanings:
(a) Legally on the board; in other words, still has at least 1 liberty.
(b) Alive shape.

Just because some stones are legally on the board -- they have at least 1 liberty -- does not tell us whether they make an alive or dead shape.

We can rewrite your two sentences above as follows:

But it is not actually removed from the board until black removes it from the board -- a tautology.

So the invading white stone isn't yet removed from the board -- a truth, but tells us nothing about its life status.

Example (1): unconditionally alive

Click Here To Show Diagram Code

[go]$$
$$ -------------
$$ | . O . O . .
$$ | O O O O . .
$$ | . . . . . .
$$ | . . . . . .[/go]

We ask about the two properties, (a) and (b).

Does it have at least 1 liberty ? Yes; it has 8.
It's legal to sit on the board; it satisfies (a).

Is it alive ? Even if White passes forever,
can Black, via certain moves, remove it from the board ?
No: there is no legal way for Black to capture it.
This White group (1) is alive. It also satisfies (b).

Example (2): unsettled

Click Here To Show Diagram Code

[go]$$
$$ -----------
$$ | . O . O .
$$ | O O O z .
$$ | . . . . .
$$ | . . . . .[/go]

We ask about the same two properties, (a) and (b).

Does it have at least 1 liberty ? Yes; it has 7.
It's legal to sit on the board; it satisfies (a).

Is it alive ? Is it possible for Black, via certain moves,
to remove it from the board ?
Yes: it is possible.

Click Here To Show Diagram Code

[go]$$
$$ -------------
$$ | y O x O X .
$$ | O O O X . .
$$ | X X X . . .
$$ | . . . . . .[/go]

Is it also possible for White, via certain moves,
to make it alive ? Yes: W can play (z) and make it unconditionally alive.

This White group (2) is not yet alive.
It does not yet satisfy (b).

Example (3): dead

Click Here To Show Diagram Code

[go]$$
$$ -----------
$$ | . X . W X
$$ | X X X X X
$$ | . . . . .
$$ | . . . . .[/go]

Same two questions for :

Does it have at least 1 liberty ? Yes; it has exactly 1.
It's legal to sit on the board; it satisfies (a).

Is it alive ? No.
This stone satisfies (a) but not (b).

Example (4): seki

Click Here To Show Diagram Code

[go]$$
$$ -------------------------
$$ | . X . X Q . X O . O . |
$$ | X X X X Q . X O O O O |
$$ | . . . X Q X X O . . . |
$$ | . . . X X O O O . . . |
$$ | . . . . . . . . . . . |[/go]

Same two questions for :
Does it have at least 1 liberty ? Yes; it has 2. It satisfies (a).

Can Black, via certain moves, remove from the board ?
Yes:

Click Here To Show Diagram Code

[go]$$B tenuki
$$ -------------------------
$$ | . X . X O 1 X O . O . |
$$ | X X X X O 3 X O O O O |
$$ | . . . X O X X O . . . |
$$ | . . . X X O O O . . . |
$$ | . . . . . . . . . . . |[/go]

puts both B and W strings in atari,
and if W ignores , then removes from the board.
( This could happen in a ko fight and W does not reply to as a threat.)

This string is currently in seki; it currently satisfies (b).
Whether it remains in seki -- whether it continues to satisfy (b) --
at the end of the game, we don't know yet.

Territory scoring is a misnomer. All it does is indicate one of the two main ways of scoring go. Yes, territory is counted, but so are prisoners and dead stones. That's all you need to know to use territory scoring. Unfortunately, telling which stones are dead is not always obvious. (And, under some rules, telling what is territory is not always obvious.) That is why, unless you play against someone who can tell you which stones are dead, it is easier to use area scoring.



A bit of an overgeneralization, but that' another topic.



Right.



Where did you read that?



OK.



Where did you read that?



There is a difference between playing stones and placing stones. Black can prove that White is dead by placing stones. Having proven that the White stone is dead, Black can take the stones placed on the board in the proof off the board before counting. They were not played, merely placed.

Edit: I stand corrected. Black cannot prove that the White stone is dead in this case. See Kirby's post below.

In practice, people do not actually place stones on the board to prove life and death. However, there are territory rules that allow life and death disputes to be settled by actual play, such as my rules and Lasker-Maas rules.

But if this kind of thing bothers you, just play by area rules, such as AGA rules.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Your example is interesting

You've probably read that it's the end of the game when both players pass.

Well, in this position, if white passes, white is forfeiting the right to try to make the white stone live. He is saying, "Ok, that white stone is dead". If black also passes, agreement has been achieved, and it's done.

Let's say that black passes, but white thinks, "Hey, this white stone can still live!" Then instead of passing, white keeps playing:

Click Here To Show Diagram Code

[go]$$W
$$ ----------
$$ | . O X . . |
$$ | . O X O . |
$$ | . O X W . |
$$ | . O X . . |
$$ | . O X . . |
$$ -----------[/go]

Now it's black's turn again. If black thinks there is nothing, he can pass again to avoid playing a move in what he thinks is his territory.

Or, if he thinks white actually made a real threat, he can play a move. For example, let's say he plays here:

Click Here To Show Diagram Code

[go]$$
$$ ----------
$$ | . O X . . |
$$ | . O X O . |
$$ | . O X O . |
$$ | . O X B . |
$$ | . O X . . |
$$ -----------[/go]

Now, if white passes, he is basically saying, "Ok, you were right. I cannot do anything here." Note that, since both black and white played a move, black gains an extra point from the white stone, but loses a point from the one played inside his territory, for a net effect of zero.

Now let's say white wasn't satisfied, yet, and instead of passing after black's move, above, kept going. Let's say he played here:

Click Here To Show Diagram Code

[go]$$
$$ ----------
$$ | . O X . . |
$$ | . O X O . |
$$ | . O X O . |
$$ | . O X X W |
$$ | . O X . . |
$$ -----------[/go]

Now, again, black has the option of passing, and not playing a stone in "his" territory. But if black does...

Click Here To Show Diagram Code

[go]$$
$$ ----------
$$ | . O X W . |
$$ | . O X O . |
$$ | . O X O . |
$$ | . O X X O |
$$ | . O X . . |
$$ -----------[/go]

!!!

Black will be captured. So let's say that black plays a move to try to stop this, and white responds as below:

Click Here To Show Diagram Code

[go]$$
$$ ----------
$$ | . O X 1 a |
$$ | . O X O 2 |
$$ | . O X O . |
$$ | . O X X O |
$$ | . O X c b |
$$ -----------[/go]

You might notice that it's difficult for black to play 'a', because it is self-atari. Likewise, 'b' would create a ko, but there are no ko threats.

Similarly, white cannot play 'a' due to self atari, and playing at 'c' would be ko, but there are no ko threats.

It's now seki

-----

So the conclusion here is that it is possible, if white keeps playing, that something "magical" might happen

If black passes, he doesn't believe such magic is possible, and therefore doesn't want to spend a point by defending inside his own territory.

*That* is why black is not required to play an additional three moves. He is betting that he can stop anything white can try.

If white passes, white is agreeing to this.

----

At your level, if you're white, I would recommend trying to keep playing if you think there's the smallest possibility that you might be able to do something inside the opponent's territory.

If you believe in it, magic might happen

_________________
be immersed

Argghhhh. I have lost my carefuly thought out post because the forum timed out and logged me out with no warning before I'd finished. Time and brain power lost! Very annoyed at the forum at the moment!

In thanks to the two players who replied to my post I will write it again, but I've gone off this forum now.

No I do not have the stamina to reconstruct the post that the forum lost. In any case I see the thread has moved on.

Let me start again. I think this issue is due to my misunderstanding of the rules. I thought that in my example in the orginal post that blacks territory was not actually blacks territory and still in dispute until all white had been removed from within it. I have been playing and scoring incorectly.

This is clearly incorrect because as topazg explains, the end testing procedure which happens after consecutive passes can result in invaders being found to be dead with no penalty to the invaded. Black removes the black stones placed during this testing in my example (as well as keeping captured white stones).

This explains EdLee distinction of legaly alive but with dead shape. That made no sense under my incorrect understanding.


Also -
Me: So it is definitely to whites advantage to invade as in the diagram.

Bill Spight: Where did you read that?

I didn't read it. I read that it was not to whites advantage and couldn't understand why this was from the rules as I understood them.

Also-
Bill : Yes, territory is counted, but so are prisoners and dead stones. That's all you need to know to use territory scoring.

Well I also need to know that the testing stones used in the end testing procedure are removed after the test.

Also-
Bill: ... That is why, unless you play against someone who can tell you which stones are dead, it is easier to use area scoring.

Well, it should be possible to unambiguously decide the score from the rules. Unfortunately the rules that came with my set, plus reading on various sites didn't make things clear. Perhaps I should have got a full ruleset, but I had no reason to think this was necessary. I think this is a trap for the beginner.


I still have a couple of questions:

1) What happens if the testing finds that the invasion turns out to be viable and a live invasion is formed? Are the new stones of both colours that were placed since the end of the game left on the board? (So that the score is counted using the revised board.)

2) Do seperate territories resolve independently? (Perhaps multiple territories for both black and white.) I.e. are there no moves where an otherwise dead invasion in one territory can be brought to life by play elsewhere? ("Magic" accross territories as Kirby might phrase it.) I think this is true by a move matching argument, but I'm not sure. If not then it is not possible to independently examine each territory to see if any invaders are alive or dead.

3) It still seems a little fishy. Surely it is well known if the smaller territories are viable for invasion, so players will tend to agree. I suppose a player has to put up (and create a live invasion without passing) or shut up (and not invade). Actually that's not a question is it.

Just to be clear, I was annoyed at the forum and not the excellent people taking the time to post here.

This is indeed complicated, and somewhat grey. My expectation in a real situation is as you describe, with the "invaded" player continuing to seal in new walls to deal with the fact he now has a live group in it, and then re-count. In reality, once past the beginner stages, I highly doubt White would claim a single stone of his is alive inside Black territory once beyond absolute beginner level - if it's left, I'd guess both players made the conclusion it was dead. It's more common in complex corner shapes where life is complicated, such as the bent four in the corner (actually, that's a really complicated one to prove, and one that has caused a few issues even in real life tournament play).

My experience is that this problem sort of resolves itself fairly quickly. If a group doesn't have two eyes, and the player with it tenukis, it's safe to assume he considers it dead. If he plays another move, then the other player will play again to demonstrate that it's dead, or fail - normally it ends up resolving itself. Certainly in the picture you linked, White being alive renders all of Black's territory gone, and likely also means Black's stones will die too. For amusement's sake, with regards to your original position, if White plays again, it's actually alive:

Click Here To Show Diagram Code

[go]$$
$$ ----------
$$ | . O X 5 . |
$$ | . O X O . |
$$ | . O X 2 6 |
$$ | . O X 3 4 |
$$ | . O X . . |
$$ -----------[/go]

In this position, there are no ko threats, and neither player can take away a liberty without dropping to one himself after the opponent responds, so although only one group has two eyes, everything is alive and White is the only one with points.



Also very complicated. At the end of the game, all territories should be sealed off, so they should be considered independently without problem. There may be issues where one player can create a ko, but needs an enormous amount of ko threats to win, and therefore doesn't want to start it (see ten thousand year ko).

In this case, technically White could kill black, but the reality is that the potential cost of the ko is larger than the gain (as the only way to kill is to open the possibility of dying himself). In this position it is normal that it resolves as mutual life. Without a ko, certainly every territory should be able to be treated independently.



Yes, put up or shut up is a general par for the course with this sort of thing. If you think you can invade, prove it - as long as the defender plays no more stones than the attacker, he loses nothing to demonstrate that the invasion was in fact not playable. And if it lives, there may be a lesson in there for the invaded player

Sorry that wasn't the simplest post - I'm trying to include the greyest areas that are likely to crop up in real play - I promise it's still unlikely to find yourself unstuck by one of these situations in actual games you play

So, first things first: Questions about scoring and how you know when the game ends and what is and isn't territory and what's alive and dead are something everyone goes through learning about the game. Unfortunately, I haven't seen a good way to really explain it simply unless you discuss examples as they come up, because there are always questions. Honestly, experience is probably the best teacher, and with a bit of time knowing when the game is over, what's dead and not, etc. will come pretty naturally. It's actually fairly rare for there to be scoring disputes in games even at a relatively novice level.

As for your questions:
1) This is a bit of a deficiency in territory scoring, as the rules to some degree assume skilled players, not beginners. As a general rule, the invasion and proceeding play should have happened in the game instead of hypothetically after the game has ended and the status of groups is being discussed. Until it's pretty clear, I'd just leave the stones on the board following the required play rule that Bill suggested, or use area counting. By the rules, you should take them off and score based on the determined status, but this breaks down when you're playing out an invasion sequence, and not just checking if an existing invading group is alive or dead.

2) This is a pretty technical question. Honestly, if you need to ask it about a game, you should have played along farther until the situation or situations are more clear. There are some complicated cases that can come up where multiple groups get involved in capturing races for example, but it's not worth worrying about at the moment. By the Japanese rules, as I understand them, you can have either situation: One where all the groups or many are involved, and one in which two separate situations are treated separately because they don't have a direct bearing on each other. Other rulesets may handle this differently. As I said, don't worry about it for a long while. The more you play, the less scoring disputes should come up at all because it becomes obvious to you what is alive and what isn't.

3)Yeah, it's best to do this during a game. If there's just a single stone, say, and you think it should live, play it out before you pass. Also, don't worry about the result too much for now. Just do your best, ask questions when confused, and move on. In a few years, when you're much stronger than you are now, you're not going to care whether or not you won, say, your 15th game of go, because you'll have surpassed it.

Actually, as an addendum, I've realised your original position is an interesting one, and a useful example that could reflect a real life 5x5 game between two beginners. With that in mind, I'll try to offer a "this is how it could have happened" explanation, Clue style:

Click Here To Show Diagram Code

[go]$$Bm1
$$ ----------
$$ | . 6 5 . . |
$$ | . 4 3 . . |
$$ | . 2 1 . . |
$$ | . 8 7 . . |
$$ | . 0 9 . . |
$$ -----------[/go]

This could have been the beginning of the game, at which point, if both players pass, Black clearly has 5 more points of territory than White. The end. But ... what if the following happens?

Click Here To Show Diagram Code

[go]$$Bm11
$$ ----------
$$ | . O X . . |
$$ | . O X 2 . |
$$ | . O X . . |
$$ | . O X . . |
$$ | . O X . . |
$$ -----------[/go]

Black passes on move 11, and White plays here... now what? If Black now responds to keep White dead, we have the following position:

Click Here To Show Diagram Code

[go]$$Bm11
$$ ----------
$$ | . O X . . |
$$ | . O X 2 . |
$$ | . O X 3 . |
$$ | . O X . . |
$$ | . O X . . |
$$ -----------[/go]

And again, White has 5 points, Black has 9 plus a prisoner, so Black is still 5 points better off. However, what if Black is convinced White is dead regardless of White's next move, he should pass again. and we could end up with:

Click Here To Show Diagram Code

[go]$$Bm11
$$ ----------
$$ | . O X 7 . |
$$ | . O X 2 . |
$$ | . O X 4 8 |
$$ | . O X 5 6 |
$$ | . O X . . |
$$ -----------[/go]

Suddenly we end up with my example from the previous post, and White did manage to create life... now White has 5 more points than Black! Black will have learned his lesson from passing prematurely.

The awkward bit for which I have no answer

However, what if Black passes on move move 13, and White also passes, leaving it in the position of your original diagram. In this situation, resumption has a problem - whoever plays first is right about the status of the group. The problem is, whoever requests the resumption of the game, according to Japanese rules, allows the other person to play first. So neither side will request a resumption to prove that the other person is wrong. I have no idea how this is supposed to be resolved

On the bright side, in all my years of playing Go, I've never had this happen!

I have had the forum time me out, but, unlike at other sites, I did not lose any text. Sorry that this happened to you.


Bill : Yes, territory is counted, but so are prisoners and dead stones. That's all you need to know to use territory scoring.



Actually, testing stones are not actually used. Rules such a Lasker-Maas or mine that allow life and death to be decided by actual play in an encore do not remove the stones played in the encore.

Bill: ... That is why, unless you play against someone who can tell you which stones are dead, it is easier to use area scoring.



That is true.



I am sorry that you got a crummy set of rules with your go set. That really should not happen.




I am afraid that we have compounded the confusion. All rules allow play to resume after two consecutive passes. In that case, stones played during the resumption are not taken back. Some rules, such as mine and Lasker-Maas rules, have an encore after two consecutive passes in which the rules are different from the first round of play, and in which a player is not penalized for capturing dead stones. Under those rules, also, stones played in the encore are not taken back. No rules actually place unplayed stones on the board to decide life and death. If you do that, it is by informal agreement between the players.



If there is a resumption of play or an encore, whether territories are independent or not is the same as in original play.



You don't know the half of it! There have been plenty of arguments about the rules in the past 100 years. (The fact that there were hardly any in the preceding centuries should give you some perspective. )

I like my rules, but may I suggest that you use area scoring, such as under AGA rules? Then you can just play until all stones remaining on the board are assumed to be alive.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Many thanks Bill. This has been the way it has happened in the couple of occurrences I witnessed in BGA tournaments. I suspect I misinterpreted an arbiter's resolution suggestion as a rules issue. I stand corrected!

Beginners can use simple rules with area scoring:
http://home.snafu.de/jasiek/simple.html
http://home.snafu.de/jasiek/simpcom.html

Beginners who cannot avoid the "temptation" to use territory scoring rules, can read these explanations:
http://home.snafu.de/jasiek/j_verbal_status.pdf
http://home.snafu.de/jasiek/sj.html
In particular, status assessment at the end of the game is only imagined. Therefore, it does not matter when more approach plays to remove opposing stones are needed than invading plays of the opponent.

(Since WWW 2.0 lacks the Save feature of the Usenet 1.0, copy & paste and save in an external text editor prevents one from losing drafts of messages.)

The position if both players pass after move 12 is inherently problematical, because it is a hot position, one in which at least one player can gain from playing first. It is not a proper final position, and it does not have a proper score. There is no getting around that. A surprising number of scoring problems that people come up with are of this type. All I do is shrug my shoulders and say that the rules cannot come up with an unambiguously correct score for a position that does not have one.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Well, I don't know. The BGA may have special tournament rules that say what the arbiter should do.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Hi beginsA291,

Again, to be clear: in Go, the terms 'alive' and 'dead' have very specific meanings.
In the case above, you meant to say "legally sitting on the board (with at least 1 liberty)", but dead -- it is not alive. You ask a very good question.
And as you can see from the discussions so far,
it is not easy to answer. As skydyr suggests, you need to play many more games to gain the experience necessary to understand some of these nuances.

I think that beginsA291 is in a situation where he cannot play a game because he cannot tell which stones are dead or not. In that case, switching to AGA rules would allow him to play and get experience. (As would playing the Capture Game. )

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

It sounds like, with beginsA291 frustration with the forum, that he may not be back.
It may also be possible that with his poor introduction to the rules and confusion with the complicated explanations, that he may not come back to the game either.

Both would be very sad.


I like to explain territory-based rules and scoring as merely an agreed upon shortcut to its "cousin", area-based rules/scoring. While its not technically an accurate description, I think it serves the purpose quite nicely for beginners. Because effectively, the result of the game should not change, regardless of which ruleset you use (also, not technically accurate, but close enough for beginners)

Bill is right. You should switch to using area-base rules until you gain more experience. I think it'll make things easier to understand. And then you don't have to worry about changing the score with more or less prisoners (because prisoners don't count), or filling in your own territory, because you can continue playing, removing all the "dead" stones without changing the final score/result.

Its really a great game. Don't give up on it (or us), yet.

edit: we all actually love answering/discussing these types of beginner questions.

Except that most players forget that in the beginners forum, you have to explain in a beginner-frindly way. Was it nessesary to mention at least 5 different rulesets (most of which are theoretical and have never been used for actual play)? Plus, I assume that the position was supposed to be just one dead stone somewhere in the opponent's territory, not asking about this specific position leading to a seki with the possibility of a ko fight.

beginsA291, please don't give up. People who have been playing for a long time tend to forget how confusing every game (including go) is untill you get the hang of it.

If I am allowed to slightly modify the position to simplify:

Click Here To Show Diagram Code

[go]$$Bm11
$$ ----------
$$ | . . O X . . |
$$ | . . O X O . |
$$ | . . O X . . |
$$ | . . O X . . |
$$ | . . O X . . |
$$ | . . O X . . |
$$ | . . O X . . |
$$ -----------[/go]

The rule is that "stones that cannot avoid being captured" are removed after two consecutive passes and become prisoners (just as if they were captured during the game). If white claims that his/her lonely stone can avoid capture, and black claims it cannot, the situation is played out on a another board. While there are many possible sequences for white to try, the result will always be the same: black will capture all white stones in his territory.

Click Here To Show Diagram Code

[go]$$Wm1
$$ ----------
$$ | . . O X 6 . |
$$ | . . O X O 8 |
$$ | . . O X 1 3 |
$$ | . . O X 2 4 |
$$ | . . O X 5 . |
$$ | . . O X 7 . |
$$ | . . O X 9 . |
$$ -----------[/go]

Click Here To Show Diagram Code

[go]$$Bm10
$$ ----------
$$ | . . O X X . |
$$ | . . O X . X |
$$ | . . O X . . |
$$ | . . O X X X |
$$ | . . O X O 1 |
$$ | . . O X O 2 |
$$ | . . O X O 3 |
$$ -----------[/go]

One of many possible sequences, they all lead to white being captured.

So now it is clear white's lonely stone cannot avoid capture. Players return to the original board and remove the stone (having proven it cannot avoid capture), and add it to any other prisoners captured during the game. Now the prisoners and territory of both players are counted to find out the result of the game.

_________________
“Discussion is an exchange of knowledge; argument an exchange of ignorance.” ― Robert Quillen

I feel your pain. I recommend Lazarus: Form Recovery, a browser add-on, and it will never happen again.

_________________
Patience, grasshopper.