Size And Safety Of Territory/ Discussion

I felt this discussion really ought to be factored out from the main page. Perhaps a differently-titled subpage would be more appropriate. Karl Knechtel

One or two eyes?  

Ex1: Black is playing to kill, and White to live.

The original description for this diagram went as follows:

Here both sides have to worry, it's only worth 2 points for White, but letting it die would give 7 points to Black.

Andrew Grant: 12 points, not 7. Each dead white stone is worth 2 points. Thus the value of the move at a is 12+2 = 14 points in gote.

Iago: Um, not sure I got that ... the value of a dead stone is 2 points because it counts as a prisoner and as a free space ? 14 points in gote means that the one playing here gains[1] 14 points, but lose sente?

Andrew Grant: That's correct. You count not just the prisoner but also the point of territory underneath when the prisoner is removed. So each dead stone counts for 2 points. If black plays at a and kills white, there are five dead stones sitting inside a seven point territory, which equals 12 points. Add the two points white would have if she played first to get the full value, 14 points.

And yes, 14 points in gote means just what you say - you gain 14 points compared with letting your opponent play there, but you lose sente.

Karl Knechtel: The deiri value is 14 points, yes. The miai value is 7 points, since two plays separate the two results.

Iago: Uhm... not sure I got that either: I mean if White plays first he lives with 1 move, but killing requires 3 moves if Black plays first... wouldn't that be a swing of 4? And I don't understand how you make those counts with multiple choices...

Karl Knechtel: Capturing takes 3 moves; Black doesn't have to capture in order to claim the stones as dead.

As for "multiple choices", only the play at a needs to be considered here; other options are dominated.

Perhaps Bill or Charles can explain this better, being so practiced at it? :)

Charles Let me try to clarify one thing at a time. The diagram shows seven black stones and five white stones. This can be our baseline for looking at the local tally: it stands currently at BB. If Black adds one to kill, at a, this goes to BBB. If White adds one to live, it goes to B. So that's a difference of two plays, as one expects for a normal gote move.

How to deal with several choices? I'd say that conceptually one has to start with a clear vision of tree-representation of the game (or local part of the game). Naturally this is much deeper than a tally concept.

[1] Bill: We have to be careful about that word, gains.

White lives  

White dies  

The difference between these two results is 14 points. We might say that whoever plays first gains 14 points by comparison with the other player playing first.

But when we say, "White gains 14 points," without modification, we think that White started with X points and ended up with X + 14 points.

Original position  

This is what White started with. The value of White's corner is halfway between the other two positions (5 points for Black, to be exact), and whoever plays there gains 7 points. (5 + 7 = 12, and 5 - 7 = -2, or 2 points for White).

Size And Safety Of Territory/ Discussion last edited by KarlKnechtel on October 27, 2004 - 19:03
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