# subset of miai counting? [#2627]

emeraldemon: subset of miai counting? (2011-09-05 19:34) [#8746]

In miai counting (as described in Mathematical Go, for example), this position is 1 point for black:

1 point for black

From the definition of 1-territory, I gather this would also be counted as 1 point using that system. In either system it is 1/2 of 2 points. But miai counting also handles positions like this:

1+1/4 points for black

By miai counting, this territory is worth 1+1/4 points, whereas if I understand 1-territory it would be worth 1 point, correct? From this I'm interpreting 1-territory (and I guess it's descendants 2-territory etc.) as a kind of simplification or estimation of miai counting. Is that correct?

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RobertJasiek: Re: subset of miai counting? (2011-09-05 19:50) [#8747]

n-territory is not a subset of miai counting but relies on current territory. I will look later whether your examples coincide with miai values accidentally. No time now.

RobertJasiek: Re: subset of miai counting? (2011-09-06 01:44) [#8748]

Current territory and n-territory are designed for the middle game. For the endgame, accurate values cannot be guaranteed. Nevertheless, it is fun to study your positions just for the sake of doing it:

This could become Black's territory. Therefore a reduction sequence by White is tried. However, a sente reduction sequence does not exist here! Therefore no reduction sequence is actually played here. After the attempt of making a reduction sequence, Black has still not surrounded any intersections. Therefore his current territory is 0.

gaining 1-territory

A White reduction sequence is then not needed. The inside intersection is Black's 1-territory. 50% * 2 points = 1 point.

position

Here a sente reduction sequence starting by White is possible:

sente reduction

afterwards

Now Black's current territory, which is also called 0-territory, is apparent: 1 point.

Black makes 1 play

For the sake of achieving 1-territory, Black makes 1 play. Afterwards (White cannot make a sente reduction sequence, so execution of none is imagined) the resulting position is studied:

studied position

n-territory

a is Black's 0-territory; it is 1 intersection worth 1 point. b is Black's 1-territory; it is 1 intersection worth 50% * 1 point = 1/2 point. The total value of Black's n-territory is 1 + 1/2 = 1.5 points.