Endgame Question 2
Jono: I'm trying to work out this endgame thing, however to complicate matters I play with NewZealandRules. I'd like to run through the same example as in EndgameQuestion but under the influence of area scoring.
Consider the following diagram in which all outside stones are considered alive.
Assuming a is sente for Black, then its value is the difference between a white play at a and black play at a followed by white at b. If black a then he makes 2 points, if white a then she makes 2 points. Thus a is worth 4 points in sente for black.
Things get trickier for the play at c, which we are assuming is gote.
We take the average of the scores when black also gets d, and when white gets d. For black this is the average of 2 points for c only and 5 points for c and d, giving 3.5 points. For white this is the average of 4 when white gets d and 0 when she does not, giving 2 points. Thus c is 5.5 points in gote, or 2.75 by miai counting.
I'm not too sure about factoring in the additional dame point that is created when black plays both c and d - this is worth one point to the player who will now play last.
It seems strange that the gote move produced the same result as territory scoring, but the sente move is valued one higher under under area scoring. Where have I gone wrong?
Bill: Let's take the gote. If White plays at c the local score in the disputed area is -6 (6 points for White). If Black plays at c and White plays at d, the net local score is -2. If Black plays at both c and d, the local count is 5. Depending on who gets the dame, the final net score will be 4 or 6.
Taking the average of 5 and -2, the local count after Black's play at c is 1.5, and the miai value of the play at d is 3.5.
Taking the average of 1.5 and -6, the original local count is -2.25, and the miai value of the play at c is 3.75.
Jono: All clear, sir! Calculate the local score. Traverse the possibilities to get the new local score. Find the difference. Simple as pie. =)