So in the chilled game it’s that black gets the last move. In the unchilled game black gets the number of points indicated in the marking, which is either 3 or 2 points.
I assume there are no kos, and for simplicity,
I default assuming it is Positive’s turn.
Under these assumptions, if the board has
Count at Sensei's Library
count C and temperature T, then:
Positive can guarantee that the final score will be at least C, and Negative
can guarantee that the final score will be at most C+T. In particular:
There is always at least one integer in the closed interval [C,C+T].
If T < 1 and C is an integer, then the board is settled with final score C.
If T <= 1 and C is not an integer, then under correct play the final score
will be the rounding of C in the direction that favors whoever’s turn it is.
If T = 1 and C is an integer, then the final score will be C or C+1,
depending on who get the last play at temperature at least 1.
In the absence of sente - this explanation handles ambiguous moves
Ambiguous Move at Sensei's Library just fine - the reasoning is simple:
The players start each making 1-point plays, so the count keeps shifting
C → C+1 → C → C+1 → C → C+1 → …
, until someone can’t make a 1-point play.
If it’s Positive who can’t make a 1-point play, then Positive’s pass or smaller play results
in a count strictly less than C+1 with Negative to move, for a final score of at most C.
If it’s Negative who can’t make a 1-point play, then Negative’s pass or smaller play results
in a count strictly greater than C with Positive to move, for a final score of at least C+1.
I’m surprised it’s not C-T, like in a position where you have C being the average of two options, the the temperature bringing the counts to either C+T or C-T.
E.g. {2| 0}, with count (is that the count?) 1, going to either 0 or 2, and temperature T=1.
Or I guess it’s something to do with “positive” going first is it? So even if you added more options down the line, it’s some bound by C. Whichever positive means.
correct
Looks like Board n stones/ Brett und stein are going to publish a translation of O Meien’s book on endgame “Absolute counting”
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Do you know if he actually uses full-blown CGT or just miai counting (as I gather from Sensei’s)?
I think it’s just miai counting, but becuase I want to be able to do both to some extent, like the discussions in this thread, to be able to tie the two together, I thought it might be relevant 
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