The position is mentioned at
https://senseis.xmp.net/?MiaiValuesList%2F000To099#toc5
where only the initial move value and count are stated. Bill gives another hint. However, we do not determine values by guessing.
Instead, we must calculate systematically and, if necessary, verify that the calculated values are correct. There are different methods of doing so:
- combinatorial game theory a la Mathematical Go Endgames using infinitesimals and cooling tax
- graphical thermography a la Spight et al
- thermography as linear algebra a la Spight
- iterative calculation of counts, gains and move values (modern endgame theory described by various people including Spight and Jasiek) combined with verification by the method of making a hypothesis a la Jasiek
- sometimes applicable, possibly much faster, sophisticated methods
When long sequences are involved, I find the method of making a hypothesis the easiest, although an explicit verification is needed. Since the position is a standard shape, I have already solved it much earlier in the attachment.
Needless to say, calculation of values is iterative and backwards: we determine the values of follow-up positions before the values of the initial position.
Initially, we do not know whether the values of the initial position are derived from the follow-up position created by move 1, move 2 or move 3 of Black's alternating sequence. Longer sequences override shorter ones so we first verify that it is correct to calculate the initial values from Black's long alternating sequence. We find that these tentative values are confirmed because they are consistent with the (tentative) gains of the moves of Black's alternating 3-move sequence and White's 1-move sequence: the move value is at most each gain of the moves of both alternating sequences starting from the initial position.
The values of "Black's long gote" endgame position are: count C = 1/2, move value M = 1/2, gain of Black 1 = Gb1 = 3/4, gain of White 1 = Gw1 = 1/2.
EDIT: stating the values.
