Citation reference:

https://www.lifein19x19.com/viewtopic.p ... 75#p273675John Fairbairn wrote:

Apparently there is a "well-known fact" that I did not know, to the effect that "in a half-point game the side that fills in the last dame loses." I assume that dame here is being used somewhat loosely (as is common) for the last necessary move.

It was mentioned in 1997 on rec.games.go that a Japanese journalist observed a relation between last move, 1/2 point game and winner. Then, I devised a first proof for the special case of 5.5 komi and some further simplifying assumptions. Later, I generalised a bit. However, the so far most general version appears in my book Endgame 5 - Mathematics.

"

**Definition 40** [standard area komi]

Standard area komi has the form K := 2z - 0.5 for some whole number z.

[...]

Presuppositions

Assume no handicap stones and single passes. Apply the territory score together with the conditions 'unequivocal', 'without two-sided dame and teire', 'without capturable stones in sekis', 'without asymmetric sekis'. Have no suicide, standard area komi, an odd parity of the number of intersections on the board, a final position with an even seki parity and the territory score 0.5.

**Theorem 144** [last play indicates winner]

The winner under territory and area scoring is the player of the last play."

Note that 6.5 komi is non-standard area komi. See pp. 215 - 226 of Endgame 5 - Mathematics for explanations for the presuppositions and the mathematical proof of the theorem. The proof of theorem 144 is a one-liner but the proofs of some of its referenced, applied theorems each cover several pages. For informal descriptions, see the book Endgame 2 - Values, chapter 6.1.