Eureka! I just came up with a totally sane explanation why the value of a reverse sente move is traditionally doubled. We are going to decipher the following example in which Black reverses 3 points, which is valued at 6 points gote:
In order to get to the bottom of this mystery, we will move our thinking up by one level, from the value of move layer to the positional judgement layer on which everything is halved.
E.g., the move at A is worth gote 2 points, but when counting the score in the middle of a game, you count 1 point for Black there on the triangle. (It is 50/50 whether Black or White gets to play A, so by assuming 50%, you get half the value. It is very important that you do not confuse both layers of thinking!)
This process is the step I’ve been missing all these years 🙂 Next, we take the good old 6-point second line hanetsugi to further this logic:
In this case, we can average the positional judgement situation visually (left):
When Black gets to play the endgame (right), we will reformulate the following statement to the positional one, both of which are correct:
- Black plays a 6-point gote endgame.
- Black spends a move to shift the positional judgement by 3 points to his favour.
Going back to the original example (scroll up), this is exactly what happens when Black plays the reverse sente 3-point move in the right diagramme. In positional judgement, sente sequences, i.e. White’s sente hanetsugi in the left diagramme, are assumed as having been played out. So when Black plays the reverse-sente move, Black “spends one move in order to shift the positional judgement to his favour by 3 points”, the same as in the statements above. That makes the 6-point value a mathematically accurate number and not an approximation (as I’ve thought before).
(Bonus: If Black makes an endgame mistake and plays a 6-point gote move instead of an 8-point gote move, and White plays the 8-point gote move instead, Black loses 1 (!) point.)