Previous posts:
- Berlekamp Figure 1.3 B is sometimes better but A is never better
- Go Corridor Counting as per Rational Endgame
- Estimating move values with averages 1
- Sente as per Rational Endgame
- Some small games with and without chilling Berlekamp
- Berlekamp Figure 2.5 calculations
- Berlekamp Figure 2.7 calculations
- Left and Right Stops, Incentives and cooling
- Area scoring vs territory scoring 1
- Area scoring 2 and the number translation theorem
- Mean and temperature
- Mean temperature and chilling 2, with Martins example games
Another thing I wanted to come back to, related to mean and temperature, chilling and thermographs was the idea of left and right stops of a game.
I was starting to read Endgame Mathematics by Robert Jasiek, and he mentions the notion of a score of a position of white or black plays first.
That is B(P) is the score of the position if Black plays first and the players alternate with black maximising and White minimising the score.
W(P) is the same but with White moving first.
Then it finally clicked with me when rereading Siegel which he references that this is also what the left and right stops of a game are. He actually says it explicitly under definition 3.16.
That is if you have a game G, L(G) is the score (number) you end up with if the players play alternately with left moving first until the game hits a number.
Similarly R(G) is with right moving first.
So it’s maybe some kind of minimax play on the game tree. I was looking at some examples with fairly randomly constructed game trees.
I want to explore then what means for Go positions and how that bounds the actual values of the positions.
Ideally I want to understand clearly and somewhat partially maybe the connection between how Go players and books count/estimate and the numbers (stops, mean, temperature) from CGT.
Ideally if I can put it in a short summary, even if it’s only partially complete, I’ll be somewhat happy 