CGT values in semeai
The idea of a move to capture, or approach move, appears to be similar to that of atomic weight in CGT. However, there is no direct translation between the two. Research is being done in this area by Martin Mueller, Teigo Nakamura, and myself (Bill Spight).
Black is one move ahead in this race to capture. This fact is captured in the game tree (below). However:
Black has captured 2 White stones.
In CGT terms this position is equivalent to the original one. Each player has made one play, which were miai. (White had sente, but it was a 0 point sente.) Both positions are worth 4* in CGT terms, or 4 points for Black with a dame.
Game tree: A / \ 4 C / \ / \ B D / \ / \ 4 4 -4 -4
So to capture our intuitions about moves to capture, we cannot use the real game. We have to construct a similar game which reflects our intuitions. There does not seem to be any single way to do so.
One solution is to stop play when one of the groups is captured, and ignore any subsequent dame or smaller plays. That gives us this tree:
Game tree 1: A / \ 4 C / \ / \ 4 -4
Now we have a White sente, or tiny (ignoring the number, as usual).
In CGT the important fact is winning the game, which getting the last play will do. So we can transform this tree further by making all the final scores 0.
Game tree 2: A / \ 0 C / \ / \ 0 0
This gives us ^ (UP), which has an atomic weight of 1, which is just what we want. :-)
Things are not always so simple, OC. There are times when we will care about other outcomes, such as connecting, living, and making seki, or about the smaller plays that are left, or about losing some stones but not all of them. But this is OK for starters. (I am writing a paper about these things.)
More later. :-)
-- Bill Spight