If I understand correctly your example is equivalent to the following problem: You prove by a difference game that a black move at "a" dominates a black move at "b".Bill Spight wrote:Even if she does not play the infinitesimals correctly.Gérard TAILLE wrote:It is little worrying Bill. That means that I probably miss something.Bill Spight wrote:you can win many chilled games without playing the infinitesimals correctly.
Take my definition of what is a win in a chilling game. When you compare two sequences then
1)if the score of the two sequences is different the best sequence for a player is the one which gives her the best score
Well, since infinitesimals occur frequently, even if they don't alway matter, I think that it is important to learn correct play that applies in general, if it exists. You learn that through difference games.Gérard TAILLE wrote:2)if the score of the two sequences is equal then the best sequence for a player is the one which gives her tedomari
In my view the first case is there to avoid incorrect play and the second case is there to play correctly the infinitesimals.
IOW I hoped that this definition allows me to detect if infinetisamls are playing correctly.
Now you say that it may not be the case (?). What is your criterias to know if infinitesimals are played correctly or not?
For instance, is it best for Black to play in ↓ or in {1|0||0}? Let's play the difference game. We set up the 0 game where we subtract these two from each other. Then let Black play in {1|0||0} to {1|0} and White play in {0||0|0} to {0|0}, leaving
{1|0} + {0||0|-1} + {0|0||0} + {0|0}
Black to play can win by playing to 1 in {1|0}, leaving 1 plus some infinitesimals.
If White plays in {1|0} to 0, then Black can win by playing to {0|0} in {0|0||0}, leaving {0||0|-1}, which is positive.
If White plays in {0||0|-1} to {0|-1}, then Black can win by playing to {0|0} in {0|0||0}, for a sum equal to 0.
If White plays in either of the other two games Black can win by playing to 1 in {1|0}.
So for Black to play in {1|0||0} instead of ↓ is always correct, even though ↓ has atomic weight -1.
What about the other way around? Is it better for Black to play in {0||0|-1} or in ↑? For the difference game we set up the same 0 game, but this time let Black play in {0||0|-1} and White play in {0|0||0}, leaving
{0||0|0} + {1|0||0}
Obviously, Black can win by playing to {1|0} in {1|0||0}.
White's best chance is to play to {0|0} in {0||0|0}, but then Black can win by playing to {1|0} in {1|0||0}.
So it is always correct for Black to play in {0||0|-1} instead of ↑.
OC, the ko caveat applies.
OC your example is relevant because with the chilled game I cannot distinguish between the sequence beginning by "a" and the sequence beginning by "b".
But there are no contradiction. If the chilled games cannot distinguish between the two sequences you can always try a difference game OC.
Now let me add a * to the game Now you can see clearly that the chilled game beginning by black "a" is better than the chilled game beginning by black "b" and you will be able to play correctly at "a".
Two points here:
1) A chilled game is easier to visualize in practice than a difference game (at least for me). If the chilled game is able to distinguish between two sequences then it's fine and I am happy to avoid playing a difference game
2) If the chilled game is not able to distinguish between two sequences you have two solutions:
2.1) you play at random one or the other sequence. You know that you may not play the infinitesimals in the best way but you know that for this specific game it does not harm
2.2) you try a difference game to be sure to play the infinitesimal in the best possible way. From a theoritical point of view it is far better but in practice it is not quite easy.
