Gérard TAILLE wrote:I do not know in detail the definition of the various ideal environment you mentionned but I think my reasonning works with any of these environments?
My "ideal environment consists of simple gotes without follow-ups, with move values T ≥ T_1 ≥ T_2 ≥... ≥ T_N-1 > 0 and move values dropping constantly by D > 0 at N > 0 drops, with the smallest move value T_N-1 = D". [Definition 24] [22]
On many occasion I use this score1 = score2 to calculate a miai value and you never argue on this point. What is wrong here?
I do not know yet if it is right or wrong here. I do not always study your texts closely enough to be sure whether your earlier instances of such score equations have always been right. I am cautious and do not make the assumption that because something worked in a different study instance it needs to work again for a particular new study instance. Until there is a general theorem, if possible, one must verify validity each time afresh. Here I am looking a bit more carefully so you won't get away with "I have done it before":)
When temperature of the environment is greater than vb then it is correct for black to play in the environement (it may happen that a local black move could also be correct but playing in the environment is always correct).
When temperature of the environment is lesser than vb then the only correct move for black is to play locally (playing in the environment is not correct)
When temperature of the environment is equal to vb the situation is ambiguous and it is correct to play either in the environment or locally.
Note : the situation for white is exactly the same.
Let me see.. You are making very strong claims here... B can be a simple gote without follow-up, simple gote with simple follow-up, simple sente or some Black's long type. For long types, I have not studied it in environments yet so your claim is premature (you also have not studied it in environments in general yet). For now, let me restrict it to simple types (from B, at most two plays starting with Black). So what have been my results?
Case B is a simple gote without follow-up:
"Presuppositions
Suppose the starting player's value perspective, simple gotes without follow-ups and with the move values T_1 ≥ T_2 ≥ ... ≥ T_N ≥ 0.
Theorem 11 [decreasing order]
Playing in order of decreasing-or-constant move values is correct." [22]
So what you say is correct for B being a simple gote without follow-up.
Case B is a simple local endgame with (Black's) follow-up:
"Theorem 62 [creator's perspective and start, late endgame, low temperature]
If T ≤ F, the creator starts
- in the environment or locally if M_SENTE ≤ 2∆T_1 or
- locally if M_SENTE > 2∆T_1.
Theorem 63
[preventer's perspective and start, late endgame, low temperature]
If T ≤ F, the preventer starts
- in the environment if M_SENTE ≤ 2∆T or
- locally if M_SENTE ≥ 2∆T.
Theorem 68 [creator's perspective and start, late endgame, high temperature]
If T > F, the creator starts
- in the environment if 2T - M_SENTE - F ≥ Ω,
- locally if 2T - M_SENTE - F ≤ Ω.
Theorem 69
[preventer's perspective and start, late endgame, high temperature]
If T > F, the preventer starts
- in the environment if M_SENTE + F - 2T ≤ Ω,
- locally if M_SENTE + F - 2T ≥ Ω.
Theorem 84 [early endgame, low temperature, creator]
If T ≤ F and T_1, T_2,... form an ideal environment, as a good approximation, the creator starts
- in the environment or locally if M_SENTE ≤ T_1,
- locally if M_SENTE > T_1.
Theorem 85 [early endgame, low temperature, preventer]
If T ≤ F and T, T_1,... form an ideal environment, as a good approximation, the preventer starts
- in the environment if M_SENTE ≤ T,
- locally if M_SENTE ≥ T.
Theorem 89
[early endgame, starting player's perspective, high temperature, conclusion]
If F < T, it is a good approximation that the starting player starts
- in the environment if M_GOTE ≤ T,
- locally if M_GOTE ≥ T.
Theorem 90
[early endgame, starting player's perspective, high temperature, sente]
If F < T and we have a local sente, it is a good approximation that the starting player starts in the environment."
Needless to say, I have given examples for all the cases of the theorems. [22] [23]
Hence, in the case of B being a simple local endgame with (Black's) follow-up, your statements are only (approximately) correct during the early endgame at high temperature if B is a (here: Black's) simple sente. For all other cases of Black or White starting and low or high temperature relative to Black's follow-up move value F, you are wrong because both cases of correct play locally or in the environment can occur!
Hence, your later conclusions might be wrong, too.
References:
https://www.lifein19x19.com/viewtopic.p ... 45#p143245