Amazing discovery confirms the end is not nigh

[Elom0]

Advantage of first move = half the value of a move
Margin of error = half the advantage of first move

What a coincidence, I've been using that standard recently in my game reviews, I guess if it has pro approval it must be right!

0.75 any loss more than this is a style difference
1.5 any loss ore than this is an inaccuracy
3 is half the value of sente, anything more than this is a mistake
6 is the inherent value of sente, losing more than this is a big mistake
12 equals a pass in the opening, one handicap stone after the first, anything more than this is a blunder.

[RobertJasiek]

Advantage of first move = half the value of a move
Margin of error = half the advantage of first move

What a coincidence, I've been using that standard recently in my game reviews, I guess if it has pro approval it must be right!

Pro approval is just one opinion. Rather, the first statement is right as approximation due to my theorem 50, which Bill Spight motivated, I formulated and proved for the temperature T:

"For the net profit P of starting, then alternating, in an ideal environment [with N value drops], N >> 0 => P ~= T/2." [26]

As to the second statement, a margin of error can be chosen so a particular one is not right or wrong but rather a matter of preference. Bill has suggested a reason why to use this particular margin of error, which I have formulated as follows:

"[...] the minimum value of having the turn is 0 and the maximum value of having the turn is T. Then 0 is the estimated minimum error of having the turn and T/2 is the estimated maximum error of having the turn. Now, we can also estimate the average error as T/4. The maximum error of this estimation is T/4. [...]" [27]

However, apart from playing around with more numbers, I am not convinced that using any margin of error at all provides more practical information than not using any and instead only using the primary value, that is, the value (which is a net profit) of starting in an environment.

6 is the inherent value of sente, losing more than this is a big mistake
12 equals a pass in the opening, one handicap stone after the first, anything more than this is a blunder.

7 and 14.


References: https://www.lifein19x19.com/forum/viewt ... 45#p143245

[Gérard TAILLE]

For me the explanations given by John are quite clear and make sense.
What can happen in practice? You have two local positions P1 and P2 and an environment E so that the board looks like: P1 U P2 U E
When you calculate the miai value mP1 of position P1 you assume the environment of P1 is an ideal environment but here the environment is P2 U E which could be a quite complex environment. That means that the miai value mP1 is only an information you can take into account and a lot of other informations have also to be taken into account to play the best move. I think it is exactly what John explained.

[RobertJasiek]

P1 and P2, if significantly larger than the temperature T(E), are the ensemble, which can be solved together with the consideration per variation of its player then starting in the environment E and gaining T(E)/2. Ignore if necessarily always the same player starts in E.

[Gérard TAILLE]

P1 and P2, if significantly larger than the temperature T(E), are the ensemble, which can be solved together with the consideration per variation of its player then starting in the environment E and gaining T(E)/2. Ignore if necessarily always the same player starts in E.

Oops I do not consider mP1 and mP2 are significantly larger than temperature T(E). On contrary I assume T(E) significantly larger than mP1 and mP2 and I am waiting temperature drops in order to play in P1 or P2.

I do not really understand why you consider P1 U P2 being the ensemble. The basic advantage of theory is precisely to handle separatly independant local positions like P1 and P2: instead of considering a difficult P1 U P2 local position, in my view, the idea of the theory is to handled separately local position P1 and local position P2.

I agree with John presentation. I am happy to calculate mP1 and mP2 (or at least an approximation) because I consider they are a (very) useful information but they are not all the picture. if mP1 and mP2 are not so different and taking into account that a real environment is never ideal then a strong player (a pro?) must consider more reading before choosing between a move in P1, in P2 or in the environment.

[RobertJasiek]

could be a quite complex environment [...] I assume T(E) significantly larger than mP1 and mP2 and I am waiting temperature drops in order to play in P1 or P2.

Yes, then, if you want an exact solution, it can be complex. However, why not simply ignore the details of P1 and P2 and only consider T(E U P1 U P2)/2 = T(E)/2? (Or, during the late endgame, the alternating sum Δ(E U P1 U P2).)

[Gérard TAILLE]

could be a quite complex environment [...] I assume T(E) significantly larger than mP1 and mP2 and I am waiting temperature drops in order to play in P1 or P2.

Yes, then, if you want an exact solution, it can be complex. However, why not simply ignore the details of P1 and P2 and only consider T(E U P1 U P2)/2 = T(E)/2? (Or, during the late endgame, the alternating sum Δ(E U P1 U P2).)

If with "an exact solution" you mean playing the god move my answer is "no". I am not strong enough and I am too lazy to look for the god move in the endgame.
The best I can do is the following: I consider all board as made of local positions P1, P2, P3, P4 ....(without any environment). if my intuition tells me that I should play in P1 or P2 (I mean I hesitate between these two areas) then I calculate an estimation of mP1 and mP2 and I choose to play where the miai value is the largest.
I know perfectly it may not be the god play but I am happy with this (thanks for the theory!)
As you see I use the environment notion only indirectly by calculating mP1 and mP2, but not explicitly for example by saying that playing first in the environment will give me an advantage of T(E)/2.
Putting aside the miai value calculation itself, do you use the environment in some way?

[RobertJasiek]

Putting aside the miai value calculation itself, do you use the environment in some way?

I am not sure exactly what you are asking. My (and sometimes others') mathematical theory involving the [global] temperature sometimes only uses it but most of the time uses it and other values, which include the second largest value of the environment, move values, counts or the gote-sente-difference.

[Gérard TAILLE]

Putting aside the miai value calculation itself, do you use the environment in some way?

I am not sure exactly what you are asking. My (and sometimes others') mathematical theory involving the [global] temperature sometimes only uses it but most of the time uses it and other values, which include the second largest value of the environment, move values, counts or the gote-sente-difference.

I have a theoritical question Robert.
Assume a board P1 U P2 U E with E being an ideal environment. Assume mP1 > mP2 (move value of P1 > move value of P2)
Is it proved that a god play is to wait till T(E) = mP1 in order to play in local position P1?
If not, is it proved that it is correct on condition that no ko can occur in P1 and P2?

[RobertJasiek]

Assume a board P1 U P2 U E with E being an ideal environment. Assume mP1 > mP2 (move value of P1 > move value of P2)
Is it proved that a god play is to wait till T(E) = mP1 in order to play in local position P1?
If not, is it proved that it is correct on condition that no ko can occur in P1 and P2?

See https://www.lifein19x19.com/viewtopic.p ... 72#p278372

[ArsenLapin]

The ISBN is 4-416-70461-5. I have no idea whether it is still available (I've had my copy, unread, for some 20 years), but quite apart from recommending a good book, my aim has been to offer encouragement to those like me who have been left confused by the FEOAF treatment of counting boundary plays.

Apparently it is still available:

https://www.biblio.com/book/eye-number- ... 1468681326
目数小事典―出入計算・見合計算 / 誠文堂新光社
Eye number of small encyclopedia - and out calculation and commensurate calculation (Japanese Edition)

Or perhaps more accurately
"Small encyclopedia for counting points: deiri and miai calculations"