OK let me try to understand the meaning of this example.
Is it a good understanding to say that a move at "a" ot "b" is a local move while a move at "c" is considered to be in the environment?
If it is true does that mean that you consider black "a" as a sente option and black "b" as gote option?

Because FD is sente I prefer drawing the tree as follows:


Your calculation looks good for me.
Now what is the answer to my initial question (what is the best intitial white move : a or b?
Secondary question. How can you give the answer to this initial question with the minimum calculation?
Hint : I just want to know the best move. IOW I do not ask for the miai value of the initial position.

Sry, LOL!

Click Here To Show Diagram Code

[go]$$B Black to move
$$ -----------------------------------
$$ | X X X X X . X X X O O X X X X X |
$$ | X X X X X . X . g . O X O O O X |
$$ | X X X X X X X X O O O X O O O X |
$$ | X X X X X X X X O X X X O O O X |
$$ | X X X X X X X O O X X X O O O X |
$$ | . O O O O O O O X X X O O O O X |
$$ | . O X X X X X X X X X O O O O X |
$$ | X s X . . . . . X . X t X X X X |
$$ | O X X X X X X X X u O O O O O O |
$$ | O O O O O O O O O O O . . . . . |
$$ -----------------------------------[/go]

The environment comprises T and U (I cannot put captital letters or T1 on this board).

If the preventer Black does not play local reverse sente but starts in the environment, then the creator White chooses the gote option G or the sente option S. As you should have understood by tactical reading. Now find all 42s!

But, but... this depends on the whole board!



What is truth, eh, calculation? Are counting a score or comparing scores of settled whole board positions "calculations", in your opinion? If not, use reading and counting with zero calculations. If yes, draw the right lottery ticket with zero calculations;)

OK then let's assume black plays in the environment.
Now it is white to play in the followibg position:

Click Here To Show Diagram Code

[go]$$B Black to move
$$ -----------------------------------
$$ | X X X X X . X X X O O X X X X X |
$$ | X X X X X . X . g . O X . . . X |
$$ | X X X X X X X X O O O X . . . X |
$$ | X X X X X X X X O X X X . . . X |
$$ | X X X X X X X O O X X X . . . X |
$$ | . O O O O O O O X X X . . . . X |
$$ | . O X X X X X X X X X . . . . X |
$$ | X s X . . . . . X . X X X X X X |
$$ | O X X X X X X X X u O O O O O O |
$$ | O O O O O O O O O O O . . . . . |
$$ -----------------------------------[/go]

Considering only the local position :
if black plays first at "s" we reach a position R with a count B+41
if white plays first at "g" then white is gote and we reach a position G with a count B+1
if white plays first at "s" then white gets sente and we reach a position S with a count B+2

Now, if your theorem can be applied to this position, that means that F < T.
Robert, what is the value of F and T in this example, in order to apply your theorem?

This is a late endgame position. For a local endgame with gote and sente options in an environment during the late endgame, the theory for move values applies only if the local sequences consist of single moves (the sente sequence of one plus one moves). This works for game trees but I do not know any such position on the board. For the early endgame, the theory for move values can be applied because it is an approximative model anyway.

For the late or early endgame, reading and counting can be applied. Theorems tend to differ.

For this example, please try to calculate final global counts to better appreciate it!

Yes I agree, but we were looking for a position for which your theorem can be applied. If you cannot apply here your theorem (because F < T is not fullfilled) then this position is not an appropriate example.
My question remains. Does it exist a position for which your theorem can be applied? If not can you at least give us an example of tree for which your theorem can be applied?

This example was for warming up. Every local endgame with sente and gote options in an early endgame position not too far from an ideal environment at high temperature can be used for application of the theorem. For low temperature, other theorems apply. The warm up example is too hot for a suitable whole board position.

Oops, assuming simply T = MGOTE, I am asking for only one example for which:
1) one player has a gote and a sente option
2) F < T
That way I would know that this theorem makes sense.

Only showing T but not the remaining part of the environment, my example in [22], [23] has a remaining basic endgame ko so only |T - MGOTE| = 1/6:

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------
$$ | O . X X . . . . X . X X .
$$ | O O . O X . O . O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

Hint: T - F = 1/2 > 0, that is, the temperature is high, as we desire. You can easily modify this example from 2021 to emphasise a start either locally or in the environment. I do not recall exactly how long I needed to construct this example but I had invented this example shape class a few years earlier so I think it took me at most one hour to tweak the values of T and MGOTE close enough maintaining a high temperature. Therefore, you should have been able to find such an example yourself. For gote and sente options, I worked mostly with this shape class so, unlike for quite a few of other theorems, I do not already have exact equality, here T = MGOTE. If we should be lucky, shrinking the "42" example would do the trick - otherwise put it on a huge board with a suitable T to allow for an almost ideal environment with drop 1/2 or 1.

(Continuing my previous post.)

Besides calculating the move values and gote-sente-difference and applying the theorem, it is interesting to compare a start locally versus in the environment by counts and initiative:

Click Here To Show Diagram Code

[go]$$B count -23, Black continues in the environment
$$ ---------------------------
$$ | O . X X . . 2 3 X . X X .
$$ | O O . O X . O 1 O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X 4 O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B count -23 1/3, Black continues in the environment
$$ ---------------------------
$$ | O . X X . . . 2 X . X X .
$$ | O O . O X . O . O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X 1 O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

The counts are close and the same player, Black, continues in the remaining environment.


Minor EDITs.

white plays first : white "c" : count = ((-34.33) + (-23.33)) / 2 = -57.66/2 = -28.83
black plays first :
1)black "a", gote option : count = (-12 + -23)/2 = -17.5
2)black "b", sente option : count = -23.33
MGOTE = ((-17.5) - (-28.83)) / 2 = 11.33/2 = 5.66
MSENTE = (-23.33) - (-28.83) = 5.5

MGOTE > MSENTE => in this position your theorem does not apply; you know that the sente option is not a good option without looking at T or F.

If you cannot find a position in which your theorem can be applied can you simply give us a tree showing the idea behind your (strange?) theorem?

White starts in reverse sente: the local count is R := -23 1/3.

White starts locally and Black replies in the environment taking T: the count of the settled regions is -23 1/3.

White starts with two successive moves, one local, one in the environment taking T: the count of the settled regions is -34 1/3.

You treat the position after White's local start as one in which to calculate the gote count of the largest region in the environment and ignore the remaining the environment, wherefore you calculate accordingly getting -28 5/6.

This is not what the theory uses.

The theorem is:

"If F < T, usually start
- in the environment if MGOTE ≤ T,
- locally if MGOTE ≥ T (the creator chooses the gote option)."

To apply the theorem, we need to determine F, T and MGOTE.

The temperature T is determined by analysing only the T region locally as a local gote and calculating its gote move value T = (11 - 0 ) / 2 = 5 1/2 or by counting 5 stones (contributing 5) and 1 inside intersection (contributing 1/2) to the move value. You have failed to determine T at all.

You have failed to calculate F. To determine the sente option's follow-up move value F, you need to consider the suitable intermediate local follow-up position after the start of the sente sequence:

Click Here To Show Diagram Code

[go]$$B start of the sente sequence
$$ ---------------------------
$$ | O . X X . . 1 3 X . X X .
$$ | O O . O X . O 2 O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B intermediate follow-up position
$$ ---------------------------
$$ | O . X X . . X X X . X X .
$$ | O O . O X . O O O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B Black continues locally
$$ ---------------------------
$$ | O . X X . 1 X X X . X X .
$$ | O O . O X . O O O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$W White continues locally
$$ ---------------------------
$$ | O . X X . 1 X X X 2 X X .
$$ | O O . O X 3 O O O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

Now, calculate F.



Black starts locally taking the gote option: the local count is H := -12.

You have failed to identify the meaning of this value as such.

In more careful annotation, you would have calculated a gote count = (-12 + (-23))/2 = -17.5 for the combination of the gote option after Black taking it and the T region but we do not need such a value.



Black starts locally taking the sente option: the local count is S := -19.

The gote option's gote move value is

MGOTE = (H - R) / 2 = (-12 - (-23 1/3)) / 2 = 5 2/3.

You have calculated the gote move value wrongly.

The sente option's sente move value is

MSENTE = S - R = -19 - (-23 1/3) = 4 1/3.

You have calculated the sente move value wrongly.

Although the theorem does not explicitly refer to H, S and MSENTE, a careful use before its application verifies these additional conditions:

H ≥ S > R <=> -12 ≥ -19 > -23 1/3 (so that the gote and sente options are meaningful).

F > MSENTE (so that the sente option is such indeed).

The theorem requires the other assumption of having a high temperature explicitly: F < T.

You can verify the latter two relations after you will have calculated F.



This relation is irrelevant for using the theorem. Both as implicit presupposition or as explicit condition in the theorem.



Correct your mistakes, complete your missing parts and then judge about my example again!


3 EDITs: calculations related to F > MSENTE and MGOTE > MSENTE.

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------
$$ | O . X X . . b c X . X X .
$$ | O O . O X . O a O X X X .
$$ | . O O O . O O X O X . X .
$$ | . O . O O O . X O X . X .
$$ | . O X X X O X X O X . X .
$$ | . O X X . O O O O X . X .
$$ | O O O O X X X X X X X X .
$$ | . . . . . . . . . . . . .[/go]

Maybe I see why we cannot have a common understanding.

Looking at the tree above tree, Black b is for me only a bad gote option while you consider this move as a sente option.

OC if T < 5 black b is a sente MOVE but when I use the wording sente OPTION I do not refer to the ambiant temperature T. For me a sente option is a notion depending only on the local position and not on the environment and its ambiant temperature T.

By definition in a sente OPTION I must have F ≥ miai value (here F ≥ 5.66).

Obviously you use another defintion. I can try to use your defintion but what is for you the exact defintion of a sente OPTION?

Sure, an option of a local endgame is identified locally. In an arbitrary local endgame, some such options might be dominated, in which case they are ignored. Not only in Bill Spight's or my use but also in CGT use, each option once started by its first move is analysed for itself while ignoring the other options. Only when all options are analysed individually, they are compared and possibly pruned.

Analysing option b while ignoring option a reveals
- the follow-up move value F = 5 of option b,
- the (at first tentative) sente move value MSENTE = 4 1/3,
- the comparison F > MSENTE <=> 5 > 4 1/3 and thereby, since the follow-up is more valuable than Black's start in b, determines the local endgame analysed in its sente option to be a local sente (so not a local gote).

The MGOTE = 5 2/3 is the move value of option a. This does not belong to option b and must not be used to characterise option b itself.

Within option b, there is also an M_SENTE_OPTION_TENTATIVE_GOTE = (-14 - (-23 1/3)) / 2 = 4 2/3. Within option b, we have

F > M_SENTE_OPTION_TENTATIVE_GOTE > MSENTE <=>

5 > 4 2/3 > 4 1/3

and, in particular, each of these three comparisons defines option b as a local sente.

(Equality defines an ambiguous local endgame rather than a local sente.)

Now I see you use a different definition for a "sente option" and for that reason we cannot have a common understanding on all points of the theory depending of this sente option notion.

on SL https://senseis.xmp.net/?AmbiguousMove you find in particular the following point:
sente raises the local temperature, creating the privilege of forestalling the reverse sente.

With my defintion it is true but not with yours:
1)The local temperature at the root is 5.66 and if you use the sente option this local temperature does not raise.
2)You cannot say either that the sente option is here a privilege because white will be able to play first when temperature is T ≤ 5.66
3)How do you call the white move at the root? A gote or a reverse sente move?
In addition, with your definition (but not with mine) I believe you can build a position where it exists both a black sente option and a white sente option to reach a potential double sente position.

Sorry Robert I prefer my defintion (in fact I think Bill's one but I am not sure) than yours because your defintion will in fact change many "known" statements relating to sente and reverse sente notions.

As pointed by my point 3) above you have now to define what you mean by a "reverse sente" move. May be you will say that a gote move can at the same time be a reverse sente move?

Sensei's Library is a weak source. Do not use it as if it would be a strong source!

The SL page on Ambiguous claims it would be of CGT but this is not so. Bill Spight has invented the term outside CGT.

The SL page description including the characterisation of sente
- is informal
- overlooks that a local endgame with one player's follow-up differs from a local endgame with gote and sente options
- refers to local temperature but this is a formal CGT term, whose details I forgot, which I do not use, which using together with informal SL descriptions needs explanation.

Bill Spight studied both in the manner now also I do and characterised by value comparisons, which now also I use. He suggested their equivalance, which I have proved mathematically.

You mention your definition but do not state it. What is it? Instead, you refer to SL.

You write: "The local temperature at the root is 5.66" If you use a formal term, then please stop using approximative decimal notation but write the correct 5 2/3!

Do you know the accurate CGT definition of local temperature? If so, please explain, also why you need such an overkill term instead of simply doing what Bill and I do: characterise sente by comparing two move values to see if they increase!

What is, and how to calculate, the local temperature of the root in a local endgame with gote and sente options according to your opinion?

Why, in this example, is the local temperature of the root 5 2/3 and how to determine this?

Suppose it is. This does not contradict my system of multiple tentative move values, on which my theory and theorems rely.

You keep using privilege but this term is not needed for my theory of tentative values.

You ask how I call a move at the root. Gote, sente or reverse sente (or ambiguous). It is non-essential for my theory. I sometimes use such move terms informally. My theory classifies (simple) local endgames as local gote, ambiguous, local sente etc. For this, such a classification of moves is not needed!!!

Again, therefore there might not be a contradiction you suspect.

The theorem and proof of non-existence of local double sente are for a local endgame with both players' simple follow-ups, i.e., a tree of depth 2 with 4 leaves. In the theory for a local endgame with gote and sente options, the reverse sente is a single move, wherefore a local double sente cannot exist. For practical purposes, however, we must consider longer sequences so that then a local double sente is a principal possibilty because we have no proof for that. If you (or anybody) know a double sente example with gote and sente options, show it!

Since you prefer your definition, again, what is it?

You may prefer your definition but your preference does not cancel my and Bill's definitions and theorems. Research is free. There is scope for other definitions and theorems. However, too similar names must be clearly distinguished. If indeed you want your definitions, you should show that they are useful. Bill and I have shown usefulness of ours in many theorems.

What are those many statements about gote and sente you refer to? What of them do Bill's and my theory alter? Or none because the sets of definitions differ?

I do not need to define a reverse sente move for the purpose of this thread because my theory classifies local endgames instead of individual moves. The theory determines move values without needing terms for individual moves.

And this is good because values depend on sequences of both players.

Informally, a gote move of the gote option's opponent's (preventer's) move is a reverse sente move of the sente option's opponent's move.

(continued)

SL in its faith on infinitesimals defines [local] temperature [but only of a short, i.e., ko-free game] on

https://senseis.xmp.net/?TemperatureCGT

Application requires cooling and consideration of infinitesimals. Now, have fun actually applying it to the SL description of ambiguous move etc...! I cannot apply it within reasonable time. Cooling immediately increases necessary time to hours for simple examples.

Have fun explaining your claim why local temperature is independent of the environment when in fact the CGT definition of temperature does depend on T, i.e., the environment!

For comparison, my theory allows purely local move value calculation. Move value is a concept of go - not a concept of CGT. Therefore, it has been easier to define move value locally than temperature.

See https://lifein19x19.com/viewtopic.php?p=277735#p277735 and the following posts to have some information on my method. BTW, when we discussed this post, you were not very interested to get more information.


Very clear, now I understand why you cannot define what is a gote, sente, reverse sente or ambiguous option at the root.


I know you cannot calculate the miai value of this root position because it is too time consuming.
For what I call the local temperature it is here just (H - R)/2 = ((-12) - (-23.33) = 5.66.
I did not take into account black b because black a is better than black b (5.66 > 4.33).

Coming back to my very first post of this thread. Are you able to apply one of your numerous theorems to tell us which is the best white move (a or b) ?

Currently, I have not asked for a complete method, for whose reading currently I lack time.



I identify a gote option or sente option. I can also classify the local endgame. What I do not do formally is identifying types of single moves.



This is ambiguous as to the "you" and meaning of the phrase "miai value". If with "you" you mean me, I can calculate a move value, and this is some of the kind "miai value". If with "you" you mean "we" and with "miai value" you mean "local temperature", I agree: too time consuming.



Since you do not determine the local temperature, do not call it the local temperature! You calculate the move value of the gote option so call it this. Then you proceed to claim that this would be a candidate for the, let us call it, move value of the local endgame.



Reminder: yours are approximative numbers.

This is not how we may forgo the "sente" option b. According to theorem 5 in [22], which is theorems
II.2.4 + II.2.5 in [32], we may simplify a game tree by removing dominated or reversible options. Here, it cannot be reversible but it might be dominated.

According to definitions 5 in [22], "In go theory, a black play to PB1 is dominated by another black play to PB2 if PB2 ≥ PB1; a white play to PW1 is dominated by another white play to PW2 if PW2 ≤ PW1.". Here, Px are positions! To possibly remove a dominated play, we cannot just compare (tentative) move values. Instead, we are required to compare positions, which we might do by playing a difference game on the two positions to be compared!

That is, if there is, and will be no ko! Otherwise, we do not have a short game, which is a presupposition for playing a difference game.

https://www.lifein19x19.com/viewtopic.p ... 45#p143245



I have explained to you in great detail that such is a matter time, which I do not have, because your position is by far too complicated for my available time unless you or everybody else does the time-consuming preliminary work so that then I can simply apply a theorem.


EDIT: no ko in difference game.