Bill Spight wrote:
When you are considering two different plays, difference games can be very useful, if they give a clear preference. When that happens you don't have to read the whole game tree to find that out.
Very often, however, they will tell you that the two plays are incomparable, so you are still at square 1. (Or maybe a bit further along because of what you have learned by the analysis.) One advantage of difference games is that they do not always require optimal play to make a decision. Good enough play will do. Thermographs, however, require optimal play at each temperature to be correct. Working on them will help to find optimal play, though. And difference games easily generalize as heuristics for similar situations. For instance:
- Click Here To Show Diagram Code
[go]$$Wc White to play
$$ -----------------
$$ | . . . . . . O |
$$ | X X . . . . O |
$$ | . X O O O O O |
$$ | . X X X O . . |
$$ | . . . X O O O |
$$ | . . X X X X . |
$$ | . . X O O O O |
$$ -----------------[/go]
Once White realizes that the reverse sente gains 4 points, connecting on the bottom side is obvious if you have done certain simpler difference games.
IMO, doing thermographs and difference games can improve both your reading and intuition.
When reading your post here above I clearly understand that you agree thermography is very useful but I also understand that it may be a good idea to use also difference games and I take your example as an illustration of that last point.
Now reading your last posts I have the impression that you confirm thermograph is useful (I agree at 100%) but I cannot see a point concerning difference game.
Anyway, taking your example, let me try to explain in more details what appears useful for me with thermography
- Click Here To Show Diagram Code
[go]$$W
$$ ------------------------
$$ | . . . . . . O . . O X|
$$ | X X a . . . O O O O X|
$$ | . X O O O O O X X X X|
$$ | X X X X X X X X X . X|
$$ | X . . . . . . . . X X|
$$ | X . . . . . . . . . X|
$$ | X . . . . . . . . . X|
$$ | X . . . . . . . . . X|
$$ | b O . . . . . . O O c|
$$ | X O O O O O O O O . X|
$$ | X X X O . O . O O . X|
$$ ------------------------[/go]
First of all, though you find "graph" in the word "thermography", I consider that the thermograph itself is only a visual result of a fondamental analysis based on an ideal environment at temperature t.
In practice many players use thermography without knowing they use it.
Taking the now very well known area at the top of the board, any good player is able to say that, at the beginning of yose, this area is worth 4 points for black in sente. Thermography will explain this in other words : instead of the wording "at the beginning of yose ..." thermography will claim that at a "temperature above 2 then ...". Here is the genius of thermograpy : the value of an area depends on the temperature of the idea environment.
For the same configuration, if we are in the late yose, each player will recognize that the area is a good 3 points gote point. Thermography will precise that this fact will happen when temperature drops under 2.
As you see, without knowing thermography a good player knows the two major points of thermography
- we can give a value to a local area by assuming an ideal environment
- this value depends on the value of the best gote move in this environment
The difference between a pure thermography analysis and the analysis made by a real player is the following : the real player calculates the value of the local environment taking into account only a temperature equal or slightly under the current temperature, ignoring all others and saving a lot of time : if the current temperature is around say 4, who cares about the fact that under temperature 1 the area can be evaluated to 4 points in double sente?
Let's take now the above diagram, white to move. The upper part is the local area we are interested in, the bottom left is the four points gote you proposed and in the bottom right you see a point "c" I consider as a gote point with value g :
0 ≤ g ≤ 4
The temperature of the environment is equal to 4 and the value of our local area (against an ideal environment) is 4 points in reverse sente.
Here is a fondamental comment: though a real environment can very often be approximated by an ideal environment, a real environment can never be ideal. Amongs the various caracteristics of an ideal environment one is really essential: the gain expected from a play in the environment at temperature t, is equal to t/2.
In the above diagram if g = 0 (or very near from 0) then the gain from the environment (4) is far greater than expected value (t/2 = 2). I call such environment a tedomari environment. Taking the fact that a move at "a" is equal to a move at "b" (against an ideal environment) when g= 0 I do not hesitate to guess that the best move is at "b" because in tedomari environment the advantage to play in the environment grows.
In the other hand if g = 4 (or very near from 4) the gain from the environment (0) is far lower than expected value (t/2 = 2). I call such environment a miai environment. In that case I guess the best move is at "a" because in miai environment the advantage to play in the environment diminishes.
if g = 2 the environment looks neither tedomari nor miai and you have to read more to find the best move. Anyway you cannot consider the environment as ideal because after a move at "b" (by either player) the temperature drops suddenly to 2 and the environment becomes a tedomari environment!
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Gérard TAILLE
gains as much, on average, as the reverse sente, and lets White get the last play (locally) of that size. After 
the local temperature has dropped to 2.
sets a small trap for White. 
loses ⅓ of a point on average, as discussed above. After 
the local temperature has dropped to ⅚.
captures 
and 
. 
tenuki
tenuki
But assuming no ko threats, White will just take and win the ko. So let 
In calculating the count you correctly took sente into account. 
Let's do it right.
prisoner
prisoner 
can tenuki, but the sente exchange, 
connects
takes point at temperature 2
takes a play in the environment and White wins the ko, and then Black plays in the environment again. Both Black plays gain 2 points, because there are plenty of 2 point plays in the environment.