RobertJasiek wrote:
Bill Spight wrote:
RobertJasiek wrote:
Does this mean that proving t <= G1, G2,..., Gk is trivial? Similarly for White's such alternating sequence. Next, we derive the initial count and move value.
Since you use different notation from combinatorial game theory, I assume that Gi is not a game.
Earlier, I declared that Gi are the gains (of the plays of Black's alternating sequence)!
OK, let's call the original position G, with mean value m(G). Given correct play in an ideal environment with temperature, t, Black to play moves to A, then White moves to B, then Black plays in the environment instead of moving to C. The move to A gains, on average, m(A) - m(G), the move to B gains, on average, m(A) - m(B), and the move to C gains, on average, m(C) - m(B). It should also be the case that m(B) ≥ m(G),
something that simply talking about gains instead of mean values does not make clear. That yields the following.
m(A) - m(G) ≥ m(A) - m(B) ≥ t ≥ m(C) - m(B)
RobertJasiek wrote:
A couple of years ago, you suggested that proving the correct initial values would require thermography.
Quote:
If so, I did not mean to suggest that.
RobertJasiek wrote:
Now that you know that I speak of gains, please reconsider:)
The most importantly, see the method of making a hypothesis in [16] in
https://www.lifein19x19.com/forum/viewt ... =17&t=8765I did, and still do, believe that thermography provides a conceptually superior way to think about these matters, as everything rests upon the concept of mean value. That is not to say that thermography is necessary to prove mean values, or any other values.
Kano is a good example of a pro 9 dan who does not quite get the concepts. For instance, in his
Yose Dictionary he correctly states that the following corner is an example of miai. (By convention the outside region is Black territory.)
- Click Here To Show Diagram Code
[go]$$ Strict miai
$$ ----------------
$$ | . O . . . . . .
$$ | . . . O X X . .
$$ | . O O O O X X .
$$ | . O X X X . . .
$$ | . X . . . . . .
$$ | . . X . . . . .
$$ | . . . . . . . .
$$ | . . X . . . . .
$$ | . . . . . . . .[/go]
So far, so good.
But then he shows the following sequence and states that
is the last play of the game.
- Click Here To Show Diagram Code
[go]$$ Strict miai
$$ ----------------
$$ | . O . 6 4 5 . .
$$ | . . . O X X . .
$$ | 2 O O O O X X .
$$ | 1 O X X X . . .
$$ | 3 X . . . . . .
$$ | . . X . . . . .
$$ | . . . . . . . .
$$ | . . X . . . . .
$$ | . . . . . . . .[/go]
That's bizarre. The whole point is that
and
are miai. Sure, you can consider
to be the last play, but doing so ignores
. In theory the players could agree to the score without playing the miai out. The correct way to think about this is that White got the last play somewhere else, and then Black played the miai.