So the local temperature IS defined as the smallest ambient temperature (the temperature of the enviroment) at which both players are indifferent between playing locally and playing in the environment? If so, why is it defined like this? Is this local temperature the same as the local miai value of a local move? The miai value is supposed to be a particular, fixed number while temperatures can vary. It seems that there is a range of "local" temperatures at which both players are indifferent between playing locally and playing in the environment. This ranges varies from the smallest value, which appears to be called the "local temparature", to the greatest value. Is the greatest such value always (except for ko considerations) equal to the gote move value at the intermediate position's tree node on the tree's currently considered sente path?
And then I would have more questions about the nature of the environment, but I postpone them for now:) Already the questions above are enough I do not understand at the moment.
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In my next attempt at understanding value calculation of sente, I visit the sente example on this webpage
http://senseis.xmp.net/?MiaiCountingWithTrees and learn a new way of determining the local temperature: pruning those parts of the tree dominated by sente sequences. I do not know if this method is correct. However, since it looks like another interesting candidate method, let me try to apply it. Please clarify if this method is correct and why.
Now I use the usual convention of positive values favouring Black.
Given tree:
Gote counts:
Gote move values:
Note that move values are expressed as positive numbers. If Black plays a move, he gains this value and the count changes accordingly when moving from a position to its child position. If White plays a move, he gains the same value, but this gain for him is Black's loss so that Black's gain is the negative of this value.
Code: Select all
A:-1.25:1.25
/ \
0 B:-2.5:1.5
/ \
-1 -4
MA = 1.25 < MB = 1.5
Therefore the assumption of A being gote has been wrong; A is sente for White. We need to proceed with the sente calculation for A:
Reset given tree:
Pruning the tree:
Inherited count CA:
Note that B does not have any sente count at all.
Sente move value:
This calculation (not an inheritance) is a bit tricky. Of the position A, we have the 0 leaf as the black follower and the -1 leaf as the white follower. From A to the black follower, the number of black excess moves is b = 1. From A to the white follower, the number of white excess moves is w = 0 (*). The miai value of a move in A is defined as swing divided by tally. The swing is the difference of the followers' values: 0 - (-1) = 1. The tally is the sum b+w of the numbers of excess moves to the followers: 1 + 0 = 1. Hence, we get the sente miai move value at A = swing / tally = 1 / 1 = 1.
Provided this is the right kind of calculation, this caluclation is correct and the miai value equals the local temperature, I would now understand why lightvector says: "[...] temperature at A = 1.0".
Summary of the pruning method:
1) prune the tree along the sente sequence except for its start and end
2) inherit the count from the sente follower
3) calculate the sente miai move value as swing / tally along the sente sequence
(*) Note for those who do not get it: When a tree bends rightwards, it is White's move; when a tree bends leftwards, it is Black's move. On the sente way from A via B to the -1 leaf, White makes the first move, then Black makes the second move. Each player makes one move, so the number of White's excess moves (expressed from Black's perspective) is -1 + 1 = 0.
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lightvector also says: "white's move is forcing as long as elsewhere moves are worth less than 1.5." To understand this at least from its local game tree perspective, we need to consider both the gote move values and the sente move values:
Code: Select all
A: -1 (sente count) : 1 (sente move value) or 1.25 (gote move value)
/ \
0 B: -2.5 (gote count) : 1.5 (gote move value)
/ \
-1 -4
White would play in A because he considers his move with its sente move value 1 forcing. After White's move, we are at B. There, Black must decide if he should accept White's move as a sente or if Black should play a gote move elsewhere. In the latter case, Black's reference is the gote move value 1.5 at B. If Black finds elsewhere a move with at least the gote value 1.5, he can (if greater than 1.5, should) play. Else, if all gote moves elsewhere have a gote value smaller than 1.5, then Black must accept White's local move from A to B as forcing, reply and move to the leaf -1.
Have I now understood correctly what lightvector has been saying and what Bill seems to be referring to when mentioning the ambient temperature?
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Earlier
viewtopic.php?p=178175#p178175 I wrote: "how do we determine the value of a move in the initial sente position in Dia. 1? It is also inherited. However, we inherit it from the value of a move in Dia. 7, of which we know the move value because this position, if it were an initial position, is a gote position. Since the value of a move in Dia. 7 is 4, Dia. 1 inherits this move value 4."
Although Bill Spight and lightvector "liked" that post, I am still unsure about the correct calculation of the local temperature and local sente miai move value. The citation relies on inheriting the gote move value, but isn't the pruning method discussed above correct?
Now assuming the pruning method is correct, I correct (?) the calculation of the sente miai move value for the example in
viewtopic.php?p=178128#p178128$$W Initial position
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$$ . . O O X O O X . .
$$ . . . . X X X X . .
$$ . . . . . . . . . .
$$ . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$W Initial position
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$$ . . O . . O X . . .
$$ . . O X X O X X . .
$$ . . O O X O O X . .
$$ . . . . X X X X . .
$$ . . . . . . . . . .
$$ . . . . . . . . . .[/go]
Given tree:
Pruning the tree:
Inherited count CA:
Sente move value:
Code: Select all
A: 8 (sente count) : 1 (sente move value)
/ \
9 B
/
8
Swing = 9 - 8 = 1.
Tally = 1 + (-1 + 1) = 1 + 0 = 1.
Sente move value = swing / tally = 1 / 1 = 1.
Oops. This may be the reverse sente move value, but it is certainly not what Bill would call the sente move value.
So why is the method of inheriting the move value correct in some examples and is the pruning method correct in other examples? What else do I not understand here? There is more: I do not have the slightest idea yet when and why min or max comes into play. I have a suspicion about an explanation for Bill's (a+b+c+d)/4 tems, but I am not sure yet what exactly I need to ask, except that it migh be related to my confusion about which is the right method.
However, timing covers a lot of territory. Not to reply to a properly played sente may be correct, as a matter of timing, but it is unusual, normally something to note and explain. Nowhere did the game commentaries note that a player ignored a double sente or give a reason for playing elsewhere. That was part of what made it puzzling.
is sente, much less double sente. The only reason to think that this is double sente is because "the double kosumi on the second line is double sente". That is how the concept of double sente leads people astray.
is hardly inevitable. (At some point I calculated White's threat as gaining a little more than 3 points. It is a monkey jump, but without much of a follow-up. I could have misread the position or miscalculated, so that this is actually a White sente. But a double sente? Puleaze!)
) Try playing it out and see if it is.