So maybe that was too long of a reply, you can read as much of it as you care for. 
It’s hard to know though where to go into detail and where to be brief though because it’s hard to tell where the confusion is.
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Thanks once again to everyone. It is a 9x9 board where black is required to win by 44 to 38. That is all the info I have. The puzzles seem to fluctuate wildly in difficulty but I feel like I’m slowly improving. Perhaps I will master the endgame before my endgame?
Regards,
Buri
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Maybe we can start another thread on it, if necessary. I just generally there’s some confusion for me with your notion of value, which if it’s to do with the final local score, then it’s not the move value right?
As in the stops in the CGT aren’t the temperature. The amount the position is worth on average isn’t the same as the difference or gain from one player playing to said average.
Though what you’re saying I think, is that if we end up with a position whose score is V no matter what, when one player plays and the other commits to answering, then the move value has to be zero?
I’m going to have to reread what you’re saying with an example maybe. I’ll have a bit more time later to pick it apart properly.
As in the stops in the CGT are the temperature.
No: For Negative moves to 3 , Positive moves to 4
, the stops are 3 and 4, but the temperature is 1/2.
The amount the position is worth on average isn’t the same as the difference or gain from one player playing to said average.
If they really are playing to said average, then I’d need to think more.
If you instead mean they are playing from said average, then Yes.
if we end up with a position whose score is V no matter what, when one player plays and the other commits to answering, then the move
values only matter for potential kos elsewhere: Other than as threats
for such kos, the region simpifies to one in which there are no moves.
I was writing quickly and meant aren’t. I probably mis-hit space instead of apostrophe.
Fixed it now.
That seems to bring in more confusion than necessary. If we’re talking about P the position and calling it’s value V as per
then on the one hand we’re saying P is as least as big as the right stop R(P) or W(P) which is when white plays first and black always answers. That “value” isn’t a move value like the temperature, it’s kind of a lower bound on what black can expect for territory in some sense.
So what @hexahedron is saying makes sense, but I’m missing the connection to the original question.
I was wondering then what the “value” being inferred actually means. If it’s a mean value then it’s not necessarily integral but
but this doesn’t say that it’s integral, just that it’s >= some integral value.
Basically we added in a lot of new context and terminology to address something, and then we’re wondering why I’m confused
I’m trying my best here to understand.
If we just do the common sense, one is saying there’s no points to gain here for black by not answering.
If I try to tie this to the complications brought in by the “theorem” then there’s confusion but in this simple case I guess @hexahedron is saying in a way (and directly in the last recent paragraph even) that if white plays and black commits to answering the value of the position is at least 0, and if black plays first the value is also 0, so the bound on the position is that it should be between 0 and 0 and hence be worth 0 (assuming territory rules - maybe you just shift the values slightly in the area case)
The thing I wonder though, is that it doesn’t really account for what might happen if a player tenukis once or more than once. For instance if you were trying to calculate the “value” of a move, not the expected territory, of a multiple approach ko, you would need to account for one player playing several moves in a row, to try to work out a reasonable size on average for each move, and so you couldn’t rely on such analysis where Black always answers whites moves and hence guarantees at least such a score.
One or more of Black’s “local plays” or “answers” would be to pass, while ko-banned.
(To get a bound, one assumes the other player - White in this case - can ignore ko-bans.)
the final local value if white plays there first and black precommits to answer each white play there
Call that value V
but this doesn’t say that it’s integral, just that it’s >= some integral value.
I’m saying V is, by definition, that integral value. The definition of V is that it is the final local value if white plays first and black answers locally each time. Then V of course must be an integer because positions that are fully played out on the board always end up as integers.
The thing I wonder though, is that it doesn’t really account for what might happen if a player tenukis once or more than once. For instance if you were trying to calculate the “value” of a move, not the expected territory, of a multiple approach ko, you would need to account for one player playing several moves in a row, to try to work out a reasonable size on average for each move, and so you couldn’t rely on such analysis where Black always answers whites moves and hence guarantees at least such a score.
How are you arriving at move values in the first place, without also computing (accounting for sente/gote) of the position values lower down in the game tree resulting from each player moving first, and possibly moving more than once? Do you have a method of computing move values that entirely skips having to assign scores to positions, including skipping having to sometimes compute averages to assign to intermediate positions when the local game tree has multiple steps?
The analysis where you assume one player always answers to compute bounds on the value of a position should be relevant for analyzing move values, because they can give you bounds for the values of positions lower down within the tree (such as revealing when you’ve made a calculation error), which are the intermediate numbers you are computing in the process of coming up with move values for the root.
For example, can you outline how you arrived at 1 and 1/3 as the move value for E9?
I can’t with game trees because I’m still in the process of trying to understand how to calculate with ko. An actual game tree allowing passes to lift a ko ban, would be arbitrarily long, so it’s not like you can just reach a singular final position, you’d have to start doing infinite sums.
Or alternatively you’d have to do what you mentioned where you take multiple copies of a position, 3 or 30 or whichever you like to arrive at an average value right?
My guess, and I said it was a guess, was to apply the idea that a value involving a ko might be 2/3 the swing and the swing was 2. I was also trying to make sense of why OGS Katago was preferring the capture to the one point reverse sente moves in some variations at the time.
It’s fine that I’m incorrect but I would like to understand eventually when it’s supposed to be obvious to either apply it or to ignore it as a rule of thumb.
In terms of game trees then, if one “provokes” the ko one move earlier, as opposed after a delay it’s making a difference in the move value generally?
With alternating play, one would expect the position P to have value between 0 and 1 right? If white plays first black guarantees at least 0. If black plays, white can guaratee at most 1 by answering.
Then how would one arrive at “move value” different but larger than the scores from alternating play of 1 and 1/3.
Maybe trying to understand this example will help me find my lack of understanding of the previous example.
The swing of 2, would be for something earlier. Once the ko arises, the swing of that position is 1.
In terms of game trees then, if one “provokes” the ko one move earlier, as opposed after a delay it’s making a difference in the move value generally?
Yes, roughly because it’s a single move, doing more.
Then how would one arrive at “move value” different but larger than the scores from alternating play of 1 and 1/3.
Well, one would have to come up with some other region for 1 and 1/3.
For the region you just showed, the move value is only 2/3.
However, for move values other than 1 and 1/3, this is easy.
I imagine the most intuitive examples are “double sente”.
+-------------------------+
| - - - - - - - - - - - - |
| - - - - - B W - - - - - | more-typical
| - - - - - B W - - - - - |
| B B B B B B W W W W W W |
(In each case, outer stones assumed alive.)
B B B B B B W W W W W W
B W W W W B W W B B B B W
B W W W W - - - B B B B W easier to analyze
B W W W W B B W B B B B W
B B B B B B W W W W W W
The bounds are 4 points for the top diagram , 1 point for the bottom diagram
apart, but you hopefully understand that these two regions should
each be played much sooner than is suggested by 4 and 1.
We now have two positions to compare.
Position 1 as discussed above (after black has captured the white stone)
Position 2: your new diagram
The common feature is that one player can block at ‘A’ threatening a ko capture as the followup move.
The difference:
- In position 1, white ‘A’ does not defend any territory. (Black wouldn’t want to play ‘A’!)
- In position 2, black ‘A’ secures one point of territory.
This means that in position 1, a move at ‘A’ is local sente: the followup is worth more than the block. But in position 2, a move at ‘A’ is gote.
Imagine a full board where the only unresolved positions are position 2 plus a half-point gote by miai counting (i.e. 1 point swing). Then it’s correct for black to play ‘A’, and white should tenuki and take the certain point elsewhere, so the ko will actually be played out.
In contrast, if you have position 1 plus a half-point gote on the board, then white ‘A’ would be a mistake (black will still tenuki). Instead, white should take the point elsewhere, and the ko capture won’t happen.
How to count position 2? White A results in a count of zero. Black A results in a point of settled territory plus a threatened ko capture, for a count of 1 1/3. Both options are gote, so we average them to get a count of 2/3. It’s between 0 and 1 as you guessed (-:
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I think this is definitely one thing confusing me, the count is 1 1/3 not the move value is it?
And the count of the position is 2/3, so that moving from 2/3 to 1 1/3 is also worth 2/3.
“I think this is definitely one thing confusing me, the count is 1 1/3 not the move value is it?”
The count of Position 2 + black A is 1 1/3 . The move value is not 1 1/3 .
“And the count of the position is 2/3, so that moving from 2/3 to 1 1/3 is also worth 2/3.”
If the position is Position 2 , then Yes.
Right. You need to start with counts of final positions, then work backwards to deduce counts of earlier positions and move values.
Yes: That site uses the confusing numbers as its answers.
Deiri Counting at Sensei's Library
(However, even without that, move value can still be
different but larger than the scores from alternating play:
See the 2 examples from post 51.)
Well,once again I have no idea and wonder what the meijin think. Sorry there are no numbers. I think the first move is I3. Black to move and win by 44 points to 38
Sorry. I 4 Hane.
Please add numbers/coordinates. Help us to help you!