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Life In 19x19
Life in 19x19. Go, Weiqi, Baduk... Thats the life.
John Fairbairn wrote:5. I do not understand your sentence "Now let’s figure out the value of the position in Diagram 2, as though it were gote." Obviously I understand all the words, and even I can guess that 6.5 is based on 9 + 4, but I am at a loss to follow the procedure - why certain things are done and in a certain order. I gather RJ may have a similar problem, though maybe a bit beyond that (clearly I can't make progress to his level as I haven't crossed the first barrier yet).
I can't speak for Bill, but this looks like the way I was taught about valuing gote endgame. My mathematical interpretation of this model is as a recursive function:
Value of (Position) = ( Value of (Position + best local Black play) + Value of (Position + best local White play) ) / 2
That is, we assume that it is equally likely that either player will play the next move. This can be a bit complex because you have to consider every sequence of moves in a large binary tree to get the valuation (Black-White-Black, Black-White-White, Black-Black-White, Black-Black-Black + ... etc.) and could the sequence of plays could be infinite (say if there's some sort of ko for example). But for this case it resolves very quickly after a few moves, just White, Black-White, Black-Black (assuming that both groups are unconditionally alive outside of this region.) So:
Value of (Position) = ( Value of (Position + Black) + Value of (Position + White) ) / 2 Value of (Position + Black) = ( Value of (Position + Black-Black) + Value of (Position + Black-White) ) / 2 Value of (Position + Black-Black) = 0 Value of (Position + Black-White) = 8 Value of (Position + Black) = ( 0 + 8 ) / 2 = 4 Value of (Position + White) = 9 Value of (Position) = ( 4 + 9 ) / 2 = 6.5
your clearly local gote example might, under exceptional circumstances, be sente or reverse sente if the outer strings are not unconditionally independently alive and, e.g., the answering player might need to play a local negative ko threat.
I was following the standard convention that the framing stones are immortal. I have added an edit to that effect.
Your value calculations presume using (the obvious) locales.
What, then, is the value of the original position in Diagram 2, as a sente? It cannot be less (for Black) than that of the position after the sente sequence, because then White would lose points by the sente exchange. OTOH, it cannot be more, because then Black would not reply. So the value of the original position is 8 points, and the sente play, , gains 4 points. Then the reply, , also gains 4 points, for a net gain of 0. The reverse sente play moves to a position worth 9 points, and gains only 1 point. (Even though it is the reverse sente that gains points, we call this a 1 point sente.) This asymmetry of the values of the sente and reverse sente is characteristic of local sente.
Can you please explain the calculation of each of these values in greater detail?
It is quite possible to make a local gote or reverse sente play that leaves a reply that is the best play on the whole board. That kind of sente does gain points.
In which sense does it gain points?
Gote and reverse sente plays and sequences gain points (unless you want to include infinitesimals, such as dame.)
what about local double sente? The same considerations apply as with regular sente. The value of the resulting position after both sente sequences is the same as the value of the original position
Please explain why the value (which value?) is still the same.
In positions without kos the value of the position lies between the values of the correct plays or alternating sequences of plays when Black plays first and when White plays first. As we have seen, if a position is sente the value of the position is unchanged after the sente sequence. Assuming that a position is double sente does not alter that fact. If a supposed sente sequence gains points, then the reply is worth less than the initial play, which means that the initial play is not (local) sente.
Clearly, you do not mean the position's territory count because, if Black gets e.g. a hane-connect, White's territory has been decreased by 2 points while, if White gets a hane-connect, Black's territory has been decreased by 2 points. There is a difference of 4 points between the two resulting positions, which have the territoy count values X-2 and X+2. However, the original position's territory count must be in between at X.
The double hane-connect that you describe is not a local double sente. It is double sente only if both replies are better than playing elsewhere. (Edit: Which means that the sense of double sente is global.) The Kano examples are double hane-connects, but one is a 7 point sente and one is a 20 point gote. Neither are local double sente. The 20 point gote is very likely to be global sente, but the 7 point sente is not.
Last edited by Bill Spight on Sat Dec 06, 2014 2:20 pm, edited 2 times in total.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
The Kano examples are double hane-connects, but one is a 7 point sente and one is a 20 point gote. Neither are local double sente. The 20 point gote is very likely to be global sente, but the 7 point sente is not.
Sorry to harp on these points to do with Kano, but is it not the case that in practical terms he is correct? According to Ishida's book on counting, moves in the fuseki are typically worth something like 25 points. I assume middle-game moves are typically worth that and more - at any rate too much to make it feasible to play the 20-point sente referred to. But at certain points during the middle game the game goes quiescent (the temperature drops?) and when it does, the value of plays drops dramatically and the large boundary plays come to the fore (i.e. yose but not yet the endgame). At that point it seems easy to imagine the 7-point side getting the right to play first. Statistically I presume we can say that it's a 50-50 chance that the player who emerges from the middle-game turbulence with the move will be the one with the 7-point gote. The only factor then is at what level the large boundary plays (at least those unconnected with unfinished middle game fights) start. If it's 8 or 9 points, the 7-point sente guy perhaps loses out (and we can assume the 20-point guy never will), but will that really be often enough to dismiss Kano's example.
For those unfamiliar with Kano's book, he himself points out the different values for each side in this position, and - as I have said before - plainly states that it is an important task of the players to manoeuvre in the fighting beforehand to get the right to play the sente move. The 7-point guy may have to be manoeuvre harder, or compromise more, but he is aware of the goal and can decide accordingly.
By sheer chance, I was browsing through some chess books today and I came across a similar concept there. The rather nice phrase used by John Watson in "Secrets of Modern Chess Strategy" was "The Initiative Dance". This is the heading of a whole chapter, mostly text, and it all seems highly relevant to go and sente - may even be the same thing. To pick out a few phrases to illustrate, he also uses "the mysteries of momentum", "dynamic potential", "mysticism", "Continental Metaphysics", "strategy of long-term provocation", "dynamic give-and-take", "dynamism and provocation", "paradoxical comings and goings of momentum and initiative". His final sentence is "And the correct use of provocation is a skill which separates the finest players from the rest of us."
He also says that this is an area likely to become increasingly important among top chess players (and Mihail Suba seems to be the guru). I have mentioned before the notion that mysterious and very early probes are becoming an increasing feature of modern fuseki. It seems plausible to wonder whether this parallels the chess innovation - rather than probes we should be calling this provocation and rather than simply trying to see how the opponent will react the agent provocateur us really trying to control the "initiative dance" by adding dynamic potential and momentum to the position.
Several other chapters in the Watson book seem to cover areas in which modern go is changing along the same lines as chess.
I infer from all that that this initiative/sente business is nothing like as simple as some people claim, and I'm relieved to see that Watson adds "to an ultra-logical critic, this may just sound like the ravings of a weak player" and then chops the ULC off at the knees.
Before you go too far, some points you may wish to take on board from the non-mathematical part of your audience.
1. You appear to be using non-Japanese terms. The Japanese categories that you call "gote, sente and double sente" are to them "double gote, kata sente and double sente". I find the Japanese terms superior as double gote allows them to further talk about "gote sente" and "sente gote" and kata sente gets over one aspect of sente being used ambiguously in English.
If I had been writing for a Japanese audience I would have used those terms.
2. I have never seen a proverb I Japanese that tells us to play double sente quickly, much less immediately. The only one I know advises us simply not to give them up to the opponent. Given that this advice is accompanied by comments (as in Kano) to manoeuvre (i.e. rather the opposite of quickly!) so as to get to a double sente ahead of the opponent), I think that covers aspects your version does not cover.
The English version that I recall is to play double sente early. I thought that it came from Go Proverbs Illustrated, but I guess not, since you surely have a copy handy. I picked it up way back when, so I do not recall where.
(The above is part of the reason I think that criticism of the Japanese texts can be unfair at times - they are being criticised either for things they didn't say or conceived differently. It is legitimate to address the whole problem from a western perspective, of course, but if that is the case it should be made plain and kept separate.)
Well, for one thing I am not criticizing the proverb, either version of it. For another, I do not regard my critique as Western. Sure, I am a Westerner, but I did study Oriental philosophy starting at age 11, and pre-modern Western thought in my 20s. I am hardly an avatar for modern Western thinking.
3. There seems to be an unexpressed assumption that we are starting with some sort of base count for the whole board (White has an estimated X points and Black Y points), otherwise comments like "White gains 0 points" don't make sense.
Think Absolute Counting (TM).
4. "Value of position" needs definition, or at least discrimination.
Again, see O Meien.
5. I do not understand your sentence "Now let’s figure out the value of the position in Diagram 2, as though it were gote." Obviously I understand all the words, and even I can guess that 6.5 is based on 9 + 4, but I am at a loss to follow the procedure - why certain things are done and in a certain order. I gather RJ may have a similar problem, though maybe a bit beyond that (clearly I can't make progress to his level as I haven't crossed the first barrier yet).
OK, let's look at a similar (local) gote.
$$W Diagram 3 Gote $$ ------------------- $$ . . O . . O O . O . X . . $$ . . O O O X X X X X X . . $$ . . . . . . . . . . . . .
I apologize in advance if my commenting here confuses things, and also to Bill if he was intending to present things in different way. Here's my attempt at an overview.
There are two main notions involved in what Bill is describing:
The "count" or "value" of a local position:. This is obtained by assuming that all locally sente sequences are played and responded to, and taking the average when playing is locally gote for both sides. This also applies recursively - for example, if in a double gote situation one of the moves has a later sente followup, when we compute the value for it to be averaged, we assume the player who played it also gets the sente followup after that. This is roughly what many strong players do when they want to estimate a territory but cannot read out everything - tentatively assume sente moves are played with sente, split the difference on gote.
So in a simple one sided-sente position, the value of the position is equal to the value after the sente move or sequence is played and responded to. In a double-gote position, the value is the average of the two possible values after the gote sequences by each player (and recursively if there are further followups thereafter).
The "temperature" or "urgency" of a local position, or what spending a move "gains" in that position: This is simply how much you change the value above by taking gote in a position - what you gain by investing your turn. (A sente sequence gains nothing since we're already assuming sente is played and responded to). So if playing is locally gote for at least one player, then the urgency is the difference between the value of the current position and the value after that player plays the gote move or sequence. If neither player's playing is locally gote, that is, if both are locally sente, then the the urgency is zero (see below for why zero makes sense).
So in a simple one-sided sente position the urgency is the difference between the value after the sente sequence is played and responded to, and the value after the reverse sente is played. In a double-gote position, the urgency is the half the difference of the possible values after each player plays (which again are computed recursively).
Other Terminology: A move is locally gote for a player if playing it decreases the urgency of the position. A move is locally sente for a player if playing it increases the urgency of the position. A move or sequence of moves gains a certain number of points for a player if playing that sequence changes the value of the position in favor of that player by that many points.
A note: a bunch of the above may appear circular as stated - value and urgency are defined using gote and sente, and gote and sente are defined using value and urgency. But it's not too hard to make it non-circular. You define things inductively/recursively, where given a game tree you begin with the leaves and gradually work your way up the tree assigning values and urgencies as you go, so that you never actually circularly depend on anything. I actually haven't seen the exact full procedure laid out anywhere for computing these values, but in the process of reading what's on Sensei's library and from Bill's posts (and based on what makes mathematical sense), I think I've reverse-engineered the algorithm. I can try to post it for the math-minded if anyone is are interested.
Note that locally gote and locally sente refer to the idea of "urgency" here, rather than a comparison of how many points appear to be made secure by the move versus the threat/followup it enables (some people's intuitions more closely adhere to the latter notion). With these particular definitions, double-sente generally can't happen. In any situation that one would want to call double-sente, although responding to the sente move by either side might be huge and urgent, playing a move in the original position is also extremely urgent. So urgent in fact that for at least one player, the act of playing the supposed double-sente move in the original position will not cause the urgency to rise any further, but rather to lower.
The only time playing is locally sente for both players, as defined above, is when the moves fail to gain points, or even lose points, as in the following. This is why we define the urgency to be zero if both players playing is locally sente.
A is locally sente for black and B for white, because they both raise the urgency of playing in that area. But despite making a threat these moves don't actually gain anything overall. C is locally sente for both players for the same reasons - it raises the urgency of another play in the area, but is a losing sente for both.
$$c $$ ----------------------------- $$ . . X a O b O . O X . O X . . $$ . X . X X O . O O X c O X . . $$ X X X O O O O O X X O O X X X $$ . . . . . . . O O O X X X . . $$ . . . . . . . . . . . . . . .
[go]$$c $$ ----------------------------- $$ . . X a O b O . O X . O X . . $$ . X . X X O . O O X c O X . . $$ X X X O O O O O X X O O X X X $$ . . . . . . . O O O X X X . . $$ . . . . . . . . . . . . . . .[/go]
Any locally double-sente positions are usually just variations on these kinds of positions where except for zero-net-value cleanup exchanges and dame moves, the positions are all already finished.
Other comments: This counting system does extremely well at putting endgame moves on a single numeric scale such that always playing the move with the highest number (urgency) is close to optimal. In some sense, it is the unique best way, up to scaling, of doing so. Which means that if you play a good endgame, you likely have learned to evaluate and rank endgame moves by something quite close to Bill's particular notion of what moves "gain", even if you don't consciously do so.
Lastly, why is Bill adamant on resisting the idea of the the second-line diagonal as a double sente?
Here's my understanding. Usually either: * It's so urgent that it will be played almost immediately after the position itself forms. Then, it's closer to being part of the local tactics that generated that position, as opposed to an endgame move that remains on the board to be played later at an appropriate time.
* Or else one side, say Black, threatens significantly more than the other. In this case, it's locally sente for Black and locally gote for White. Then conditional on the move actually staying on the board for a little while, thinking of it as Black's sente is also usually correct globally. Why? Assuming it was correct for the move to remain unplayed so far, White's threat must not be large enough relative to other moves to make it forcing. So Black will likely get to play it with sente, because he can play it any time his own threat has become large enough to make it forcing but where White's threat hasn't.
* Or else both sides threaten about the same amount, such as when the position is nearly symmetric. In this case, it's large but locally gote for both sides. Then conditional on the move staying on the board for a while, large double gote is also a good way to think about the move globally. It will likely be played right around when it becomes the biggest/most urgent move remaining. Since the response to it is a few points less urgent than the move itself, it will often not be responded to immediately or at all. Which is what happens not-infrequently in pro games, consistent with it being gote. Even if it is responded to, that's no different than if there were two separate large gotes on the board, one of them a few points less than the other, but both larger than other moves. One player gets the larger one, then the other player gets the smaller one.
Just as an aside I was surprised when Bill showed such a small position as his 2nd line kosumi. I assumed it was more like this one (where the teritorrial loss from tenuki is far bigger (and very hard to count), nevermind the eyespace implications):
Edit: Ooops, I missed out some of this thread with my reduced posts per page setting to avoid errors, so I see this point (except my surprise) has been made already.
John Fairbairn wrote:6. I dispute that there is a proverb "sente gains nothing". That is just a western joke.
It is neither Western nor a joke. If (local) sente gained any points, then the calculation of the size of gyaku yose as the difference between the value of the result after the gyaku yose and the value after the sente sequence would be wrong. Also, if (local) sente gained any points, then assuming that local sente are played when estimating the value of the whole board would be wrong.
7. With various usages of sente washing around, should we not try to get away from the term "reverse sente"? I am sure the Japanese avoid it for good reason.
Japanese is sometimes more logical than English. Darn those inscrutable Occidentals, anyway.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
The Kano examples are double hane-connects, but one is a 7 point sente and one is a 20 point gote. Neither are local double sente. The 20 point gote is very likely to be global sente, but the 7 point sente is not.
Sorry to harp on these points to do with Kano, but is it not the case that in practical terms he is correct? According to Ishida's book on counting, moves in the fuseki are typically worth something like 25 points.
Sorry, the 20 points is Absolute Counting (TM). Ishida uses deiri counting, so divide by 2 to compare the two. The 20 point gote is likely to be a (global) double sente at almost any time. As for the 7 point sente, the sente threat is 17 points by Absolute Counting, so Black can play the sente at almost any time. However, the threat for White after the gyaku sente is only 3 points by Absolute Counting. That means that if White should make the play, it will almost certainly not be sente, no matter how White may maneuver.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
[go]$$B Black first, White second - B $$ ------------------- $$ . . O C 2 O O 1 W C X . . $$ . . O O O X X X X X X . . $$ . . . . . . . . . . . . .[/go]
If Black plays first and later White plays second, the local result is +2.
$$B Black first and last - C $$ ------------------- $$ . . O . 3 O W 1 W C X . . $$ . . O O O X X X X X X . . $$ . . . . . . . . . . . . .
[go]$$W Diagram 3 Gote $$ ------------------- $$ . . O . . O O . O . X . . $$ . . O O O X X X X X X . . $$ . . . . . . . . . . . . .[/go]
As a gote, the original position is worth 1.5 points, and a play gains 2.5 points. Since the White reply gains only 2 points, this is indeed a gote.
In a real game, since the difference between 2.5 points and 2 points is only 0.5 points, it is possible that Black will be able to make a play with sente. But this is a local gote.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
The mean value of the game is the middle value of b, c, and (a+b+c+d)/4.
If (a+b+c+d)/4 > b, the game is a Black sente.
If b > (a+b+c+d)/4 > c, the game is gote.
If c > (a+b+c+d)/4, the game is a White sente.
Note that in no case is it double sente.
The game, {a | b || b | c}, a > b > c, equals b. (In go, ko considerations may invalidate that equality by destroying the independence of the position.)
Edited for clarity.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
, gains 4 points. Then the reply, 
, also gains 4 points, for a net gain of 0. The reverse sente play moves to a position worth 9 points, and gains only 1 point. (Even though it is the reverse sente that gains points, we call this a 1 point sente.) This asymmetry of the values of the sente and reverse sente is characteristic of local sente. 
is +4, and the next play gains 2 points.